Model Validation: Latent Class Framework for Measuring Learning

Introduction

Naive measures of learning—the difference between post-test and pre-test scores—systematically underestimate actual learning. The reason is straightforward: people who don’t know the answer to a closed-ended question often guess, and guessing inflates scores. Since pre-test scores contain more guessing (people know less before the informative process), the bias is larger in the pre-test. The difference thus attenuates the true learning effect.

This vignette validates the implementation of the latent class model for measuring learning against the theoretical framework from Cor and Sood. We first walk through a typical analysis workflow, then derive the cell probability formulas from first principles, verify that the implementation matches these derivations, and demonstrate parameter recovery through simulation.

Typical Workflow

This section demonstrates a complete analysis workflow from raw data to final estimates.

Step 1: Prepare Your Data

Your data should be two data frames with the same dimensions: - pre_test: Pre-test responses (0 = wrong, 1 = correct, optionally “d” for Don’t Know) - post_test: Post-test responses (same coding)

Each row is a respondent, each column is an item.

pre_test <- data.frame(
  item1 = c(1, 0, 0, 1, 0, 1, 0, 0, 1, 0),
  item2 = c(0, 0, 1, 1, 0, 0, 1, 0, 1, 0),
  item3 = c(1, 1, 0, 1, 0, 0, 0, 1, 1, 0)
)

post_test <- data.frame(
  item1 = c(1, 1, 0, 1, 1, 1, 0, 1, 1, 0),
  item2 = c(1, 0, 1, 1, 1, 0, 1, 0, 1, 1),
  item3 = c(1, 1, 1, 1, 0, 1, 0, 1, 1, 0)
)

Step 2: Compute Naive Learning Estimate

Before applying the LCA correction, compute the naive estimate for comparison:

naive_learning <- colMeans(post_test) - colMeans(pre_test)
cat("Naive learning estimates (biased downward):\n")
#> Naive learning estimates (biased downward):
print(round(naive_learning, 3))
#> item1 item2 item3 
#>   0.3   0.3   0.2
cat(sprintf("\nMean naive learning: %.3f\n", mean(naive_learning)))
#> 
#> Mean naive learning: 0.267

Step 3: Fit the LCA Model

Use lca_fit() to estimate the latent class proportions:

fit <- lca_fit(pre_test, post_test)
#> 
#> Iter: 1 fn: 10.8890   Pars:  0.3000000156 0.2999999952 0.3999999889 0.0000000674
#> Iter: 2 fn: 10.8890   Pars:  0.30000000824 0.29999999506 0.39999999670 0.00000004436
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 10.8890   Pars:  0.3000000156 0.2999999952 0.3999999889 0.0000000674
#> Iter: 2 fn: 10.8890   Pars:  0.30000000824 0.29999999506 0.39999999670 0.00000004436
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 10.2965   Pars:  0.29999999877 0.19999997903 0.50000002191 0.00000001239
#> Iter: 2 fn: 10.2965   Pars:  0.299999996737 0.199999979626 0.500000023637 0.000000004354
#> solnp--> Completed in 2 iterations
print(fit)
#> LCA Model Fit
#> ----------------------------------------
#> Items: 3  | Observations: 30 
#> Model: Without Don't Know 
#> 
#> Learning estimates:
#> item1 item2 item3 
#>   0.3   0.3   0.2 
#> 
#> Use summary() for parameter details, coef() to extract parameters.

Step 4: Extract and Interpret Results

The key output is the gk parameter—the proportion who learned:

summary(fit)
#> LCA Model Summary
#> ==================================================
#> Items: 3  | Observations: 30 
#> Model: Without Don't Know 
#> 
#> Parameter Estimates:
#> --------------------------------------------------
#>       item1 item2 item3
#> gg      0.3   0.3   0.3
#> gk      0.3   0.3   0.2
#> kk      0.4   0.4   0.5
#> gamma   0.0   0.0   0.0
#> 
#> Learning Estimates (gk):
#> --------------------------------------------------
#> item1 item2 item3 
#>   0.3   0.3   0.2 
#> 
#> Mean learning: 0.2667

cat("\nComparison: Naive vs. LCA-adjusted learning:\n")
#> 
#> Comparison: Naive vs. LCA-adjusted learning:
comparison <- data.frame(
  Item = colnames(pre_test),
  Naive = naive_learning,
  LCA_Adjusted = fit$learning,
  Difference = fit$learning - naive_learning
)
print(comparison, row.names = FALSE)
#>   Item Naive LCA_Adjusted    Difference
#>  item1   0.3          0.3 -4.937121e-09
#>  item2   0.3          0.3 -4.937121e-09
#>  item3   0.2          0.2 -2.037401e-08

The LCA-adjusted estimates should be larger than naive estimates because they correct for the downward bias from guessing.

Step 5: Get Standard Errors via Bootstrap

For inference, use lca_se() to obtain bootstrapped standard errors:

se_results <- lca_se(pre_test, post_test, n_boot = 100)

Step 6: Assess Model Fit

Check how well the model fits each item:

fit_stats <- fit_model(pre_test, post_test,
                       fit$params["gamma", ],
                       fit$params[c("gg", "gk", "kk"), ])
print(fit_stats)
#>            item1 item2 item3
#> chi-square     0     0     0
#> p-value        1     1     1

Non-significant p-values (> 0.05) indicate adequate fit.

Step 7: Compare Across Groups (Optional)

To compare learning between groups, fit the model separately:

group <- c(rep("treatment", 5), rep("control", 5))

pre_treat <- pre_test[group == "treatment", ]
post_treat <- post_test[group == "treatment", ]
pre_ctrl <- pre_test[group == "control", ]
post_ctrl <- post_test[group == "control", ]

fit_treat <- lca_fit(pre_treat, post_treat)
#> 
#> Iter: 1 fn: 5.2746    Pars:  0.199999982215 0.400000011922 0.400000005571 0.000000009794
#> Iter: 2 fn: 5.2746    Pars:  0.199999981201 0.400000010826 0.400000007973 0.000000005512
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 5.2746    Pars:  0.199999982215 0.400000011922 0.400000005571 0.000000009794
#> Iter: 2 fn: 5.2746    Pars:  0.199999981201 0.400000010826 0.400000007973 0.000000005512
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 4.7514    Pars:  0.19999998373 0.19999997993 0.60000003605 0.00000001857
#> Iter: 2 fn: 4.7514    Pars:  0.199999981958 0.199999980304 0.600000037738 0.000000009839
#> solnp--> Completed in 2 iterations
fit_ctrl <- lca_fit(pre_ctrl, post_ctrl)
#> 
#> Iter: 1 fn: 5.2746    Pars:  0.40000002775 0.19999997091 0.40000000104 0.00000004602
#> Iter: 2 fn: 5.2746    Pars:  0.40000002176 0.19999997415 0.40000000409 0.00000002864
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 5.2746    Pars:  0.40000002775 0.19999997091 0.40000000104 0.00000004602
#> Iter: 2 fn: 5.2746    Pars:  0.40000002176 0.19999997415 0.40000000409 0.00000002864
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 5.2746    Pars:  0.40000002775 0.19999997091 0.40000000104 0.00000004602
#> Iter: 2 fn: 5.2746    Pars:  0.40000002176 0.19999997415 0.40000000409 0.00000002864
#> solnp--> Completed in 2 iterations

cat("Treatment group learning:", round(mean(fit_treat$learning), 3), "\n")
#> Treatment group learning: 0.333
cat("Control group learning:", round(mean(fit_ctrl$learning), 3), "\n")
#> Control group learning: 0.2
cat("Difference:", round(mean(fit_treat$learning) - mean(fit_ctrl$learning), 3), "\n")
#> Difference: 0.133

The Latent Class Model

Three Latent Classes

The model assumes three mutually exclusive latent classes representing knowledge states before and after an informative process:

Class Name Interpretation
gg guess-guess Did not know before, did not know after (stable ignorance)
gk guess-know Did not know before, knows after (LEARNED)
kk know-know Knew before, knows after (stable knowledge)

The key simplifying assumption is no forgetting: we rule out know-to-guess transitions. This is reasonable for short-term learning interventions where forgetting is unlikely.

Let \(\gamma\) denote the probability of answering correctly when guessing. For a K-option multiple choice question with random guessing, \(\gamma = 1/K\).

Cell Probability Derivation

On a pre-post test, we observe a 2×2 transition matrix:

Pre  Post 0 (Wrong) 1 (Right)
0 (Wrong) \(n_{00}\) \(n_{01}\)
1 (Right) \(n_{10}\) \(n_{11}\)

Each latent class generates a specific pattern of responses:

Class gg (guess both times):

  • Pre-test: correct with probability \(\gamma\), wrong with probability \((1-\gamma)\)
  • Post-test: correct with probability \(\gamma\), wrong with probability \((1-\gamma)\)

Class gk (guess pre, know post):

  • Pre-test: correct with probability \(\gamma\), wrong with probability \((1-\gamma)\)
  • Post-test: always correct (probability 1)

Class kk (know both times):

  • Pre-test: always correct (probability 1)
  • Post-test: always correct (probability 1)

The probability of each observable cell is the sum over latent classes:

\[ \begin{aligned} P(0 \to 0) &= gg \cdot (1-\gamma)(1-\gamma) \\ &= (1-\gamma)^2 \cdot gg \end{aligned} \]

\[ \begin{aligned} P(0 \to 1) &= gg \cdot (1-\gamma)\gamma + gk \cdot (1-\gamma) \cdot 1 \\ &= (1-\gamma)\gamma \cdot gg + (1-\gamma) \cdot gk \end{aligned} \]

\[ \begin{aligned} P(1 \to 0) &= gg \cdot \gamma(1-\gamma) \\ &= (1-\gamma)\gamma \cdot gg \end{aligned} \]

\[ \begin{aligned} P(1 \to 1) &= gg \cdot \gamma \cdot \gamma + gk \cdot \gamma \cdot 1 + kk \cdot 1 \cdot 1 \\ &= \gamma^2 \cdot gg + \gamma \cdot gk + kk \end{aligned} \]

Worked Example

Suppose the true parameters are \(gg = 0.35\), \(gk = 0.30\), \(kk = 0.35\), and \(\gamma = 0.25\).

gg <- 0.35
gk <- 0.30
kk <- 0.35
gamma <- 0.25

p00 <- (1 - gamma)^2 * gg
p01 <- (1 - gamma) * gamma * gg + (1 - gamma) * gk
p10 <- (1 - gamma) * gamma * gg
p11 <- gamma^2 * gg + gamma * gk + kk

cat("Cell probabilities:\n")
#> Cell probabilities:
cat(sprintf("  P(0→0) = %.4f\n", p00))
#>   P(0→0) = 0.1969
cat(sprintf("  P(0→1) = %.4f\n", p01))
#>   P(0→1) = 0.2906
cat(sprintf("  P(1→0) = %.4f\n", p10))
#>   P(1→0) = 0.0656
cat(sprintf("  P(1→1) = %.4f\n", p11))
#>   P(1→1) = 0.4469
cat(sprintf("  Sum    = %.4f\n", p00 + p01 + p10 + p11))
#>   Sum    = 1.0000

Note that the probabilities sum to 1, as they should.

Identification

The model has:

  • 4 observable cell proportions
  • 4 parameters: \(gg\), \(gk\), \(kk\), \(\gamma\)
  • 1 constraint: \(gg + gk + kk = 1\)

This gives 4 observations to estimate 3 free parameters. The model is just-identified: we have exactly enough information to solve for the parameters, but no degrees of freedom for goodness-of-fit tests within a single item.

Implementation Verification

The guess package implements the likelihood function in guess_lik(). Let’s verify it matches our derivation:

guess_lik_manual <- function(gg, gk, kk, gamma, data) {
  vec <- numeric(4)
  vec[1] <- (1 - gamma) * (1 - gamma) * gg        # P(0→0)
  vec[2] <- (1 - gamma) * gamma * gg + (1 - gamma) * gk  # P(0→1)
  vec[3] <- (1 - gamma) * gamma * gg              # P(1→0)
  vec[4] <- gamma * gamma * gg + gamma * gk + kk  # P(1→1)

  -sum(data * log(vec))
}

test_data <- c(100, 150, 50, 200)

ll_manual <- guess_lik_manual(0.35, 0.30, 0.35, 0.25, test_data)

cat(sprintf("Manual implementation: %.4f\n", ll_manual))
#> Manual implementation: 645.1621

Parameter Recovery Demonstration

The strongest test of any estimator is whether it can recover known parameters from simulated data. We simulate data with known parameters and check if the fitted model recovers them.

true_params <- c(gg = 0.35, gk = 0.30, kk = 0.35, gamma = 0.25)

sim <- simulate_lca(
  n = 1000,
  n_items = 5,
  gg = true_params["gg"],
  gk = true_params["gk"],
  kk = true_params["kk"],
  gamma = true_params["gamma"],
  seed = 123
)

fit <- lca_fit(sim$pre, sim$post)
#> 
#> Iter: 1 fn: 1218.3536     Pars:  0.34757 0.31134 0.34109 0.25483
#> Iter: 2 fn: 1218.3536     Pars:  0.34757 0.31134 0.34109 0.25483
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1221.5848     Pars:  0.36093 0.28551 0.35356 0.25747
#> Iter: 2 fn: 1221.5848     Pars:  0.36092 0.28551 0.35357 0.25746
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1196.7124     Pars:  0.31559 0.33276 0.35166 0.24269
#> Iter: 2 fn: 1196.7124     Pars:  0.31559 0.33275 0.35166 0.24268
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1197.0520     Pars:  0.33367 0.27400 0.39233 0.17883
#> Iter: 2 fn: 1197.0520     Pars:  0.33367 0.27400 0.39233 0.17883
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1218.6913     Pars:  0.35320 0.30648 0.34032 0.27237
#> Iter: 2 fn: 1218.6913     Pars:  0.35320 0.30648 0.34032 0.27237
#> solnp--> Completed in 2 iterations

estimated <- c(
  gg = mean(fit$params["gg", ]),
  gk = mean(fit$params["gk", ]),
  kk = mean(fit$params["kk", ]),
  gamma = mean(fit$params["gamma", ])
)

comparison <- rbind(
  true = true_params,
  estimated = estimated,
  difference = estimated - true_params
)

knitr::kable(comparison, digits = 3,
             caption = "Parameter Recovery: True vs. Estimated")
Parameter Recovery: True vs. Estimated
gg gk kk gamma
true 0.350 0.300 0.350 0.250
estimated 0.342 0.302 0.356 0.241
difference -0.008 0.002 0.006 -0.009

The estimated parameters should be close to the true values. Small differences are expected due to sampling variability.

Monte Carlo Validation

A single simulation might be lucky. To properly validate the estimator, we run many simulations and examine the distribution of estimates.

n_sims <- 100
n <- 500
n_items <- 2
true_params <- c(gg = 0.35, gk = 0.30, kk = 0.35, gamma = 0.25)

set.seed(789)
estimates <- matrix(NA, nrow = n_sims, ncol = 4)
colnames(estimates) <- names(true_params)

for (sim in seq_len(n_sims)) {
  sim_data <- simulate_lca(
    n = n, n_items = n_items,
    gg = true_params["gg"], gk = true_params["gk"],
    kk = true_params["kk"], gamma = true_params["gamma"]
  )

  tryCatch({
    fit <- lca_fit(sim_data$pre, sim_data$post)
    estimates[sim, ] <- c(
      mean(fit$params["gg", ]),
      mean(fit$params["gk", ]),
      mean(fit$params["kk", ]),
      mean(fit$params["gamma", ])
    )
  }, error = function(e) NULL)
}
#> 
#> Iter: 1 fn: 613.2829  Pars:  0.35383 0.32412 0.32204 0.25954
#> Iter: 2 fn: 613.2829  Pars:  0.35383 0.32412 0.32204 0.25954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.8657  Pars:  0.35028 0.34238 0.30735 0.24060
#> Iter: 2 fn: 614.8657  Pars:  0.35028 0.34238 0.30735 0.24060
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.8621  Pars:  0.33618 0.34661 0.31721 0.23256
#> Iter: 2 fn: 609.8621  Pars:  0.33618 0.34661 0.31721 0.23256
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0534  Pars:  0.33998 0.32892 0.33110 0.27642
#> Iter: 2 fn: 606.0534  Pars:  0.33998 0.32892 0.33110 0.27642
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0969  Pars:  0.34348 0.30474 0.35179 0.22556
#> Iter: 2 fn: 608.0969  Pars:  0.34348 0.30474 0.35179 0.22556
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.8707  Pars:  0.32535 0.32535 0.34929 0.24390
#> Iter: 2 fn: 601.8707  Pars:  0.32535 0.32535 0.34929 0.24390
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.3769  Pars:  0.38304 0.28798 0.32897 0.28467
#> Iter: 2 fn: 618.3769  Pars:  0.38304 0.28798 0.32898 0.28467
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.2921  Pars:  0.37711 0.30059 0.32230 0.26812
#> Iter: 2 fn: 619.2921  Pars:  0.37711 0.30059 0.32230 0.26812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.1708  Pars:  0.28139 0.34791 0.37070 0.21818
#> Iter: 2 fn: 585.1708  Pars:  0.28140 0.34791 0.37070 0.21818
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.2893  Pars:  0.32712 0.32176 0.35112 0.25410
#> Iter: 2 fn: 601.2893  Pars:  0.32712 0.32176 0.35112 0.25410
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1912  Pars:  0.31752 0.29484 0.38764 0.20635
#> Iter: 2 fn: 595.1912  Pars:  0.31752 0.29484 0.38764 0.20635
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.0018  Pars:  0.35021 0.32725 0.32254 0.30328
#> Iter: 2 fn: 607.0018  Pars:  0.35021 0.32725 0.32254 0.30328
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.8767  Pars:  0.36409 0.31004 0.32587 0.29687
#> Iter: 2 fn: 611.8767  Pars:  0.36409 0.31004 0.32587 0.29687
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.6453  Pars:  0.35617 0.30609 0.33774 0.28125
#> Iter: 2 fn: 609.6453  Pars:  0.35617 0.30609 0.33774 0.28125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.4966  Pars:  0.37747 0.22204 0.40049 0.27941
#> Iter: 2 fn: 602.4966  Pars:  0.37747 0.22204 0.40049 0.27941
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.5013  Pars:  0.35384 0.28091 0.36525 0.25955
#> Iter: 2 fn: 606.5013  Pars:  0.35384 0.28091 0.36526 0.25954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 626.0749  Pars:  0.40772 0.26904 0.32325 0.27891
#> Iter: 2 fn: 626.0749  Pars:  0.40772 0.26904 0.32325 0.27891
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 631.7191  Pars:  0.43073 0.24850 0.32078 0.27564
#> Iter: 2 fn: 631.7191  Pars:  0.43073 0.24850 0.32078 0.27564
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4454  Pars:  0.36450 0.23490 0.40060 0.25926
#> Iter: 2 fn: 601.4454  Pars:  0.36450 0.23490 0.40060 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.4661  Pars:  0.34553 0.28423 0.37024 0.28226
#> Iter: 2 fn: 600.4661  Pars:  0.34553 0.28422 0.37025 0.28226
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.4011  Pars:  0.37869 0.21486 0.40646 0.25532
#> Iter: 2 fn: 603.4011  Pars:  0.37869 0.21486 0.40646 0.25532
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.7771  Pars:  0.35388 0.24641 0.39971 0.23704
#> Iter: 2 fn: 600.7771  Pars:  0.35388 0.24641 0.39971 0.23704
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3894  Pars:  0.37194 0.28653 0.34153 0.27407
#> Iter: 2 fn: 614.3894  Pars:  0.37194 0.28653 0.34153 0.27407
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.9866  Pars:  0.34699 0.35277 0.30024 0.30833
#> Iter: 2 fn: 607.9866  Pars:  0.34699 0.35277 0.30024 0.30833
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.7209  Pars:  0.36513 0.23692 0.39796 0.28244
#> Iter: 2 fn: 599.7209  Pars:  0.36513 0.23691 0.39796 0.28244
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.4293  Pars:  0.34951 0.31335 0.33714 0.33621
#> Iter: 2 fn: 598.4293  Pars:  0.34951 0.31335 0.33714 0.33621
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.0655  Pars:  0.35511 0.31818 0.32670 0.29600
#> Iter: 2 fn: 609.0655  Pars:  0.35511 0.31818 0.32670 0.29600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.2867  Pars:  0.33075 0.31500 0.35425 0.23810
#> Iter: 2 fn: 603.2867  Pars:  0.33075 0.31500 0.35425 0.23810
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.8568  Pars:  0.30756 0.32895 0.36349 0.25217
#> Iter: 2 fn: 592.8568  Pars:  0.30756 0.32895 0.36349 0.25217
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.2439  Pars:  0.33779 0.27613 0.38609 0.25397
#> Iter: 2 fn: 598.2439  Pars:  0.33779 0.27613 0.38609 0.25397
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.0905  Pars:  0.33322 0.25183 0.41495 0.21374
#> Iter: 2 fn: 593.0905  Pars:  0.33322 0.25183 0.41495 0.21374
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1403  Pars:  0.32916 0.27214 0.39869 0.22835
#> Iter: 2 fn: 595.1403  Pars:  0.32916 0.27214 0.39869 0.22835
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.4499  Pars:  0.34142 0.33058 0.32800 0.26190
#> Iter: 2 fn: 608.4499  Pars:  0.34142 0.33058 0.32800 0.26190
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.7861  Pars:  0.35676 0.28598 0.35726 0.29365
#> Iter: 2 fn: 604.7861  Pars:  0.35676 0.28598 0.35726 0.29365
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5147  Pars:  0.34387 0.29802 0.35811 0.21481
#> Iter: 2 fn: 607.5147  Pars:  0.34387 0.29802 0.35811 0.21481
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.0710  Pars:  0.37690 0.30523 0.31787 0.24648
#> Iter: 2 fn: 621.0710  Pars:  0.37690 0.30523 0.31787 0.24648
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.7930  Pars:  0.35406 0.26349 0.38245 0.27132
#> Iter: 2 fn: 601.7930  Pars:  0.35406 0.26349 0.38245 0.27132
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.1098  Pars:  0.34317 0.22698 0.42985 0.25984
#> Iter: 2 fn: 588.1098  Pars:  0.34317 0.22698 0.42985 0.25984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.0683  Pars:  0.39837 0.28946 0.31216 0.30216
#> Iter: 2 fn: 623.0683  Pars:  0.39837 0.28946 0.31216 0.30216
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.4270  Pars:  0.38136 0.29443 0.32421 0.28677
#> Iter: 2 fn: 618.4270  Pars:  0.38136 0.29443 0.32421 0.28676
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.3742  Pars:  0.33961 0.33171 0.32867 0.24031
#> Iter: 2 fn: 609.3742  Pars:  0.33961 0.33171 0.32867 0.24031
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.7567  Pars:  0.38759 0.24493 0.36748 0.25694
#> Iter: 2 fn: 614.7567  Pars:  0.38759 0.24493 0.36748 0.25694
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.1825  Pars:  0.32629 0.30606 0.36765 0.20930
#> Iter: 2 fn: 601.1825  Pars:  0.32629 0.30606 0.36765 0.20930
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.7675  Pars:  0.31111 0.35632 0.33257 0.24786
#> Iter: 2 fn: 598.7675  Pars:  0.31111 0.35632 0.33257 0.24786
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.4324  Pars:  0.35556 0.27596 0.36848 0.24627
#> Iter: 2 fn: 607.4324  Pars:  0.35556 0.27596 0.36848 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.9027  Pars:  0.36513 0.29545 0.33943 0.28244
#> Iter: 2 fn: 611.9027  Pars:  0.36513 0.29545 0.33943 0.28244
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 638.4566  Pars:  0.46355 0.24366 0.29279 0.32692
#> Iter: 2 fn: 638.4566  Pars:  0.46354 0.24366 0.29280 0.32692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4045  Pars:  0.35451 0.28820 0.35728 0.21583
#> Iter: 2 fn: 610.4045  Pars:  0.35451 0.28820 0.35728 0.21583
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.9431  Pars:  0.36752 0.26179 0.37069 0.20548
#> Iter: 2 fn: 610.9431  Pars:  0.36752 0.26179 0.37069 0.20548
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.9396  Pars:  0.40412 0.27711 0.31876 0.30714
#> Iter: 2 fn: 622.9396  Pars:  0.40412 0.27711 0.31876 0.30714
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4203  Pars:  0.35048 0.30115 0.34837 0.22963
#> Iter: 2 fn: 610.4203  Pars:  0.35048 0.30115 0.34837 0.22963
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.3476  Pars:  0.39431 0.28367 0.32202 0.29496
#> Iter: 2 fn: 621.3476  Pars:  0.39431 0.28367 0.32202 0.29496
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 626.1756  Pars:  0.40017 0.28311 0.31672 0.26530
#> Iter: 2 fn: 626.1756  Pars:  0.40017 0.28311 0.31672 0.26531
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.6232  Pars:  0.38756 0.31058 0.30186 0.24657
#> Iter: 2 fn: 625.6232  Pars:  0.38756 0.31058 0.30185 0.24658
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.8867  Pars:  0.33256 0.30637 0.36107 0.23622
#> Iter: 2 fn: 602.8867  Pars:  0.33256 0.30637 0.36107 0.23622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 576.4982  Pars:  0.30223 0.26247 0.43530 0.24562
#> Iter: 2 fn: 576.4982  Pars:  0.30223 0.26246 0.43530 0.24561
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.3489  Pars:  0.31566 0.33333 0.35101 0.20800
#> Iter: 2 fn: 600.3489  Pars:  0.31566 0.33333 0.35101 0.20800
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.0150  Pars:  0.38431 0.29373 0.32196 0.27143
#> Iter: 2 fn: 621.0150  Pars:  0.38431 0.29373 0.32196 0.27143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.3209  Pars:  0.30057 0.35284 0.34659 0.23478
#> Iter: 2 fn: 594.3209  Pars:  0.30057 0.35284 0.34659 0.23478
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.2307  Pars:  0.34351 0.37636 0.28013 0.33043
#> Iter: 2 fn: 605.2307  Pars:  0.34351 0.37636 0.28013 0.33043
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.8958  Pars:  0.35112 0.36798 0.28090 0.28800
#> Iter: 2 fn: 613.8958  Pars:  0.35112 0.36798 0.28090 0.28800
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.0112  Pars:  0.37878 0.35009 0.27113 0.30303
#> Iter: 2 fn: 622.0112  Pars:  0.37878 0.35009 0.27113 0.30303
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4482  Pars:  0.34165 0.32871 0.32965 0.22727
#> Iter: 2 fn: 610.4482  Pars:  0.34165 0.32871 0.32965 0.22727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.3372  Pars:  0.32552 0.35677 0.31771 0.23199
#> Iter: 2 fn: 606.3372  Pars:  0.32552 0.35677 0.31771 0.23200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5127  Pars:  0.34669 0.30369 0.34962 0.25581
#> Iter: 2 fn: 607.5127  Pars:  0.34669 0.30369 0.34963 0.25581
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.9499  Pars:  0.36472 0.30165 0.33363 0.27068
#> Iter: 2 fn: 613.9499  Pars:  0.36472 0.30165 0.33363 0.27068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.2687  Pars:  0.36450 0.29160 0.34390 0.25925
#> Iter: 2 fn: 613.2687  Pars:  0.36450 0.29160 0.34390 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.6233  Pars:  0.37180 0.25220 0.37600 0.23077
#> Iter: 2 fn: 610.6233  Pars:  0.37180 0.25220 0.37600 0.23077
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.8246  Pars:  0.36009 0.31508 0.32484 0.28906
#> Iter: 2 fn: 611.8246  Pars:  0.36009 0.31508 0.32484 0.28906
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.5576  Pars:  0.33256 0.28280 0.38464 0.23622
#> Iter: 2 fn: 598.5576  Pars:  0.33256 0.28280 0.38464 0.23622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.9500  Pars:  0.30502 0.28990 0.40508 0.20661
#> Iter: 2 fn: 587.9500  Pars:  0.30502 0.28990 0.40508 0.20661
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.0333  Pars:  0.34779 0.29972 0.35249 0.29268
#> Iter: 2 fn: 603.0333  Pars:  0.34779 0.29972 0.35248 0.29268
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.4552  Pars:  0.32889 0.28343 0.38767 0.25203
#> Iter: 2 fn: 595.4552  Pars:  0.32889 0.28343 0.38767 0.25203
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 581.9277  Pars:  0.31151 0.25487 0.43362 0.22313
#> Iter: 2 fn: 581.9277  Pars:  0.31151 0.25487 0.43362 0.22314
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4647  Pars:  0.33002 0.29727 0.37271 0.20611
#> Iter: 2 fn: 601.4647  Pars:  0.33002 0.29727 0.37271 0.20611
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.8858  Pars:  0.37822 0.27982 0.34195 0.34959
#> Iter: 2 fn: 603.8858  Pars:  0.37822 0.27982 0.34195 0.34959
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.3231  Pars:  0.35556 0.31704 0.32741 0.32500
#> Iter: 2 fn: 604.3231  Pars:  0.35556 0.31704 0.32741 0.32500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.6866  Pars:  0.30762 0.34706 0.34533 0.23931
#> Iter: 2 fn: 596.6866  Pars:  0.30762 0.34706 0.34533 0.23932
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.9128  Pars:  0.35557 0.27331 0.37113 0.24627
#> Iter: 2 fn: 606.9128  Pars:  0.35556 0.27331 0.37113 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.8654  Pars:  0.35028 0.30814 0.34158 0.24060
#> Iter: 2 fn: 610.8654  Pars:  0.35028 0.30814 0.34158 0.24060
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7324  Pars:  0.33437 0.33437 0.33127 0.23437
#> Iter: 2 fn: 607.7324  Pars:  0.33437 0.33437 0.33127 0.23437
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.4327  Pars:  0.34757 0.31459 0.33783 0.21168
#> Iter: 2 fn: 611.4327  Pars:  0.34757 0.31459 0.33783 0.21168
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.9551  Pars:  0.34722 0.30833 0.34444 0.28000
#> Iter: 2 fn: 605.9551  Pars:  0.34722 0.30833 0.34444 0.28000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.5468  Pars:  0.32073 0.26727 0.41200 0.21429
#> Iter: 2 fn: 590.5468  Pars:  0.32073 0.26727 0.41200 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.2945  Pars:  0.33961 0.30276 0.35763 0.24031
#> Iter: 2 fn: 605.2945  Pars:  0.33961 0.30276 0.35763 0.24031
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.5722  Pars:  0.33275 0.35750 0.30975 0.27273
#> Iter: 2 fn: 606.5722  Pars:  0.33275 0.35750 0.30975 0.27273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.2883  Pars:  0.35750 0.29488 0.34762 0.23358
#> Iter: 2 fn: 612.2883  Pars:  0.35750 0.29488 0.34762 0.23358
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0856  Pars:  0.34314 0.29092 0.36595 0.19565
#> Iter: 2 fn: 606.0856  Pars:  0.34314 0.29092 0.36595 0.19565
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.4696  Pars:  0.34490 0.28122 0.37388 0.24615
#> Iter: 2 fn: 603.4696  Pars:  0.34490 0.28122 0.37388 0.24615
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.5986  Pars:  0.32902 0.33173 0.33925 0.26447
#> Iter: 2 fn: 602.5986  Pars:  0.32901 0.33173 0.33926 0.26446
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.5293  Pars:  0.37538 0.30140 0.32322 0.27007
#> Iter: 2 fn: 618.5293  Pars:  0.37538 0.30140 0.32322 0.27007
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.9864  Pars:  0.36445 0.29794 0.33761 0.24817
#> Iter: 2 fn: 614.9864  Pars:  0.36445 0.29794 0.33761 0.24817
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.3520  Pars:  0.32688 0.33436 0.33876 0.19847
#> Iter: 2 fn: 605.3520  Pars:  0.32688 0.33436 0.33876 0.19847
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.0370  Pars:  0.30257 0.33071 0.36673 0.14727
#> Iter: 2 fn: 593.0370  Pars:  0.30256 0.33071 0.36673 0.14729
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.1372  Pars:  0.38045 0.29740 0.32215 0.25352
#> Iter: 2 fn: 621.1372  Pars:  0.38045 0.29740 0.32215 0.25352
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.9445  Pars:  0.37538 0.32058 0.30404 0.27007
#> Iter: 2 fn: 620.9445  Pars:  0.37538 0.32058 0.30404 0.27007
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.1930  Pars:  0.35208 0.25224 0.39569 0.23881
#> Iter: 2 fn: 601.1930  Pars:  0.35208 0.25224 0.39569 0.23881
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.7308  Pars:  0.33281 0.26574 0.40145 0.22479
#> Iter: 2 fn: 595.7308  Pars:  0.33282 0.26574 0.40144 0.22480
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.5620  Pars:  0.31518 0.25624 0.42858 0.21950
#> Iter: 2 fn: 584.5620  Pars:  0.31519 0.25625 0.42857 0.21951
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.2884  Pars:  0.33275 0.26675 0.40050 0.27273
#> Iter: 2 fn: 591.2884  Pars:  0.33275 0.26675 0.40050 0.27273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.9365  Pars:  0.39312 0.24472 0.36216 0.23179
#> Iter: 2 fn: 617.9365  Pars:  0.39312 0.24472 0.36216 0.23179
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.2505  Pars:  0.38610 0.29282 0.32108 0.22819
#> Iter: 2 fn: 623.2505  Pars:  0.38610 0.29282 0.32108 0.22819
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.5912  Pars:  0.36455 0.24128 0.39416 0.23742
#> Iter: 2 fn: 604.5912  Pars:  0.36455 0.24128 0.39417 0.23741
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.4224  Pars:  0.36337 0.31105 0.32558 0.31200
#> Iter: 2 fn: 609.4224  Pars:  0.36337 0.31105 0.32558 0.31200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.6779  Pars:  0.36100 0.24429 0.39471 0.26316
#> Iter: 2 fn: 601.6779  Pars:  0.36100 0.24429 0.39471 0.26316
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.5563  Pars:  0.35735 0.25257 0.39008 0.25564
#> Iter: 2 fn: 602.5563  Pars:  0.35735 0.25257 0.39008 0.25564
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.2451  Pars:  0.35234 0.30280 0.34486 0.27344
#> Iter: 2 fn: 608.2451  Pars:  0.35234 0.30280 0.34486 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.5975  Pars:  0.32552 0.34896 0.32552 0.23200
#> Iter: 2 fn: 605.5975  Pars:  0.32552 0.34896 0.32552 0.23200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.1879  Pars:  0.32371 0.24538 0.43091 0.23387
#> Iter: 2 fn: 585.1879  Pars:  0.32371 0.24539 0.43091 0.23387
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.7404  Pars:  0.30973 0.28761 0.40267 0.27679
#> Iter: 2 fn: 582.7404  Pars:  0.30973 0.28760 0.40267 0.27679
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.7162  Pars:  0.33781 0.31142 0.35076 0.24219
#> Iter: 2 fn: 605.7162  Pars:  0.33781 0.31142 0.35076 0.24219
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.0927  Pars:  0.34806 0.25044 0.40150 0.20111
#> Iter: 2 fn: 600.0927  Pars:  0.34807 0.25041 0.40152 0.20111
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.3524  Pars:  0.36089 0.27535 0.36376 0.25185
#> Iter: 2 fn: 609.3524  Pars:  0.36089 0.27535 0.36376 0.25185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.6956  Pars:  0.39266 0.24755 0.35979 0.29710
#> Iter: 2 fn: 613.6956  Pars:  0.39266 0.24755 0.35979 0.29710
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.3154  Pars:  0.34686 0.24581 0.40732 0.26772
#> Iter: 2 fn: 594.3154  Pars:  0.34686 0.24581 0.40733 0.26772
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.2155  Pars:  0.36626 0.25046 0.38329 0.25735
#> Iter: 2 fn: 606.2155  Pars:  0.36626 0.25046 0.38329 0.25735
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.2222  Pars:  0.36009 0.31789 0.32202 0.28906
#> Iter: 2 fn: 612.2222  Pars:  0.36009 0.31789 0.32202 0.28906
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.0952  Pars:  0.34450 0.34165 0.31385 0.29752
#> Iter: 2 fn: 607.0952  Pars:  0.34449 0.34165 0.31386 0.29752
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.7043  Pars:  0.38935 0.23838 0.37227 0.24490
#> Iter: 2 fn: 614.7043  Pars:  0.38935 0.23838 0.37227 0.24490
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.1769  Pars:  0.34865 0.31224 0.33911 0.23134
#> Iter: 2 fn: 611.1769  Pars:  0.34866 0.31223 0.33911 0.23134
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.7777  Pars:  0.32189 0.30619 0.37191 0.23577
#> Iter: 2 fn: 597.7777  Pars:  0.32189 0.30619 0.37191 0.23577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.9252  Pars:  0.33067 0.34133 0.32800 0.25000
#> Iter: 2 fn: 605.9252  Pars:  0.33067 0.34133 0.32800 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.6054  Pars:  0.33793 0.37064 0.29143 0.26613
#> Iter: 2 fn: 610.6054  Pars:  0.33793 0.37064 0.29143 0.26613
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.6040  Pars:  0.34449 0.37581 0.27970 0.29751
#> Iter: 2 fn: 610.6040  Pars:  0.34449 0.37581 0.27969 0.29752
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.2155  Pars:  0.37072 0.25557 0.37370 0.28788
#> Iter: 2 fn: 606.2155  Pars:  0.37072 0.25557 0.37370 0.28788
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.3340  Pars:  0.31519 0.30494 0.37987 0.21951
#> Iter: 2 fn: 595.3340  Pars:  0.31519 0.30494 0.37988 0.21951
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.5389  Pars:  0.33602 0.29839 0.36559 0.25600
#> Iter: 2 fn: 601.5389  Pars:  0.33602 0.29839 0.36559 0.25600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.4039  Pars:  0.31822 0.27276 0.40901 0.25210
#> Iter: 2 fn: 587.4039  Pars:  0.31822 0.27276 0.40901 0.25210
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.2621  Pars:  0.38259 0.29451 0.32289 0.27338
#> Iter: 2 fn: 620.2621  Pars:  0.38259 0.29451 0.32289 0.27338
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.5488  Pars:  0.37511 0.25806 0.36683 0.24823
#> Iter: 2 fn: 612.5488  Pars:  0.37511 0.25806 0.36683 0.24823
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.8635  Pars:  0.35048 0.27000 0.37952 0.22963
#> Iter: 2 fn: 604.8635  Pars:  0.35048 0.27000 0.37952 0.22963
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.5861  Pars:  0.32444 0.31430 0.36127 0.21094
#> Iter: 2 fn: 601.5861  Pars:  0.32444 0.31430 0.36127 0.21094
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.9628  Pars:  0.33245 0.31915 0.34840 0.24800
#> Iter: 2 fn: 603.9628  Pars:  0.33245 0.31915 0.34840 0.24800
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.8320  Pars:  0.32712 0.33248 0.34040 0.25410
#> Iter: 2 fn: 602.8320  Pars:  0.32712 0.33248 0.34040 0.25410
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.6577  Pars:  0.37312 0.28298 0.34390 0.20134
#> Iter: 2 fn: 616.6577  Pars:  0.37313 0.28297 0.34390 0.20134
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.9971  Pars:  0.41626 0.27317 0.31057 0.23125
#> Iter: 2 fn: 630.9971  Pars:  0.41626 0.27317 0.31057 0.23125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.1665  Pars:  0.35234 0.33032 0.31733 0.27344
#> Iter: 2 fn: 612.1665  Pars:  0.35234 0.33032 0.31733 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.9287  Pars:  0.39299 0.29271 0.31430 0.26207
#> Iter: 2 fn: 624.9287  Pars:  0.39299 0.29271 0.31430 0.26207
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6812  Pars:  0.33320 0.36120 0.30560 0.28571
#> Iter: 2 fn: 605.6812  Pars:  0.33320 0.36120 0.30560 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.8940  Pars:  0.28270 0.35667 0.36063 0.24299
#> Iter: 2 fn: 584.8940  Pars:  0.28269 0.35667 0.36064 0.24299
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.7566  Pars:  0.37180 0.26260 0.36560 0.23077
#> Iter: 2 fn: 612.7566  Pars:  0.37180 0.26260 0.36560 0.23077
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.9148  Pars:  0.38939 0.28059 0.33002 0.30147
#> Iter: 2 fn: 617.9148  Pars:  0.38939 0.28059 0.33002 0.30147
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.0919  Pars:  0.36636 0.26692 0.36673 0.23572
#> Iter: 2 fn: 611.0919  Pars:  0.36636 0.26692 0.36673 0.23571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.5712  Pars:  0.36636 0.27477 0.35888 0.23571
#> Iter: 2 fn: 612.5712  Pars:  0.36636 0.27477 0.35888 0.23571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.6206  Pars:  0.37166 0.31741 0.31093 0.26277
#> Iter: 2 fn: 619.6206  Pars:  0.37166 0.31741 0.31093 0.26277
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.5350  Pars:  0.36938 0.26636 0.36426 0.20408
#> Iter: 2 fn: 612.5350  Pars:  0.36938 0.26636 0.36426 0.20408
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.7982  Pars:  0.32895 0.30000 0.37105 0.24000
#> Iter: 2 fn: 599.7982  Pars:  0.32895 0.30000 0.37105 0.24000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.7359  Pars:  0.30000 0.30000 0.40000 0.20000
#> Iter: 2 fn: 587.7359  Pars:  0.30000 0.30000 0.40000 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.1854  Pars:  0.35448 0.32378 0.32174 0.28346
#> Iter: 2 fn: 611.1854  Pars:  0.35448 0.32378 0.32174 0.28346
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.3525  Pars:  0.34017 0.27879 0.38104 0.21804
#> Iter: 2 fn: 602.3525  Pars:  0.34017 0.27879 0.38104 0.21805
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.9958  Pars:  0.36094 0.30562 0.33344 0.24088
#> Iter: 2 fn: 614.9958  Pars:  0.36094 0.30562 0.33344 0.24088
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.8275  Pars:  0.30498 0.28893 0.40608 0.12782
#> Iter: 2 fn: 585.8275  Pars:  0.30498 0.28893 0.40609 0.12782
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.5523  Pars:  0.32034 0.29450 0.38516 0.22582
#> Iter: 2 fn: 595.5523  Pars:  0.32033 0.29450 0.38517 0.22580
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8125  Pars:  0.34066 0.33479 0.32456 0.31897
#> Iter: 2 fn: 600.8125  Pars:  0.34066 0.33478 0.32456 0.31897
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.7510  Pars:  0.36978 0.26260 0.36761 0.25362
#> Iter: 2 fn: 610.7510  Pars:  0.36979 0.26260 0.36761 0.25362
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.7459  Pars:  0.33099 0.31289 0.35612 0.22656
#> Iter: 2 fn: 603.7459  Pars:  0.33099 0.31289 0.35612 0.22656
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.5546  Pars:  0.33833 0.28451 0.37717 0.21969
#> Iter: 2 fn: 602.5546  Pars:  0.33833 0.28450 0.37717 0.21970
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.6953  Pars:  0.35735 0.27675 0.36590 0.25564
#> Iter: 2 fn: 607.6953  Pars:  0.35735 0.27675 0.36590 0.25564
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1226  Pars:  0.33827 0.32995 0.33177 0.27869
#> Iter: 2 fn: 605.1226  Pars:  0.33827 0.32995 0.33177 0.27869
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.0729  Pars:  0.35963 0.25945 0.38092 0.22143
#> Iter: 2 fn: 607.0729  Pars:  0.35963 0.25945 0.38092 0.22143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.9822  Pars:  0.39514 0.28842 0.31644 0.30657
#> Iter: 2 fn: 620.9822  Pars:  0.39514 0.28842 0.31644 0.30657
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.9920  Pars:  0.38428 0.22589 0.38982 0.22973
#> Iter: 2 fn: 609.9920  Pars:  0.38428 0.22589 0.38982 0.22973
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.6420  Pars:  0.32209 0.32209 0.35581 0.27350
#> Iter: 2 fn: 596.6420  Pars:  0.32209 0.32209 0.35581 0.27350
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.7657  Pars:  0.34539 0.31056 0.34405 0.31092
#> Iter: 2 fn: 600.7657  Pars:  0.34539 0.31056 0.34405 0.31092
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.5514  Pars:  0.33320 0.32200 0.34480 0.28571
#> Iter: 2 fn: 600.5514  Pars:  0.33320 0.32200 0.34480 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.9774  Pars:  0.31304 0.27913 0.40783 0.23333
#> Iter: 2 fn: 587.9774  Pars:  0.31304 0.27913 0.40783 0.23333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.3372  Pars:  0.34669 0.26606 0.38725 0.25581
#> Iter: 2 fn: 600.3372  Pars:  0.34669 0.26606 0.38725 0.25581
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2747  Pars:  0.30941 0.30941 0.38119 0.19200
#> Iter: 2 fn: 594.2747  Pars:  0.30941 0.30941 0.38119 0.19200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8594  Pars:  0.32838 0.29919 0.37243 0.17778
#> Iter: 2 fn: 600.8594  Pars:  0.32838 0.29919 0.37243 0.17778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.5218  Pars:  0.30827 0.32050 0.37122 0.18254
#> Iter: 2 fn: 595.5218  Pars:  0.30827 0.32050 0.37122 0.18254
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.0751  Pars:  0.35378 0.32452 0.32170 0.24812
#> Iter: 2 fn: 614.0751  Pars:  0.35378 0.32452 0.32170 0.24812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 633.8951  Pars:  0.43835 0.30870 0.25296 0.35211
#> Iter: 2 fn: 633.8951  Pars:  0.43835 0.30870 0.25296 0.35211
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.3170  Pars:  0.36114 0.29099 0.34787 0.23022
#> Iter: 2 fn: 613.3170  Pars:  0.36114 0.29099 0.34787 0.23022
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 626.9971  Pars:  0.40675 0.30727 0.28598 0.31654
#> Iter: 2 fn: 626.9971  Pars:  0.40676 0.30726 0.28598 0.31655
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.3129  Pars:  0.36094 0.23975 0.39931 0.24088
#> Iter: 2 fn: 602.3129  Pars:  0.36094 0.23975 0.39931 0.24088
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0456  Pars:  0.36267 0.26400 0.37333 0.25001
#> Iter: 2 fn: 608.0456  Pars:  0.36267 0.26400 0.37333 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0625  Pars:  0.33779 0.33511 0.32711 0.25397
#> Iter: 2 fn: 608.0625  Pars:  0.33779 0.33511 0.32711 0.25397
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5991  Pars:  0.35448 0.31262 0.33290 0.28346
#> Iter: 2 fn: 609.5991  Pars:  0.35448 0.31262 0.33290 0.28346
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.4256  Pars:  0.31752 0.32004 0.36244 0.20635
#> Iter: 2 fn: 599.4256  Pars:  0.31752 0.32004 0.36244 0.20635
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.6275  Pars:  0.35208 0.30741 0.34051 0.23881
#> Iter: 2 fn: 611.6275  Pars:  0.35208 0.30741 0.34051 0.23881
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4737  Pars:  0.35579 0.27095 0.37326 0.26923
#> Iter: 2 fn: 604.4737  Pars:  0.35579 0.27095 0.37326 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.3028  Pars:  0.34531 0.31438 0.34031 0.22388
#> Iter: 2 fn: 610.3028  Pars:  0.34531 0.31438 0.34031 0.22388
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4356  Pars:  0.34513 0.28213 0.37274 0.26984
#> Iter: 2 fn: 601.4356  Pars:  0.34513 0.28213 0.37274 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.5933  Pars:  0.33075 0.30450 0.36475 0.23809
#> Iter: 2 fn: 601.5933  Pars:  0.33075 0.30450 0.36475 0.23809
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.6879  Pars:  0.37143 0.30286 0.32571 0.30000
#> Iter: 2 fn: 613.6879  Pars:  0.37143 0.30286 0.32571 0.30000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.4004  Pars:  0.40048 0.28171 0.31781 0.27586
#> Iter: 2 fn: 625.4004  Pars:  0.40048 0.28171 0.31781 0.27586
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.6905  Pars:  0.32184 0.33266 0.34550 0.26051
#> Iter: 2 fn: 599.6905  Pars:  0.32184 0.33266 0.34550 0.26050
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.4513  Pars:  0.37802 0.28211 0.33987 0.29105
#> Iter: 2 fn: 614.4513  Pars:  0.37802 0.28211 0.33987 0.29105
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.7429  Pars:  0.34385 0.31327 0.34287 0.21479
#> Iter: 2 fn: 609.7429  Pars:  0.34388 0.31329 0.34283 0.21482
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.2930  Pars:  0.32257 0.29628 0.38115 0.16297
#> Iter: 2 fn: 597.2930  Pars:  0.32257 0.29628 0.38115 0.16296
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.6716  Pars:  0.35230 0.21760 0.43010 0.22794
#> Iter: 2 fn: 592.6716  Pars:  0.35230 0.21760 0.43010 0.22794
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.5858  Pars:  0.35787 0.24968 0.39245 0.27907
#> Iter: 2 fn: 599.5858  Pars:  0.35787 0.24968 0.39245 0.27907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.9844  Pars:  0.33029 0.28414 0.38557 0.17647
#> Iter: 2 fn: 598.9844  Pars:  0.33029 0.28414 0.38557 0.17647
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.4088  Pars:  0.31290 0.34473 0.34238 0.24577
#> Iter: 2 fn: 598.4088  Pars:  0.31290 0.34472 0.34238 0.24576
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.9031  Pars:  0.35280 0.30240 0.34480 0.28571
#> Iter: 2 fn: 606.9031  Pars:  0.35280 0.30240 0.34480 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.4339  Pars:  0.32000 0.28533 0.39467 0.25000
#> Iter: 2 fn: 591.4339  Pars:  0.32000 0.28533 0.39467 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.8744  Pars:  0.37341 0.26788 0.35871 0.26087
#> Iter: 2 fn: 612.8744  Pars:  0.37341 0.26788 0.35871 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.8121  Pars:  0.39289 0.23787 0.36924 0.25170
#> Iter: 2 fn: 615.8121  Pars:  0.39289 0.23787 0.36924 0.25170
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.8157  Pars:  0.32986 0.33267 0.33747 0.29060
#> Iter: 2 fn: 599.8157  Pars:  0.32986 0.33267 0.33747 0.29060
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.3678  Pars:  0.36497 0.35917 0.27586 0.30952
#> Iter: 2 fn: 616.3678  Pars:  0.36497 0.35917 0.27586 0.30952
#> solnp--> Completed in 2 iterations

Bias Assessment

An unbiased estimator has \(E[\hat{\theta}] = \theta\). We check this by comparing mean estimates to true values:

mean_estimates <- colMeans(estimates, na.rm = TRUE)
bias <- mean_estimates - true_params
rel_bias <- 100 * bias / true_params

bias_table <- data.frame(
  Parameter = names(true_params),
  True = true_params,
  Mean_Estimate = mean_estimates,
  Bias = bias,
  Relative_Bias_Pct = rel_bias
)

knitr::kable(bias_table, digits = 4, row.names = FALSE,
             caption = "Bias Assessment from Monte Carlo Simulation")
Bias Assessment from Monte Carlo Simulation
Parameter True Mean_Estimate Bias Relative_Bias_Pct
gg 0.35 0.3508 0.0008 0.2196
gk 0.30 0.2961 -0.0039 -1.3012
kk 0.35 0.3531 0.0031 0.8957
gamma 0.25 0.2532 0.0032 1.2690

The bias should be close to zero for all parameters.

Standard Error Assessment

The standard deviation of estimates across simulations approximates the true standard error. For well-behaved estimators, this should decrease with \(\sqrt{n}\):

se_estimates <- apply(estimates, 2, sd, na.rm = TRUE)
rmse <- sqrt(colMeans((estimates - matrix(true_params, nrow = n_sims,
                                           ncol = 4, byrow = TRUE))^2,
                       na.rm = TRUE))

se_table <- data.frame(
  Parameter = names(true_params),
  SE = se_estimates,
  RMSE = rmse
)

knitr::kable(se_table, digits = 4, row.names = FALSE,
             caption = "Standard Errors from Monte Carlo Simulation")
Standard Errors from Monte Carlo Simulation
Parameter SE RMSE
gg 0.0236 0.0235
gk 0.0289 0.0290
kk 0.0290 0.0291
gamma 0.0259 0.0260

Coverage Assessment

For valid confidence intervals, 95% CIs should contain the true parameter 95% of the time:

coverage <- numeric(4)
for (j in 1:4) {
  ci_lower <- estimates[, j] - 1.96 * se_estimates[j]
  ci_upper <- estimates[, j] + 1.96 * se_estimates[j]
  coverage[j] <- mean(true_params[j] >= ci_lower &
                        true_params[j] <= ci_upper, na.rm = TRUE)
}

coverage_table <- data.frame(
  Parameter = names(true_params),
  Coverage_95 = coverage
)

knitr::kable(coverage_table, digits = 3, row.names = FALSE,
             caption = "95% CI Coverage from Monte Carlo Simulation")
95% CI Coverage from Monte Carlo Simulation
Parameter Coverage_95
gg 0.98
gk 0.94
kk 0.93
gamma 0.95

Coverage should be approximately 0.95 for all parameters.

Visualization

hist(estimates[, "gk"], breaks = 20,
     main = "Distribution of Learning (gk) Estimates",
     xlab = "Estimated gk", col = "lightblue", border = "white")
abline(v = true_params["gk"], col = "red", lwd = 2, lty = 2)
legend("topright", legend = c("True value"), col = "red", lty = 2, lwd = 2)
Distribution of gk (learning) estimates across simulations

Distribution of gk (learning) estimates across simulations

Sample Size Effects

The precision of estimates should improve with sample size, following the \(1/\sqrt{n}\) rule:

sample_sizes <- c(100, 250, 500, 1000)
true_params <- c(gg = 0.35, gk = 0.30, kk = 0.35, gamma = 0.25)
n_sims_quick <- 50

set.seed(456)
rmse_by_n <- matrix(NA, nrow = length(sample_sizes), ncol = 4)
colnames(rmse_by_n) <- names(true_params)

for (s in seq_along(sample_sizes)) {
  n <- sample_sizes[s]
  estimates_n <- matrix(NA, nrow = n_sims_quick, ncol = 4)

  for (sim in seq_len(n_sims_quick)) {
    sim_data <- simulate_lca(
      n = n, n_items = 2,
      gg = true_params["gg"], gk = true_params["gk"],
      kk = true_params["kk"], gamma = true_params["gamma"]
    )

    tryCatch({
      fit <- lca_fit(sim_data$pre, sim_data$post)
      estimates_n[sim, ] <- c(
        mean(fit$params["gg", ]),
        mean(fit$params["gk", ]),
        mean(fit$params["kk", ]),
        mean(fit$params["gamma", ])
      )
    }, error = function(e) NULL)
  }

  rmse_by_n[s, ] <- sqrt(colMeans((estimates_n - matrix(true_params,
                                                         nrow = n_sims_quick,
                                                         ncol = 4,
                                                         byrow = TRUE))^2,
                                   na.rm = TRUE))
}
#> 
#> Iter: 1 fn: 113.0827  Pars:  0.26667 0.30667 0.42667 0.25000
#> Iter: 2 fn: 113.0827  Pars:  0.26667 0.30667 0.42667 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 116.0346  Pars:  0.27842 0.31475 0.40683 0.17392
#> Iter: 2 fn: 116.0346  Pars:  0.27842 0.31474 0.40684 0.17391
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.7721  Pars:  0.30316 0.32842 0.36842 0.20834
#> Iter: 2 fn: 118.7721  Pars:  0.30316 0.32842 0.36842 0.20833
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 117.2678  Pars:  0.29763 0.29759 0.40478 0.16001
#> Iter: 2 fn: 117.2678  Pars:  0.29763 0.29762 0.40475 0.16001
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 112.6208  Pars:  0.24923 0.37385 0.37692 0.27777
#> Iter: 2 fn: 112.6208  Pars:  0.24923 0.37385 0.37692 0.27778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 115.5689  Pars:  0.27769 0.40923 0.31308 0.31579
#> Iter: 2 fn: 115.5689  Pars:  0.27769 0.40923 0.31308 0.31579
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 112.0066  Pars:  0.22562 0.36812 0.40625 0.15789
#> Iter: 2 fn: 112.0066  Pars:  0.22562 0.36813 0.40625 0.15789
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 114.3674  Pars:  0.27769 0.36539 0.35692 0.31579
#> Iter: 2 fn: 114.3674  Pars:  0.27769 0.36538 0.35692 0.31579
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.5102  Pars:  0.41262 0.26527 0.32211 0.32143
#> Iter: 2 fn: 124.5102  Pars:  0.41263 0.26526 0.32210 0.32143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 114.3137  Pars:  0.26450 0.31050 0.42500 0.13043
#> Iter: 2 fn: 114.3137  Pars:  0.26450 0.31050 0.42500 0.13043
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 126.7693  Pars:  0.43683 0.25363 0.30954 0.29031
#> Iter: 2 fn: 126.7693  Pars:  0.43682 0.25364 0.30955 0.29032
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.8712  Pars:  0.39130 0.28696 0.32174 0.23333
#> Iter: 2 fn: 124.8712  Pars:  0.39130 0.28696 0.32174 0.23333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 127.2159  Pars:  0.42857 0.30000 0.27143 0.30000
#> Iter: 2 fn: 127.2159  Pars:  0.42857 0.30000 0.27143 0.30000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.7141  Pars:  0.36000 0.27600 0.36400 0.16667
#> Iter: 2 fn: 121.7141  Pars:  0.36000 0.27600 0.36400 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.2363  Pars:  0.30249 0.39873 0.29878 0.27271
#> Iter: 2 fn: 119.2363  Pars:  0.30250 0.39875 0.29875 0.27272
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.4091  Pars:  0.30316 0.35369 0.34316 0.20833
#> Iter: 2 fn: 119.4091  Pars:  0.30316 0.35368 0.34316 0.20833
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.0068  Pars:  0.35579 0.27368 0.37053 0.26922
#> Iter: 2 fn: 121.0068  Pars:  0.35579 0.27368 0.37053 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 116.7448  Pars:  0.32000 0.25333 0.42667 0.25000
#> Iter: 2 fn: 116.7448  Pars:  0.32000 0.25333 0.42667 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.0656  Pars:  0.35579 0.34211 0.30211 0.26923
#> Iter: 2 fn: 123.0656  Pars:  0.35579 0.34211 0.30211 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 120.2679  Pars:  0.35266 0.33732 0.31001 0.34782
#> Iter: 2 fn: 120.2679  Pars:  0.35267 0.33733 0.31000 0.34783
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 125.5668  Pars:  0.40960 0.26880 0.32160 0.21874
#> Iter: 2 fn: 125.5668  Pars:  0.40960 0.26880 0.32160 0.21875
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.1769  Pars:  0.34572 0.48714 0.16713 0.36364
#> Iter: 2 fn: 121.1769  Pars:  0.34572 0.48714 0.16714 0.36364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 126.5135  Pars:  0.44263 0.27474 0.28263 0.34483
#> Iter: 2 fn: 126.5135  Pars:  0.44263 0.27474 0.28263 0.34483
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.0164  Pars:  0.36565 0.29000 0.34435 0.20690
#> Iter: 2 fn: 123.0164  Pars:  0.36565 0.29000 0.34435 0.20690
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.5332  Pars:  0.34722 0.31944 0.33334 0.28000
#> Iter: 2 fn: 121.5332  Pars:  0.34722 0.31944 0.33333 0.28000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.3237  Pars:  0.33800 0.26000 0.40200 0.23077
#> Iter: 2 fn: 119.3237  Pars:  0.33800 0.26000 0.40200 0.23077
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 116.4487  Pars:  0.28800 0.30000 0.41200 0.16667
#> Iter: 2 fn: 116.4487  Pars:  0.28800 0.30000 0.41200 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 110.7623  Pars:  0.22222 0.34444 0.43333 0.10000
#> Iter: 2 fn: 110.7623  Pars:  0.22222 0.34444 0.43333 0.10000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.9478  Pars:  0.36767 0.30883 0.32350 0.32003
#> Iter: 2 fn: 121.9478  Pars:  0.36765 0.30882 0.32353 0.32000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 122.7163  Pars:  0.40047 0.22095 0.37857 0.27586
#> Iter: 2 fn: 122.7163  Pars:  0.40048 0.22095 0.37857 0.27586
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 109.9621  Pars:  0.25190 0.26286 0.48524 0.08696
#> Iter: 2 fn: 109.9621  Pars:  0.25190 0.26286 0.48524 0.08696
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.4896  Pars:  0.33640 0.25520 0.40840 0.13793
#> Iter: 2 fn: 118.4896  Pars:  0.33640 0.25520 0.40840 0.13793
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 125.5365  Pars:  0.44263 0.24421 0.31316 0.34483
#> Iter: 2 fn: 125.5365  Pars:  0.44263 0.24421 0.31316 0.34483
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.5982  Pars:  0.40333 0.26889 0.32778 0.18182
#> Iter: 2 fn: 124.5982  Pars:  0.40333 0.26889 0.32778 0.18182
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 115.8544  Pars:  0.29389 0.28111 0.42500 0.21739
#> Iter: 2 fn: 115.8544  Pars:  0.29389 0.28111 0.42500 0.21739
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 112.9733  Pars:  0.25000 0.32500 0.42500 0.20000
#> Iter: 2 fn: 112.9733  Pars:  0.25000 0.32500 0.42500 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 120.1225  Pars:  0.33882 0.31059 0.35059 0.29167
#> Iter: 2 fn: 120.1225  Pars:  0.33882 0.31059 0.35059 0.29167
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.9110  Pars:  0.34722 0.33333 0.31944 0.28000
#> Iter: 2 fn: 121.9110  Pars:  0.34722 0.33333 0.31944 0.28000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.2042  Pars:  0.29400 0.40600 0.30000 0.28571
#> Iter: 2 fn: 118.2042  Pars:  0.29400 0.40600 0.30000 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.0307  Pars:  0.31117 0.33823 0.35060 0.26086
#> Iter: 2 fn: 119.0307  Pars:  0.31118 0.33824 0.35059 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 114.4562  Pars:  0.24500 0.38500 0.37000 0.14286
#> Iter: 2 fn: 114.4562  Pars:  0.24500 0.38500 0.37000 0.14286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 120.5628  Pars:  0.31250 0.37500 0.31250 0.20000
#> Iter: 2 fn: 120.5628  Pars:  0.31250 0.37500 0.31250 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.2635  Pars:  0.39131 0.16956 0.43913 0.23333
#> Iter: 2 fn: 119.2635  Pars:  0.39130 0.16957 0.43913 0.23333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.5318  Pars:  0.37333 0.24000 0.38667 0.25000
#> Iter: 2 fn: 121.5318  Pars:  0.37333 0.24000 0.38667 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.9246  Pars:  0.34087 0.24348 0.41565 0.17857
#> Iter: 2 fn: 118.9246  Pars:  0.34087 0.24348 0.41565 0.17857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 112.6085  Pars:  0.29763 0.21428 0.48808 0.15999
#> Iter: 2 fn: 112.6085  Pars:  0.29762 0.21429 0.48810 0.16000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.9195  Pars:  0.37334 0.37333 0.25333 0.25000
#> Iter: 2 fn: 124.9195  Pars:  0.37333 0.37333 0.25333 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 125.5081  Pars:  0.39200 0.33600 0.27200 0.28572
#> Iter: 2 fn: 125.5081  Pars:  0.39200 0.33600 0.27200 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 117.7011  Pars:  0.38533 0.19267 0.42200 0.11765
#> Iter: 2 fn: 117.7011  Pars:  0.38533 0.19267 0.42200 0.11765
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.1632  Pars:  0.38893 0.22393 0.38714 0.15152
#> Iter: 2 fn: 121.1632  Pars:  0.38893 0.22393 0.38714 0.15152
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 129.4398  Pars:  0.52545 0.18545 0.28909 0.35294
#> Iter: 2 fn: 129.4398  Pars:  0.52545 0.18545 0.28909 0.35294
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.8662  Pars:  0.33640 0.29000 0.37360 0.13793
#> Iter: 2 fn: 119.8662  Pars:  0.33640 0.29000 0.37360 0.13793
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.8333  Pars:  0.36000 0.28500 0.35500 0.33333
#> Iter: 2 fn: 119.8333  Pars:  0.36000 0.28500 0.35500 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 113.4078  Pars:  0.28471 0.25883 0.45646 0.22728
#> Iter: 2 fn: 113.4078  Pars:  0.28471 0.25882 0.45647 0.22727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.7721  Pars:  0.30316 0.32842 0.36842 0.20834
#> Iter: 2 fn: 118.7721  Pars:  0.30316 0.32842 0.36842 0.20833
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.3277  Pars:  0.30727 0.34273 0.35000 0.15385
#> Iter: 2 fn: 119.3277  Pars:  0.30727 0.34273 0.35000 0.15385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 115.5583  Pars:  0.27842 0.30263 0.41895 0.17391
#> Iter: 2 fn: 115.5583  Pars:  0.27842 0.30263 0.41895 0.17391
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.5895  Pars:  0.42250 0.32500 0.25250 0.38462
#> Iter: 2 fn: 124.5895  Pars:  0.42250 0.32500 0.25250 0.38462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.9999  Pars:  0.35579 0.30105 0.34316 0.26923
#> Iter: 2 fn: 121.9999  Pars:  0.35579 0.30105 0.34316 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.0307  Pars:  0.31117 0.33823 0.35060 0.26086
#> Iter: 2 fn: 119.0307  Pars:  0.31118 0.33824 0.35059 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.9816  Pars:  0.36749 0.45501 0.17750 0.42858
#> Iter: 2 fn: 119.9816  Pars:  0.36750 0.45500 0.17750 0.42857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.0743  Pars:  0.34571 0.45571 0.19857 0.36364
#> Iter: 2 fn: 121.0743  Pars:  0.34571 0.45571 0.19857 0.36364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 130.3714  Pars:  0.53895 0.25263 0.20842 0.40625
#> Iter: 2 fn: 130.3714  Pars:  0.53895 0.25263 0.20842 0.40625
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.6003  Pars:  0.38227 0.30318 0.31454 0.24138
#> Iter: 2 fn: 124.6003  Pars:  0.38227 0.30318 0.31455 0.24138
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 113.2687  Pars:  0.29400 0.26600 0.44000 0.28571
#> Iter: 2 fn: 113.2687  Pars:  0.29400 0.26600 0.44000 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.6519  Pars:  0.36751 0.38500 0.24749 0.42858
#> Iter: 2 fn: 118.6519  Pars:  0.36750 0.38500 0.24750 0.42857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.0169  Pars:  0.32895 0.27632 0.39474 0.24000
#> Iter: 2 fn: 119.0169  Pars:  0.32895 0.27632 0.39474 0.24000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.4280  Pars:  0.41143 0.39429 0.19429 0.41667
#> Iter: 2 fn: 123.4280  Pars:  0.41143 0.39429 0.19429 0.41667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 117.0244  Pars:  0.30727 0.27182 0.42091 0.15385
#> Iter: 2 fn: 117.0244  Pars:  0.30727 0.27182 0.42091 0.15385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.2894  Pars:  0.41667 0.21667 0.36666 0.40000
#> Iter: 2 fn: 119.2894  Pars:  0.41667 0.21667 0.36667 0.40000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 111.6712  Pars:  0.25941 0.27176 0.46882 0.19048
#> Iter: 2 fn: 111.6712  Pars:  0.25941 0.27176 0.46882 0.19048
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 107.6742  Pars:  0.25190 0.23000 0.51809 0.08696
#> Iter: 2 fn: 107.6742  Pars:  0.25190 0.23000 0.51810 0.08696
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 125.7906  Pars:  0.39130 0.33913 0.26957 0.23333
#> Iter: 2 fn: 125.7906  Pars:  0.39130 0.33913 0.26957 0.23333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.5540  Pars:  0.29389 0.35778 0.34833 0.21740
#> Iter: 2 fn: 118.5540  Pars:  0.29389 0.35778 0.34833 0.21739
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.0068  Pars:  0.35579 0.27368 0.37053 0.26922
#> Iter: 2 fn: 121.0068  Pars:  0.35579 0.27368 0.37053 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 125.6783  Pars:  0.42250 0.39000 0.18750 0.38462
#> Iter: 2 fn: 125.6783  Pars:  0.42250 0.39000 0.18750 0.38462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 115.5305  Pars:  0.30316 0.25264 0.44420 0.20835
#> Iter: 2 fn: 115.5305  Pars:  0.30316 0.25263 0.44421 0.20833
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.4124  Pars:  0.32895 0.26316 0.40789 0.24000
#> Iter: 2 fn: 118.4124  Pars:  0.32895 0.26316 0.40789 0.24000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.3136  Pars:  0.36450 0.25650 0.37900 0.25926
#> Iter: 2 fn: 121.3136  Pars:  0.36450 0.25650 0.37900 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.3048  Pars:  0.35636 0.33091 0.31273 0.21429
#> Iter: 2 fn: 123.3048  Pars:  0.35636 0.33091 0.31273 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.1784  Pars:  0.42251 0.30874 0.26875 0.38462
#> Iter: 2 fn: 124.1784  Pars:  0.42250 0.30875 0.26875 0.38461
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 117.5375  Pars:  0.30769 0.41538 0.27692 0.35000
#> Iter: 2 fn: 117.5375  Pars:  0.30769 0.41538 0.27692 0.35000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 131.0767  Pars:  0.53481 0.19704 0.26815 0.28947
#> Iter: 2 fn: 131.0767  Pars:  0.53481 0.19704 0.26815 0.28947
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 127.7863  Pars:  0.42667 0.36000 0.21333 0.25000
#> Iter: 2 fn: 127.7863  Pars:  0.42667 0.36000 0.21333 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 116.9563  Pars:  0.26889 0.39111 0.34000 0.18182
#> Iter: 2 fn: 116.9563  Pars:  0.26889 0.39111 0.34000 0.18182
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 118.8431  Pars:  0.40092 0.40089 0.19819 0.47619
#> Iter: 2 fn: 118.8431  Pars:  0.40091 0.40091 0.19818 0.47619
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 124.9972  Pars:  0.38368 0.35526 0.26105 0.29630
#> Iter: 2 fn: 124.9972  Pars:  0.38368 0.35526 0.26105 0.29630
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.0076  Pars:  0.39131 0.23478 0.37391 0.23333
#> Iter: 2 fn: 123.0076  Pars:  0.39130 0.23478 0.37391 0.23333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 122.9034  Pars:  0.47207 0.12759 0.40035 0.21622
#> Iter: 2 fn: 122.9034  Pars:  0.47207 0.12759 0.40034 0.21622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 129.4833  Pars:  0.53260 0.16739 0.30000 0.34286
#> Iter: 2 fn: 129.4833  Pars:  0.53261 0.16739 0.30000 0.34286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 127.2545  Pars:  0.44263 0.30526 0.25211 0.34482
#> Iter: 2 fn: 127.2545  Pars:  0.44263 0.30526 0.25211 0.34483
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 122.1582  Pars:  0.36565 0.26478 0.36957 0.20690
#> Iter: 2 fn: 122.1582  Pars:  0.36565 0.26478 0.36957 0.20690
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 116.2316  Pars:  0.29763 0.27380 0.42857 0.16001
#> Iter: 2 fn: 116.2316  Pars:  0.29762 0.27381 0.42857 0.16000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 119.9740  Pars:  0.31118 0.37882 0.31000 0.26087
#> Iter: 2 fn: 119.9740  Pars:  0.31118 0.37882 0.31000 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 126.5584  Pars:  0.41783 0.28304 0.29913 0.25806
#> Iter: 2 fn: 126.5584  Pars:  0.41783 0.28304 0.29913 0.25806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 121.1632  Pars:  0.35042 0.27792 0.37167 0.17241
#> Iter: 2 fn: 121.1632  Pars:  0.35042 0.27792 0.37167 0.17241
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 117.2259  Pars:  0.28409 0.36363 0.35227 0.12000
#> Iter: 2 fn: 117.2259  Pars:  0.28409 0.36364 0.35227 0.12000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 123.7812  Pars:  0.38368 0.29842 0.31789 0.29630
#> Iter: 2 fn: 123.7812  Pars:  0.38368 0.29842 0.31789 0.29630
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 115.9358  Pars:  0.5405399627 0.4594591545 0.0000008826 0.6299996057
#> Iter: 2 fn: 115.9358  Pars:  0.5405402919 0.4594594381 0.0000002699 0.6299998295
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 110.5165  Pars:  0.21600 0.36000 0.42400 0.16667
#> Iter: 2 fn: 110.5165  Pars:  0.21600 0.36000 0.42400 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 306.2548  Pars:  0.34847 0.32737 0.32416 0.24242
#> Iter: 2 fn: 306.2548  Pars:  0.34848 0.32736 0.32416 0.24242
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.5823  Pars:  0.32715 0.36408 0.30876 0.24194
#> Iter: 2 fn: 303.5823  Pars:  0.32715 0.36409 0.30877 0.24194
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 293.5197  Pars:  0.30752 0.27776 0.41472 0.19355
#> Iter: 2 fn: 293.5197  Pars:  0.30752 0.27776 0.41472 0.19355
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 296.9010  Pars:  0.32500 0.27000 0.40500 0.20000
#> Iter: 2 fn: 296.9010  Pars:  0.32500 0.27000 0.40500 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 292.8023  Pars:  0.28509 0.33600 0.37891 0.21429
#> Iter: 2 fn: 292.8023  Pars:  0.28509 0.33600 0.37891 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 305.1451  Pars:  0.35280 0.32480 0.32240 0.28571
#> Iter: 2 fn: 305.1451  Pars:  0.35280 0.32480 0.32240 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.6577  Pars:  0.32033 0.34617 0.33349 0.22581
#> Iter: 2 fn: 301.6577  Pars:  0.32033 0.34617 0.33350 0.22581
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.9580  Pars:  0.33827 0.32164 0.34009 0.27869
#> Iter: 2 fn: 301.9580  Pars:  0.33827 0.32164 0.34009 0.27869
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 314.6456  Pars:  0.39877 0.32123 0.28000 0.27778
#> Iter: 2 fn: 314.6456  Pars:  0.39877 0.32123 0.28000 0.27778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 305.6875  Pars:  0.36296 0.27482 0.36222 0.22857
#> Iter: 2 fn: 305.6875  Pars:  0.36296 0.27481 0.36222 0.22857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.4130  Pars:  0.32500 0.32000 0.35500 0.20000
#> Iter: 2 fn: 301.4130  Pars:  0.32500 0.32000 0.35500 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 311.2579  Pars:  0.38865 0.30416 0.30718 0.28985
#> Iter: 2 fn: 311.2579  Pars:  0.38865 0.30416 0.30718 0.28985
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 284.6279  Pars:  0.29008 0.24583 0.46408 0.18644
#> Iter: 2 fn: 284.6279  Pars:  0.29008 0.24583 0.46408 0.18644
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 282.5511  Pars:  0.29768 0.21960 0.48272 0.18033
#> Iter: 2 fn: 282.5511  Pars:  0.29768 0.21960 0.48272 0.18033
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.8202  Pars:  0.35758 0.28837 0.35405 0.30645
#> Iter: 2 fn: 301.8202  Pars:  0.35758 0.28837 0.35405 0.30645
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.3538  Pars:  0.35758 0.29414 0.34828 0.30645
#> Iter: 2 fn: 302.3538  Pars:  0.35758 0.29414 0.34828 0.30645
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 304.7963  Pars:  0.39035 0.24470 0.36495 0.31343
#> Iter: 2 fn: 304.7963  Pars:  0.39035 0.24470 0.36496 0.31343
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 294.3810  Pars:  0.31129 0.27671 0.41200 0.19048
#> Iter: 2 fn: 294.3810  Pars:  0.31129 0.27671 0.41200 0.19048
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 299.8697  Pars:  0.34513 0.27391 0.38097 0.26984
#> Iter: 2 fn: 299.8697  Pars:  0.34513 0.27391 0.38096 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 300.5952  Pars:  0.35617 0.26157 0.38226 0.28125
#> Iter: 2 fn: 300.5952  Pars:  0.35617 0.26157 0.38226 0.28125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 312.4552  Pars:  0.41290 0.24259 0.34450 0.22499
#> Iter: 2 fn: 312.4552  Pars:  0.41291 0.24258 0.34451 0.22500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 299.8697  Pars:  0.34513 0.27391 0.38097 0.26984
#> Iter: 2 fn: 299.8697  Pars:  0.34513 0.27391 0.38096 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.1073  Pars:  0.36923 0.29538 0.33538 0.35000
#> Iter: 2 fn: 301.1073  Pars:  0.36923 0.29538 0.33538 0.35000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 297.8727  Pars:  0.31293 0.33451 0.35256 0.25862
#> Iter: 2 fn: 297.8727  Pars:  0.31293 0.33451 0.35256 0.25862
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.3850  Pars:  0.38045 0.29472 0.32483 0.25352
#> Iter: 2 fn: 310.3850  Pars:  0.38045 0.29472 0.32483 0.25352
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 316.4524  Pars:  0.40992 0.32569 0.26438 0.28767
#> Iter: 2 fn: 316.4524  Pars:  0.40992 0.32569 0.26438 0.28767
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.4303  Pars:  0.37408 0.24008 0.38583 0.28358
#> Iter: 2 fn: 302.4303  Pars:  0.37408 0.24008 0.38583 0.28358
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 307.2513  Pars:  0.38533 0.26633 0.34833 0.29412
#> Iter: 2 fn: 307.2513  Pars:  0.38533 0.26633 0.34833 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.3258  Pars:  0.37341 0.31929 0.30729 0.26087
#> Iter: 2 fn: 310.3258  Pars:  0.37341 0.31929 0.30729 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 312.0971  Pars:  0.40833 0.28000 0.31167 0.31429
#> Iter: 2 fn: 312.0971  Pars:  0.40833 0.28000 0.31167 0.31429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 292.8657  Pars:  0.27874 0.35343 0.36783 0.19641
#> Iter: 2 fn: 292.8657  Pars:  0.27876 0.35342 0.36782 0.19643
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 292.9005  Pars:  0.32126 0.24596 0.43278 0.20314
#> Iter: 2 fn: 292.9005  Pars:  0.32125 0.24596 0.43278 0.20312
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.2807  Pars:  0.35957 0.27659 0.36383 0.27692
#> Iter: 2 fn: 303.2807  Pars:  0.35957 0.27660 0.36383 0.27692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 293.4114  Pars:  0.31668 0.26477 0.41855 0.22951
#> Iter: 2 fn: 293.4114  Pars:  0.31668 0.26477 0.41855 0.22951
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.3763  Pars:  0.34165 0.28988 0.36847 0.22727
#> Iter: 2 fn: 302.3763  Pars:  0.34165 0.28988 0.36847 0.22727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 293.4431  Pars:  0.28801 0.32640 0.38560 0.16667
#> Iter: 2 fn: 293.4431  Pars:  0.28800 0.32640 0.38560 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 293.9861  Pars:  0.31008 0.27958 0.41033 0.21311
#> Iter: 2 fn: 293.9861  Pars:  0.31008 0.27958 0.41033 0.21311
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 297.6058  Pars:  0.32727 0.29455 0.37818 0.26667
#> Iter: 2 fn: 297.6058  Pars:  0.32727 0.29455 0.37818 0.26667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.9721  Pars:  0.42609 0.24957 0.32435 0.34286
#> Iter: 2 fn: 310.9721  Pars:  0.42609 0.24957 0.32435 0.34286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.4959  Pars:  0.34513 0.30130 0.35357 0.26984
#> Iter: 2 fn: 302.4959  Pars:  0.34513 0.30130 0.35357 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.4935  Pars:  0.39009 0.35352 0.25638 0.34375
#> Iter: 2 fn: 310.4935  Pars:  0.39010 0.35352 0.25638 0.34375
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.1120  Pars:  0.32715 0.35353 0.31932 0.24193
#> Iter: 2 fn: 303.1120  Pars:  0.32715 0.35353 0.31932 0.24194
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 296.5011  Pars:  0.33075 0.26249 0.40676 0.23808
#> Iter: 2 fn: 296.5011  Pars:  0.33075 0.26250 0.40675 0.23810
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 287.1627  Pars:  0.31525 0.26854 0.41621 0.31482
#> Iter: 2 fn: 287.1627  Pars:  0.31524 0.26854 0.41622 0.31481
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.8367  Pars:  0.40209 0.28974 0.30817 0.32353
#> Iter: 2 fn: 310.8367  Pars:  0.40209 0.28974 0.30817 0.32353
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 311.5476  Pars:  0.37341 0.34635 0.28024 0.26087
#> Iter: 2 fn: 311.5476  Pars:  0.37341 0.34635 0.28024 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 287.6654  Pars:  0.27126 0.31646 0.41228 0.20370
#> Iter: 2 fn: 287.6654  Pars:  0.27126 0.31647 0.41228 0.20370
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 300.4966  Pars:  0.34614 0.29507 0.35879 0.29508
#> Iter: 2 fn: 300.4966  Pars:  0.34614 0.29507 0.35879 0.29508
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 306.9615  Pars:  0.36645 0.29535 0.33820 0.26866
#> Iter: 2 fn: 306.9615  Pars:  0.36645 0.29535 0.33820 0.26866
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 309.6398  Pars:  0.37556 0.34089 0.28355 0.30769
#> Iter: 2 fn: 309.6398  Pars:  0.37556 0.34089 0.28356 0.30769
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 299.6282  Pars:  0.31887 0.31396 0.36717 0.18462
#> Iter: 2 fn: 299.6282  Pars:  0.31887 0.31396 0.36717 0.18462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 312.4765  Pars:  0.39675 0.31050 0.29275 0.30435
#> Iter: 2 fn: 312.4765  Pars:  0.39675 0.31050 0.29275 0.30435
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 291.9569  Pars:  0.33561 0.35536 0.30903 0.39216
#> Iter: 2 fn: 291.9569  Pars:  0.33561 0.35535 0.30903 0.39216
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 289.8137  Pars:  0.26678 0.40833 0.32489 0.26531
#> Iter: 2 fn: 289.8137  Pars:  0.26678 0.40833 0.32489 0.26531
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 312.5087  Pars:  0.40328 0.28400 0.31272 0.29578
#> Iter: 2 fn: 312.5087  Pars:  0.40328 0.28400 0.31272 0.29577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 308.9498  Pars:  0.36981 0.30113 0.32906 0.24286
#> Iter: 2 fn: 308.9498  Pars:  0.36981 0.30113 0.32906 0.24286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 304.0459  Pars:  0.34490 0.30776 0.34735 0.24615
#> Iter: 2 fn: 304.0459  Pars:  0.34490 0.30776 0.34735 0.24615
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.5644  Pars:  0.34169 0.30311 0.35520 0.27419
#> Iter: 2 fn: 301.5644  Pars:  0.34169 0.30311 0.35520 0.27419
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 288.7011  Pars:  0.28234 0.29174 0.42592 0.14997
#> Iter: 2 fn: 288.7011  Pars:  0.28234 0.29177 0.42589 0.15000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.5175  Pars:  0.36000 0.31800 0.32200 0.33333
#> Iter: 2 fn: 302.5175  Pars:  0.36000 0.31800 0.32200 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 305.6758  Pars:  0.36300 0.29150 0.34550 0.27273
#> Iter: 2 fn: 305.6758  Pars:  0.36300 0.29150 0.34550 0.27273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 305.2659  Pars:  0.34286 0.38857 0.26857 0.30000
#> Iter: 2 fn: 305.2659  Pars:  0.34286 0.38857 0.26857 0.30000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 306.6955  Pars:  0.35559 0.31788 0.32653 0.25757
#> Iter: 2 fn: 306.6955  Pars:  0.35559 0.31788 0.32653 0.25758
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 312.5087  Pars:  0.40328 0.28400 0.31272 0.29578
#> Iter: 2 fn: 312.5087  Pars:  0.40328 0.28400 0.31272 0.29577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 318.8489  Pars:  0.45248 0.24021 0.30731 0.28395
#> Iter: 2 fn: 318.8489  Pars:  0.45248 0.24021 0.30731 0.28395
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 316.1008  Pars:  0.46933 0.18133 0.34934 0.25000
#> Iter: 2 fn: 316.1008  Pars:  0.46933 0.18133 0.34933 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 311.4645  Pars:  0.39625 0.27086 0.33289 0.20253
#> Iter: 2 fn: 311.4645  Pars:  0.39625 0.27086 0.33289 0.20253
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 309.3103  Pars:  0.38793 0.25862 0.35345 0.22667
#> Iter: 2 fn: 309.3103  Pars:  0.38793 0.25862 0.35345 0.22667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 311.3699  Pars:  0.39527 0.26693 0.33780 0.22078
#> Iter: 2 fn: 311.3699  Pars:  0.39527 0.26693 0.33780 0.22078
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 307.3125  Pars:  0.35752 0.31283 0.32966 0.19444
#> Iter: 2 fn: 307.3125  Pars:  0.35752 0.31283 0.32966 0.19444
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 300.4156  Pars:  0.33152 0.33152 0.33696 0.28813
#> Iter: 2 fn: 300.4156  Pars:  0.33152 0.33152 0.33695 0.28814
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.3538  Pars:  0.35758 0.29414 0.34828 0.30645
#> Iter: 2 fn: 302.3538  Pars:  0.35758 0.29414 0.34828 0.30645
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.6699  Pars:  0.34169 0.33067 0.32765 0.27419
#> Iter: 2 fn: 303.6699  Pars:  0.34169 0.33067 0.32764 0.27419
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 304.8636  Pars:  0.36302 0.33327 0.30371 0.32787
#> Iter: 2 fn: 304.8636  Pars:  0.36302 0.33327 0.30371 0.32787
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 311.6152  Pars:  0.38865 0.30980 0.30155 0.28985
#> Iter: 2 fn: 311.6152  Pars:  0.38865 0.30980 0.30155 0.28985
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 298.4825  Pars:  0.32667 0.29400 0.37933 0.14286
#> Iter: 2 fn: 298.4825  Pars:  0.32667 0.29400 0.37933 0.14286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 316.6576  Pars:  0.51200 0.16000 0.32800 0.37500
#> Iter: 2 fn: 316.6576  Pars:  0.51200 0.16000 0.32800 0.37500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 315.3637  Pars:  0.41257 0.28229 0.30514 0.26316
#> Iter: 2 fn: 315.3637  Pars:  0.41257 0.28229 0.30514 0.26316
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 296.3591  Pars:  0.29955 0.33283 0.36762 0.15872
#> Iter: 2 fn: 296.3591  Pars:  0.29955 0.33283 0.36762 0.15873
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.4875  Pars:  0.39303 0.33256 0.27442 0.33846
#> Iter: 2 fn: 310.4875  Pars:  0.39302 0.33256 0.27442 0.33846
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 307.8534  Pars:  0.35617 0.35617 0.28765 0.28125
#> Iter: 2 fn: 307.8534  Pars:  0.35617 0.35617 0.28765 0.28125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 294.7755  Pars:  0.30250 0.34100 0.35650 0.27273
#> Iter: 2 fn: 294.7755  Pars:  0.30250 0.34100 0.35650 0.27273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.1987  Pars:  0.33437 0.29780 0.36784 0.23438
#> Iter: 2 fn: 301.1987  Pars:  0.33437 0.29780 0.36784 0.23438
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.2807  Pars:  0.35957 0.27659 0.36383 0.27692
#> Iter: 2 fn: 303.2807  Pars:  0.35957 0.27660 0.36383 0.27692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.7648  Pars:  0.36662 0.24785 0.38553 0.22535
#> Iter: 2 fn: 303.7648  Pars:  0.36662 0.24785 0.38553 0.22535
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 302.4648  Pars:  0.33076 0.34160 0.32764 0.26229
#> Iter: 2 fn: 302.4648  Pars:  0.33076 0.34160 0.32764 0.26229
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 310.6960  Pars:  0.36981 0.33283 0.29736 0.24286
#> Iter: 2 fn: 310.6960  Pars:  0.36981 0.33283 0.29736 0.24286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.9580  Pars:  0.33827 0.32164 0.34009 0.27869
#> Iter: 2 fn: 301.9580  Pars:  0.33827 0.32164 0.34009 0.27869
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 306.1234  Pars:  0.38533 0.25500 0.35967 0.29412
#> Iter: 2 fn: 306.1234  Pars:  0.38533 0.25500 0.35967 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 306.7047  Pars:  0.36267 0.29333 0.34400 0.25000
#> Iter: 2 fn: 306.7047  Pars:  0.36267 0.29333 0.34400 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 291.0144  Pars:  0.34945 0.20855 0.44200 0.29032
#> Iter: 2 fn: 291.0144  Pars:  0.34945 0.20855 0.44200 0.29032
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 301.4952  Pars:  0.36409 0.26169 0.37422 0.29687
#> Iter: 2 fn: 301.4952  Pars:  0.36409 0.26169 0.37422 0.29688
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 304.1385  Pars:  0.36007 0.26371 0.37621 0.21127
#> Iter: 2 fn: 304.1385  Pars:  0.36007 0.26371 0.37621 0.21127
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 300.4798  Pars:  0.34007 0.27107 0.38886 0.18841
#> Iter: 2 fn: 300.4798  Pars:  0.34007 0.27107 0.38886 0.18841
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 298.4401  Pars:  0.31296 0.31777 0.36927 0.16923
#> Iter: 2 fn: 298.4401  Pars:  0.31296 0.31778 0.36926 0.16923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 304.8906  Pars:  0.40805 0.23148 0.36047 0.34326
#> Iter: 2 fn: 304.8906  Pars:  0.40808 0.23146 0.36046 0.34328
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 309.1166  Pars:  0.38088 0.28704 0.33208 0.27536
#> Iter: 2 fn: 309.1166  Pars:  0.38088 0.28704 0.33208 0.27536
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 299.7503  Pars:  0.32875 0.28891 0.38234 0.19697
#> Iter: 2 fn: 299.7503  Pars:  0.32875 0.28891 0.38234 0.19697
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 303.0013  Pars:  0.36100 0.38000 0.25900 0.36842
#> Iter: 2 fn: 303.0013  Pars:  0.36100 0.38000 0.25900 0.36842
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 309.2365  Pars:  0.40563 0.23022 0.36415 0.27027
#> Iter: 2 fn: 309.2365  Pars:  0.40563 0.23022 0.36415 0.27027
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.0545  Pars:  0.34133 0.32800 0.33067 0.25000
#> Iter: 2 fn: 609.0545  Pars:  0.34133 0.32800 0.33067 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.7417  Pars:  0.30637 0.35539 0.33824 0.18400
#> Iter: 2 fn: 598.7417  Pars:  0.30637 0.35539 0.33824 0.18400
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.8875  Pars:  0.41352 0.30619 0.28029 0.36641
#> Iter: 2 fn: 620.8875  Pars:  0.41352 0.30619 0.28029 0.36641
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.5115  Pars:  0.34892 0.29354 0.35754 0.27778
#> Iter: 2 fn: 604.5115  Pars:  0.34892 0.29354 0.35754 0.27778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.5415  Pars:  0.33552 0.30708 0.35740 0.29661
#> Iter: 2 fn: 597.5415  Pars:  0.33552 0.30708 0.35740 0.29661
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.5309  Pars:  0.31469 0.31204 0.37327 0.24370
#> Iter: 2 fn: 594.5309  Pars:  0.31469 0.31204 0.37327 0.24370
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.3295  Pars:  0.35636 0.27745 0.36618 0.21429
#> Iter: 2 fn: 609.3295  Pars:  0.35636 0.27745 0.36618 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.6662  Pars:  0.33818 0.28387 0.37795 0.18978
#> Iter: 2 fn: 602.6662  Pars:  0.33818 0.28387 0.37795 0.18978
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.6571  Pars:  0.36088 0.32347 0.31565 0.25185
#> Iter: 2 fn: 616.6571  Pars:  0.36089 0.32347 0.31564 0.25185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.2993  Pars:  0.36818 0.29182 0.34000 0.26666
#> Iter: 2 fn: 614.2993  Pars:  0.36818 0.29182 0.34000 0.26667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.2336  Pars:  0.33103 0.31172 0.35724 0.27500
#> Iter: 2 fn: 599.2336  Pars:  0.33103 0.31172 0.35724 0.27500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.4552  Pars:  0.32889 0.28343 0.38767 0.25203
#> Iter: 2 fn: 595.4552  Pars:  0.32889 0.28343 0.38767 0.25203
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.5372  Pars:  0.43109 0.25749 0.31142 0.30873
#> Iter: 2 fn: 630.5372  Pars:  0.43109 0.25750 0.31142 0.30872
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.9081  Pars:  0.38400 0.26667 0.34933 0.25000
#> Iter: 2 fn: 617.9081  Pars:  0.38400 0.26667 0.34933 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.5296  Pars:  0.36472 0.29891 0.33637 0.27068
#> Iter: 2 fn: 613.5296  Pars:  0.36472 0.29891 0.33637 0.27068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.6568  Pars:  0.30968 0.29677 0.39355 0.22500
#> Iter: 2 fn: 590.6568  Pars:  0.30968 0.29677 0.39355 0.22500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.6865  Pars:  0.41575 0.25472 0.32953 0.31690
#> Iter: 2 fn: 622.6865  Pars:  0.41575 0.25472 0.32953 0.31690
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.0190  Pars:  0.30062 0.28183 0.41754 0.14844
#> Iter: 2 fn: 584.0190  Pars:  0.30062 0.28183 0.41754 0.14844
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.5839  Pars:  0.36114 0.28060 0.35826 0.23022
#> Iter: 2 fn: 611.5839  Pars:  0.36114 0.28060 0.35826 0.23022
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.4822  Pars:  0.32500 0.31750 0.35750 0.20000
#> Iter: 2 fn: 602.4822  Pars:  0.32500 0.31750 0.35750 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.2907  Pars:  0.34341 0.31593 0.34066 0.27200
#> Iter: 2 fn: 606.2907  Pars:  0.34341 0.31593 0.34066 0.27200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.0054  Pars:  0.31888 0.32908 0.35204 0.21600
#> Iter: 2 fn: 601.0054  Pars:  0.31888 0.32908 0.35204 0.21600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.9881  Pars:  0.40825 0.24495 0.34680 0.28966
#> Iter: 2 fn: 620.9881  Pars:  0.40825 0.24495 0.34680 0.28966
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.3944  Pars:  0.35556 0.28657 0.35786 0.24627
#> Iter: 2 fn: 609.3944  Pars:  0.35556 0.28657 0.35786 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4479  Pars:  0.36998 0.25534 0.37468 0.23239
#> Iter: 2 fn: 610.4479  Pars:  0.36998 0.25534 0.37468 0.23239
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4737  Pars:  0.35579 0.27095 0.37326 0.26923
#> Iter: 2 fn: 604.4737  Pars:  0.35579 0.27095 0.37326 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.1412  Pars:  0.32758 0.29555 0.37687 0.18797
#> Iter: 2 fn: 600.1412  Pars:  0.32757 0.29556 0.37687 0.18797
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.2093  Pars:  0.32371 0.30282 0.37347 0.23387
#> Iter: 2 fn: 598.2093  Pars:  0.32371 0.30282 0.37347 0.23387
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 628.6087  Pars:  0.39928 0.32055 0.28016 0.28873
#> Iter: 2 fn: 628.6087  Pars:  0.39929 0.32055 0.28016 0.28873
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.6613  Pars:  0.37690 0.28134 0.34176 0.24648
#> Iter: 2 fn: 617.6613  Pars:  0.37690 0.28135 0.34176 0.24648
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 632.4108  Pars:  0.45163 0.25023 0.29814 0.34459
#> Iter: 2 fn: 632.4108  Pars:  0.45163 0.25023 0.29814 0.34459
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.4655  Pars:  0.38304 0.26561 0.35135 0.28467
#> Iter: 2 fn: 614.4655  Pars:  0.38304 0.26561 0.35135 0.28467
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0191  Pars:  0.36176 0.27483 0.36341 0.28682
#> Iter: 2 fn: 606.0191  Pars:  0.36176 0.27483 0.36341 0.28682
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.9769  Pars:  0.30762 0.31024 0.38214 0.23932
#> Iter: 2 fn: 590.9769  Pars:  0.30762 0.31025 0.38213 0.23932
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.0192  Pars:  0.31318 0.30332 0.38350 0.18898
#> Iter: 2 fn: 595.0192  Pars:  0.31318 0.30332 0.38350 0.18898
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.8482  Pars:  0.32838 0.27730 0.39432 0.17778
#> Iter: 2 fn: 596.8482  Pars:  0.32838 0.27730 0.39432 0.17778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2551  Pars:  0.34722 0.31667 0.33611 0.28000
#> Iter: 2 fn: 607.2551  Pars:  0.34722 0.31667 0.33611 0.28000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1266  Pars:  0.33256 0.31423 0.35321 0.23622
#> Iter: 2 fn: 604.1266  Pars:  0.33256 0.31423 0.35322 0.23622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.6846  Pars:  0.34252 0.30222 0.35526 0.20588
#> Iter: 2 fn: 607.6846  Pars:  0.34252 0.30222 0.35526 0.20588
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3815  Pars:  0.36193 0.25563 0.38244 0.20979
#> Iter: 2 fn: 607.3815  Pars:  0.36193 0.25563 0.38244 0.20979
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.4723  Pars:  0.40264 0.32435 0.27301 0.28472
#> Iter: 2 fn: 630.4723  Pars:  0.40264 0.32435 0.27301 0.28472
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 629.7776  Pars:  0.42288 0.26394 0.31318 0.29530
#> Iter: 2 fn: 629.7776  Pars:  0.42288 0.26394 0.31318 0.29530
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0303  Pars:  0.33437 0.33698 0.32865 0.23438
#> Iter: 2 fn: 608.0303  Pars:  0.33437 0.33698 0.32865 0.23437
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.5669  Pars:  0.33956 0.33154 0.32890 0.25197
#> Iter: 2 fn: 608.5669  Pars:  0.33956 0.33154 0.32891 0.25197
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.1389  Pars:  0.38578 0.29532 0.31890 0.24827
#> Iter: 2 fn: 623.1389  Pars:  0.38578 0.29532 0.31890 0.24828
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.6552  Pars:  0.37028 0.25457 0.37515 0.22222
#> Iter: 2 fn: 610.6552  Pars:  0.37029 0.25457 0.37514 0.22222
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.9919  Pars:  0.34513 0.30130 0.35357 0.26984
#> Iter: 2 fn: 604.9919  Pars:  0.34513 0.30130 0.35357 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.5407  Pars:  0.34141 0.30465 0.35394 0.23846
#> Iter: 2 fn: 606.5407  Pars:  0.34141 0.30465 0.35394 0.23846
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.1964  Pars:  0.31194 0.31701 0.37105 0.21139
#> Iter: 2 fn: 596.1964  Pars:  0.31194 0.31701 0.37105 0.21138
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2668  Pars:  0.34311 0.30854 0.34835 0.24806
#> Iter: 2 fn: 607.2668  Pars:  0.34311 0.30854 0.34835 0.24806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.4959  Pars:  0.36802 0.27270 0.35928 0.24460
#> Iter: 2 fn: 612.4959  Pars:  0.36802 0.27270 0.35928 0.24460
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.4258  Pars:  0.39776 0.26323 0.33901 0.31618
#> Iter: 2 fn: 616.4258  Pars:  0.39776 0.26323 0.33901 0.31618
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.8874  Pars:  0.33076 0.33347 0.33577 0.26230
#> Iter: 2 fn: 603.8874  Pars:  0.33076 0.33347 0.33578 0.26229
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.4133  Pars:  0.34686 0.36052 0.29262 0.26772
#> Iter: 2 fn: 613.4133  Pars:  0.34686 0.36052 0.29262 0.26772
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.9775  Pars:  0.37538 0.31236 0.31226 0.27007
#> Iter: 2 fn: 619.9775  Pars:  0.37538 0.31236 0.31226 0.27007
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.9368  Pars:  0.28802 0.32657 0.38541 0.11811
#> Iter: 2 fn: 583.9368  Pars:  0.28802 0.32657 0.38541 0.11811
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.6071  Pars:  0.43655 0.24253 0.32093 0.34028
#> Iter: 2 fn: 625.6071  Pars:  0.43655 0.24253 0.32093 0.34028
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.9833  Pars:  0.37161 0.27146 0.35693 0.24113
#> Iter: 2 fn: 613.9833  Pars:  0.37161 0.27146 0.35693 0.24113
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.5146  Pars:  0.29880 0.31114 0.39006 0.19008
#> Iter: 2 fn: 589.5146  Pars:  0.29880 0.31114 0.39006 0.19008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.5490  Pars:  0.36409 0.30151 0.33440 0.29688
#> Iter: 2 fn: 610.5490  Pars:  0.36409 0.30151 0.33440 0.29688
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.4635  Pars:  0.31250 0.29751 0.38998 0.20000
#> Iter: 2 fn: 593.4635  Pars:  0.31250 0.29750 0.39000 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.0044  Pars:  0.37023 0.31773 0.31204 0.27612
#> Iter: 2 fn: 618.0044  Pars:  0.37023 0.31773 0.31204 0.27612
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2905  Pars:  0.32189 0.28787 0.39023 0.23577
#> Iter: 2 fn: 594.2905  Pars:  0.32189 0.28787 0.39023 0.23577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.2090  Pars:  0.31645 0.30573 0.37782 0.25424
#> Iter: 2 fn: 593.2090  Pars:  0.31645 0.30573 0.37782 0.25424
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3712  Pars:  0.34384 0.33266 0.32350 0.28455
#> Iter: 2 fn: 607.3712  Pars:  0.34384 0.33266 0.32350 0.28455
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4024  Pars:  0.32009 0.30434 0.37557 0.23771
#> Iter: 2 fn: 596.4024  Pars:  0.32009 0.30434 0.37557 0.23771
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.0813  Pars:  0.31625 0.31376 0.36998 0.19685
#> Iter: 2 fn: 598.0813  Pars:  0.31625 0.31376 0.36998 0.19685
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.7753  Pars:  0.31111 0.34036 0.34852 0.24786
#> Iter: 2 fn: 596.7753  Pars:  0.31111 0.34036 0.34852 0.24786
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.3628  Pars:  0.31488 0.30286 0.38226 0.16794
#> Iter: 2 fn: 595.3628  Pars:  0.31488 0.30286 0.38226 0.16794
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.8385  Pars:  0.35556 0.26800 0.37644 0.24627
#> Iter: 2 fn: 605.8385  Pars:  0.35556 0.26800 0.37644 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.4605  Pars:  0.33244 0.29255 0.37500 0.24800
#> Iter: 2 fn: 599.4605  Pars:  0.33245 0.29255 0.37500 0.24800
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.0153  Pars:  0.30876 0.32382 0.36743 0.20325
#> Iter: 2 fn: 596.0153  Pars:  0.30876 0.32382 0.36743 0.20325
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.0274  Pars:  0.30270 0.30013 0.39717 0.22034
#> Iter: 2 fn: 588.0274  Pars:  0.30270 0.30013 0.39717 0.22034
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.3144  Pars:  0.29439 0.34723 0.35839 0.20513
#> Iter: 2 fn: 592.3144  Pars:  0.29439 0.34723 0.35839 0.20513
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.8290  Pars:  0.35234 0.28353 0.36413 0.27344
#> Iter: 2 fn: 604.8290  Pars:  0.35234 0.28353 0.36413 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.7028  Pars:  0.36449 0.29430 0.34120 0.25925
#> Iter: 2 fn: 613.7028  Pars:  0.36450 0.29430 0.34120 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 579.6205  Pars:  0.26889 0.34222 0.38889 0.18183
#> Iter: 2 fn: 579.6205  Pars:  0.26889 0.34222 0.38889 0.18182
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.0264  Pars:  0.30502 0.34535 0.34963 0.20661
#> Iter: 2 fn: 597.0264  Pars:  0.30502 0.34535 0.34963 0.20661
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.1841  Pars:  0.37379 0.27477 0.35144 0.19205
#> Iter: 2 fn: 615.1841  Pars:  0.37379 0.27477 0.35144 0.19205
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.7219  Pars:  0.38321 0.29946 0.31733 0.21192
#> Iter: 2 fn: 622.7219  Pars:  0.38321 0.29946 0.31733 0.21192
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.7222  Pars:  0.40519 0.24957 0.34523 0.31884
#> Iter: 2 fn: 616.7222  Pars:  0.40519 0.24957 0.34523 0.31884
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5027  Pars:  0.38533 0.26633 0.34833 0.29412
#> Iter: 2 fn: 614.5027  Pars:  0.38533 0.26633 0.34833 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.6696  Pars:  0.37556 0.33511 0.28933 0.30769
#> Iter: 2 fn: 618.6696  Pars:  0.37556 0.33511 0.28933 0.30769
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5918  Pars:  0.34341 0.34066 0.31593 0.27200
#> Iter: 2 fn: 609.5918  Pars:  0.34341 0.34066 0.31593 0.27200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.7176  Pars:  0.37747 0.30253 0.32000 0.27941
#> Iter: 2 fn: 618.7176  Pars:  0.37747 0.30253 0.32000 0.27941
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.6323  Pars:  0.38368 0.33821 0.27810 0.29630
#> Iter: 2 fn: 623.6323  Pars:  0.38368 0.33821 0.27811 0.29630
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5327  Pars:  0.35932 0.30464 0.33604 0.23188
#> Iter: 2 fn: 614.5327  Pars:  0.35932 0.30464 0.33604 0.23188
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.2049  Pars:  0.39463 0.27389 0.33149 0.32089
#> Iter: 2 fn: 616.2049  Pars:  0.39464 0.27389 0.33147 0.32090
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.5504  Pars:  0.38877 0.28062 0.33062 0.31579
#> Iter: 2 fn: 615.5504  Pars:  0.38877 0.28062 0.33062 0.31579
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1531  Pars:  0.33282 0.30960 0.35758 0.22480
#> Iter: 2 fn: 604.1531  Pars:  0.33282 0.30960 0.35758 0.22481
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.5334  Pars:  0.29867 0.36533 0.33600 0.24999
#> Iter: 2 fn: 593.5334  Pars:  0.29867 0.36533 0.33600 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1366  Pars:  0.29876 0.36952 0.33172 0.23684
#> Iter: 2 fn: 595.1366  Pars:  0.29876 0.36952 0.33172 0.23684
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.9567  Pars:  0.35752 0.33023 0.31225 0.26718
#> Iter: 2 fn: 614.9567  Pars:  0.35752 0.33023 0.31225 0.26718
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.6679  Pars:  0.35636 0.28509 0.35855 0.21429
#> Iter: 2 fn: 610.6679  Pars:  0.35636 0.28509 0.35855 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.4834  Pars:  0.35912 0.30552 0.33536 0.25373
#> Iter: 2 fn: 613.4834  Pars:  0.35912 0.30552 0.33536 0.25373
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.2737  Pars:  0.35750 0.25312 0.38937 0.23357
#> Iter: 2 fn: 604.2737  Pars:  0.35750 0.25312 0.38937 0.23358
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.3772  Pars:  0.37511 0.28466 0.34023 0.24823
#> Iter: 2 fn: 617.3772  Pars:  0.37511 0.28466 0.34023 0.24823
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.5971  Pars:  0.34779 0.35343 0.29878 0.29266
#> Iter: 2 fn: 610.5971  Pars:  0.34779 0.35345 0.29876 0.29268
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.9006  Pars:  0.34686 0.30043 0.35271 0.26772
#> Iter: 2 fn: 605.9006  Pars:  0.34686 0.30043 0.35271 0.26772
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.1132  Pars:  0.34779 0.32517 0.32703 0.29268
#> Iter: 2 fn: 607.1132  Pars:  0.34779 0.32517 0.32703 0.29268
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1233.8548     Pars:  0.37023 0.30944 0.32033 0.27612
#> Iter: 2 fn: 1233.8548     Pars:  0.37023 0.30944 0.32033 0.27612
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1197.9276     Pars:  0.32328 0.30283 0.37389 0.21739
#> Iter: 2 fn: 1197.9276     Pars:  0.32328 0.30283 0.37389 0.21739
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1190.2599     Pars:  0.31645 0.31645 0.36709 0.25424
#> Iter: 2 fn: 1190.2599     Pars:  0.31645 0.31645 0.36709 0.25424
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1209.4508     Pars:  0.33936 0.32819 0.33245 0.28395
#> Iter: 2 fn: 1209.4508     Pars:  0.33936 0.32819 0.33245 0.28395
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1223.0290     Pars:  0.35321 0.30017 0.34661 0.22710
#> Iter: 2 fn: 1223.0290     Pars:  0.35322 0.30017 0.34661 0.22711
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1219.5445     Pars:  0.35841 0.27761 0.36398 0.23273
#> Iter: 2 fn: 1219.5445     Pars:  0.35841 0.27761 0.36398 0.23273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1184.4734     Pars:  0.30846 0.31773 0.37381 0.24464
#> Iter: 2 fn: 1184.4734     Pars:  0.30846 0.31773 0.37381 0.24464
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1173.7399     Pars:  0.29277 0.32374 0.38349 0.22467
#> Iter: 2 fn: 1173.7399     Pars:  0.29278 0.32373 0.38349 0.22467
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1212.2665     Pars:  0.34585 0.29062 0.36354 0.23955
#> Iter: 2 fn: 1212.2665     Pars:  0.34584 0.29061 0.36354 0.23954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1203.2595     Pars:  0.33219 0.29223 0.37559 0.19925
#> Iter: 2 fn: 1203.2595     Pars:  0.33219 0.29223 0.37559 0.19925
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1243.4076     Pars:  0.39397 0.28282 0.32322 0.28928
#> Iter: 2 fn: 1243.4076     Pars:  0.39397 0.28281 0.32322 0.28929
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1222.1552     Pars:  0.34845 0.32165 0.32990 0.25385
#> Iter: 2 fn: 1222.1552     Pars:  0.34845 0.32165 0.32990 0.25385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1224.6528     Pars:  0.35822 0.29830 0.34348 0.24907
#> Iter: 2 fn: 1224.6528     Pars:  0.35822 0.29830 0.34348 0.24907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1244.3927     Pars:  0.40592 0.31095 0.28312 0.34717
#> Iter: 2 fn: 1244.3927     Pars:  0.40592 0.31095 0.28312 0.34717
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1184.6981     Pars:  0.32133 0.27085 0.40783 0.18774
#> Iter: 2 fn: 1184.6981     Pars:  0.32133 0.27085 0.40783 0.18774
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1213.9039     Pars:  0.36546 0.25813 0.37641 0.26394
#> Iter: 2 fn: 1213.9039     Pars:  0.36546 0.25813 0.37641 0.26394
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1186.2765     Pars:  0.31289 0.31424 0.37287 0.25215
#> Iter: 2 fn: 1186.2765     Pars:  0.31289 0.31423 0.37288 0.25213
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1212.6129     Pars:  0.34674 0.28896 0.36430 0.23863
#> Iter: 2 fn: 1212.6129     Pars:  0.34675 0.28896 0.36430 0.23864
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1233.0892     Pars:  0.38041 0.29603 0.32356 0.30075
#> Iter: 2 fn: 1233.0892     Pars:  0.38041 0.29603 0.32356 0.30075
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1215.5057     Pars:  0.35596 0.29111 0.35293 0.27519
#> Iter: 2 fn: 1215.5057     Pars:  0.35596 0.29111 0.35293 0.27519
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1196.2605     Pars:  0.32182 0.31126 0.36692 0.24180
#> Iter: 2 fn: 1196.2605     Pars:  0.32182 0.31126 0.36692 0.24180
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1202.0788     Pars:  0.33300 0.28945 0.37755 0.21923
#> Iter: 2 fn: 1202.0788     Pars:  0.33301 0.28946 0.37754 0.21923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1234.3083     Pars:  0.38679 0.26057 0.35264 0.26316
#> Iter: 2 fn: 1234.3083     Pars:  0.38679 0.26057 0.35264 0.26316
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1208.1388     Pars:  0.34255 0.30540 0.35205 0.27309
#> Iter: 2 fn: 1208.1388     Pars:  0.34255 0.30540 0.35205 0.27309
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1203.0633     Pars:  0.32201 0.32720 0.35079 0.22984
#> Iter: 2 fn: 1203.0633     Pars:  0.32201 0.32720 0.35079 0.22984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1221.4644     Pars:  0.35702 0.30979 0.33319 0.28016
#> Iter: 2 fn: 1221.4644     Pars:  0.35702 0.30979 0.33319 0.28016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1206.1955     Pars:  0.33166 0.31068 0.35766 0.23717
#> Iter: 2 fn: 1206.1955     Pars:  0.33166 0.31068 0.35767 0.23716
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1230.7099     Pars:  0.36558 0.30808 0.32634 0.26966
#> Iter: 2 fn: 1230.7099     Pars:  0.36558 0.30808 0.32634 0.26966
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1236.0367     Pars:  0.36833 0.32160 0.31007 0.27239
#> Iter: 2 fn: 1236.0367     Pars:  0.36833 0.32160 0.31007 0.27239
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1225.7103     Pars:  0.36090 0.29323 0.34587 0.24633
#> Iter: 2 fn: 1225.7103     Pars:  0.36090 0.29323 0.34587 0.24632
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1189.1515     Pars:  0.31115 0.32170 0.36715 0.24153
#> Iter: 2 fn: 1189.1515     Pars:  0.31115 0.32170 0.36715 0.24153
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1197.2550     Pars:  0.31205 0.34628 0.34167 0.24051
#> Iter: 2 fn: 1197.2550     Pars:  0.31205 0.34628 0.34167 0.24051
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1245.2495     Pars:  0.39453 0.28300 0.32247 0.28269
#> Iter: 2 fn: 1245.2495     Pars:  0.39453 0.28300 0.32247 0.28269
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1251.0643     Pars:  0.39469 0.28997 0.31534 0.25510
#> Iter: 2 fn: 1251.0643     Pars:  0.39468 0.28997 0.31534 0.25510
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1226.0436     Pars:  0.36540 0.30638 0.32822 0.28846
#> Iter: 2 fn: 1226.0436     Pars:  0.36541 0.30638 0.32822 0.28846
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1229.7042     Pars:  0.36235 0.32209 0.31557 0.27969
#> Iter: 2 fn: 1229.7042     Pars:  0.36235 0.32209 0.31557 0.27969
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1210.9853     Pars:  0.33282 0.31524 0.35194 0.20377
#> Iter: 2 fn: 1210.9853     Pars:  0.33282 0.31524 0.35194 0.20377
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1237.7273     Pars:  0.37636 0.31835 0.30529 0.29323
#> Iter: 2 fn: 1237.7273     Pars:  0.37636 0.31835 0.30529 0.29323
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1223.9054     Pars:  0.36284 0.27931 0.35786 0.23381
#> Iter: 2 fn: 1223.9054     Pars:  0.36284 0.27931 0.35786 0.23381
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1220.8776     Pars:  0.35916 0.28896 0.35188 0.25940
#> Iter: 2 fn: 1220.8776     Pars:  0.35917 0.28895 0.35188 0.25940
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1199.4947     Pars:  0.33632 0.27682 0.38687 0.22692
#> Iter: 2 fn: 1199.4947     Pars:  0.33632 0.27682 0.38687 0.22692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1218.7007     Pars:  0.35406 0.30329 0.34265 0.27132
#> Iter: 2 fn: 1218.7007     Pars:  0.35406 0.30329 0.34265 0.27132
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1209.1978     Pars:  0.33282 0.30896 0.35822 0.20377
#> Iter: 2 fn: 1209.1978     Pars:  0.33282 0.30896 0.35822 0.20377
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1214.6363     Pars:  0.34256 0.30248 0.35495 0.22642
#> Iter: 2 fn: 1214.6363     Pars:  0.34256 0.30249 0.35495 0.22642
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1225.9558     Pars:  0.36538 0.28096 0.35367 0.24188
#> Iter: 2 fn: 1225.9558     Pars:  0.36538 0.28096 0.35367 0.24188
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1229.5231     Pars:  0.37091 0.28880 0.34029 0.26937
#> Iter: 2 fn: 1229.5231     Pars:  0.37091 0.28879 0.34029 0.26937
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1221.4974     Pars:  0.35399 0.29412 0.35189 0.23162
#> Iter: 2 fn: 1221.4974     Pars:  0.35399 0.29412 0.35189 0.23162
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1236.2932     Pars:  0.38450 0.27800 0.33750 0.27698
#> Iter: 2 fn: 1236.2932     Pars:  0.38450 0.27800 0.33750 0.27698
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1196.2000     Pars:  0.32217 0.30284 0.37500 0.22400
#> Iter: 2 fn: 1196.2000     Pars:  0.32216 0.30284 0.37500 0.22400
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1220.8946     Pars:  0.34759 0.31454 0.33787 0.24335
#> Iter: 2 fn: 1220.8946     Pars:  0.34758 0.31454 0.33787 0.24335
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1232.4473     Pars:  0.36896 0.29868 0.33237 0.26007
#> Iter: 2 fn: 1232.4473     Pars:  0.36896 0.29868 0.33237 0.26007
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1215.1651     Pars:  0.33514 0.34322 0.32164 0.25703
#> Iter: 2 fn: 1215.1651     Pars:  0.33514 0.34322 0.32164 0.25703
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1208.8136     Pars:  0.35561 0.25946 0.38493 0.24074
#> Iter: 2 fn: 1208.8136     Pars:  0.35561 0.25946 0.38493 0.24074
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1182.4664     Pars:  0.31734 0.28946 0.39321 0.24686
#> Iter: 2 fn: 1182.4664     Pars:  0.31734 0.28946 0.39321 0.24686
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1232.5941     Pars:  0.36905 0.31976 0.31119 0.29008
#> Iter: 2 fn: 1232.5941     Pars:  0.36905 0.31975 0.31119 0.29008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1220.4081     Pars:  0.35406 0.30878 0.33716 0.27132
#> Iter: 2 fn: 1220.4081     Pars:  0.35406 0.30878 0.33716 0.27132
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1229.4126     Pars:  0.37341 0.27085 0.35574 0.23944
#> Iter: 2 fn: 1229.4125     Pars:  0.37341 0.27085 0.35574 0.23944
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1209.3045     Pars:  0.34757 0.27273 0.37969 0.21168
#> Iter: 2 fn: 1209.3045     Pars:  0.34757 0.27273 0.37969 0.21168
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1209.8900     Pars:  0.35431 0.26060 0.38510 0.22101
#> Iter: 2 fn: 1209.8900     Pars:  0.35431 0.26060 0.38510 0.22101
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1230.1638     Pars:  0.37333 0.27600 0.35067 0.25000
#> Iter: 2 fn: 1230.1638     Pars:  0.37333 0.27600 0.35067 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1232.4391     Pars:  0.38402 0.25914 0.35683 0.25525
#> Iter: 2 fn: 1232.4391     Pars:  0.38402 0.25915 0.35684 0.25524
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1209.8596     Pars:  0.33267 0.31708 0.35025 0.23047
#> Iter: 2 fn: 1209.8596     Pars:  0.33267 0.31708 0.35025 0.23047
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1233.2169     Pars:  0.36845 0.29244 0.33911 0.22378
#> Iter: 2 fn: 1233.2169     Pars:  0.36845 0.29244 0.33911 0.22378
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1244.3680     Pars:  0.39715 0.28327 0.31958 0.29749
#> Iter: 2 fn: 1244.3680     Pars:  0.39715 0.28327 0.31958 0.29749
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1213.7457     Pars:  0.33632 0.31821 0.34547 0.22692
#> Iter: 2 fn: 1213.7457     Pars:  0.33632 0.31821 0.34547 0.22692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1218.0302     Pars:  0.34047 0.33509 0.32444 0.25692
#> Iter: 2 fn: 1218.0302     Pars:  0.34047 0.33509 0.32444 0.25692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1226.5020     Pars:  0.36094 0.29376 0.34530 0.24088
#> Iter: 2 fn: 1226.5020     Pars:  0.36094 0.29376 0.34530 0.24088
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1226.4868     Pars:  0.36534 0.28430 0.35036 0.24727
#> Iter: 2 fn: 1226.4868     Pars:  0.36534 0.28430 0.35036 0.24727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1226.3248     Pars:  0.36988 0.27020 0.35993 0.23759
#> Iter: 2 fn: 1226.3248     Pars:  0.36988 0.27020 0.35993 0.23759
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1243.0956     Pars:  0.38304 0.31035 0.30661 0.28467
#> Iter: 2 fn: 1243.0956     Pars:  0.38304 0.31035 0.30661 0.28467
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1228.2346     Pars:  0.38616 0.26168 0.35216 0.29304
#> Iter: 2 fn: 1228.2346     Pars:  0.38616 0.26168 0.35216 0.29304
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1223.5114     Pars:  0.36005 0.29397 0.34598 0.25843
#> Iter: 2 fn: 1223.5114     Pars:  0.36005 0.29397 0.34598 0.25843
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1184.3395     Pars:  0.31078 0.29927 0.38994 0.21811
#> Iter: 2 fn: 1184.3395     Pars:  0.31078 0.29927 0.38994 0.21811
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1197.7854     Pars:  0.32145 0.34651 0.33204 0.28135
#> Iter: 2 fn: 1197.7854     Pars:  0.32146 0.34649 0.33206 0.28138
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1247.7166     Pars:  0.39353 0.31685 0.28962 0.30882
#> Iter: 2 fn: 1247.7166     Pars:  0.39353 0.31685 0.28962 0.30882
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1233.6225     Pars:  0.36628 0.30303 0.33069 0.24101
#> Iter: 2 fn: 1233.6225     Pars:  0.36627 0.30303 0.33069 0.24101
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1235.1282     Pars:  0.37600 0.28501 0.33898 0.25267
#> Iter: 2 fn: 1235.1282     Pars:  0.37600 0.28501 0.33898 0.25267
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1221.7476     Pars:  0.36037 0.27771 0.36192 0.22581
#> Iter: 2 fn: 1221.7476     Pars:  0.36037 0.27771 0.36192 0.22581
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1228.9589     Pars:  0.36214 0.31532 0.32253 0.27376
#> Iter: 2 fn: 1228.9589     Pars:  0.36214 0.31532 0.32253 0.27376
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1214.7620     Pars:  0.33602 0.33737 0.32661 0.25600
#> Iter: 2 fn: 1214.7620     Pars:  0.33602 0.33737 0.32661 0.25600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1213.9135     Pars:  0.35036 0.28238 0.36726 0.23507
#> Iter: 2 fn: 1213.9135     Pars:  0.35036 0.28238 0.36726 0.23507
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1244.1633     Pars:  0.38535 0.30110 0.31355 0.27599
#> Iter: 2 fn: 1244.1633     Pars:  0.38535 0.30110 0.31355 0.27599
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1233.2296     Pars:  0.38334 0.28046 0.33621 0.29044
#> Iter: 2 fn: 1233.2296     Pars:  0.38334 0.28046 0.33621 0.29044
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1246.0150     Pars:  0.38432 0.30882 0.30686 0.27143
#> Iter: 2 fn: 1246.0150     Pars:  0.38431 0.30882 0.30686 0.27143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1242.7197     Pars:  0.39368 0.27781 0.32850 0.28369
#> Iter: 2 fn: 1242.7197     Pars:  0.39368 0.27781 0.32851 0.28369
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1216.9857     Pars:  0.35202 0.28982 0.35816 0.24436
#> Iter: 2 fn: 1216.9857     Pars:  0.35202 0.28982 0.35816 0.24436
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1210.3238     Pars:  0.33632 0.30657 0.35712 0.22692
#> Iter: 2 fn: 1210.3238     Pars:  0.33632 0.30657 0.35711 0.22692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1223.3119     Pars:  0.34758 0.32379 0.32862 0.24335
#> Iter: 2 fn: 1223.3119     Pars:  0.34758 0.32379 0.32862 0.24335
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1219.7880     Pars:  0.35780 0.27800 0.36420 0.22302
#> Iter: 2 fn: 1219.7880     Pars:  0.35780 0.27800 0.36420 0.22302
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1212.0232     Pars:  0.34412 0.29309 0.36278 0.23574
#> Iter: 2 fn: 1212.0232     Pars:  0.34412 0.29309 0.36278 0.23574
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1199.6043     Pars:  0.33334 0.29452 0.37215 0.25301
#> Iter: 2 fn: 1199.6043     Pars:  0.33334 0.29452 0.37215 0.25301
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1194.9221     Pars:  0.32444 0.29022 0.38535 0.21094
#> Iter: 2 fn: 1194.9221     Pars:  0.32444 0.29022 0.38535 0.21094
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1186.2667     Pars:  0.31033 0.31294 0.37673 0.23629
#> Iter: 2 fn: 1186.2667     Pars:  0.31033 0.31294 0.37673 0.23629
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1208.9098     Pars:  0.33980 0.31377 0.34643 0.27016
#> Iter: 2 fn: 1208.9098     Pars:  0.33980 0.31377 0.34643 0.27016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1222.8261     Pars:  0.35036 0.30983 0.33981 0.23507
#> Iter: 2 fn: 1222.8261     Pars:  0.35036 0.30983 0.33980 0.23507
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1216.8080     Pars:  0.35202 0.29425 0.35373 0.25573
#> Iter: 2 fn: 1216.8080     Pars:  0.35202 0.29425 0.35373 0.25573
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1213.8288     Pars:  0.33815 0.31233 0.34952 0.22519
#> Iter: 2 fn: 1213.8288     Pars:  0.33815 0.31233 0.34952 0.22519
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1226.5644     Pars:  0.37366 0.27475 0.35160 0.27206
#> Iter: 2 fn: 1226.5644     Pars:  0.37366 0.27475 0.35160 0.27206
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1224.1044     Pars:  0.35980 0.31239 0.32781 0.28294
#> Iter: 2 fn: 1224.1044     Pars:  0.35981 0.31239 0.32781 0.28295
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 1211.7501     Pars:  0.33334 0.32935 0.33731 0.24701
#> Iter: 2 fn: 1211.7501     Pars:  0.33334 0.32935 0.33731 0.24701
#> solnp--> Completed in 2 iterations

sample_size_table <- data.frame(
  n = sample_sizes,
  RMSE_gk = rmse_by_n[, "gk"],
  RMSE_ratio = c(NA, rmse_by_n[-nrow(rmse_by_n), "gk"] / rmse_by_n[-1, "gk"])
)

knitr::kable(sample_size_table, digits = 3, row.names = FALSE,
             caption = "RMSE of gk by Sample Size (ratio should be ~sqrt(2) for doubling n)")
RMSE of gk by Sample Size (ratio should be ~sqrt(2) for doubling n)
n RMSE_gk RMSE_ratio
100 0.058 NA
250 0.034 1.680
500 0.025 1.375
1000 0.017 1.499

The RMSE ratio between adjacent sample sizes should be approximately \(\sqrt{2} \approx 1.41\) when sample size doubles, confirming the \(1/\sqrt{n}\) efficiency pattern.

DK Model Extension

When “Don’t Know” responses are available, the model extends to a 9-cell transition matrix with 7 latent classes:

Class From To Interpretation
gg guess guess Stable ignorance
gk guess know Learned
gd guess DK Became aware of ignorance
kg know guess Forgot (became uncertain)
kk know know Stable knowledge
kd know DK Lost confidence
dd DK DK Persistent uncertainty

The learning estimate in the DK model is \(gk + kd\) (true learning plus those who learned but lost confidence).

sim_dk <- simulate_lca_dk(
  n = 500, n_items = 1,
  gg = 0.25, gk = 0.15, gd = 0.10,
  kg = 0.10, kk = 0.15, kd = 0.10,
  dd = 0.15, gamma = 0.25,
  seed = 456
)

fit_dk <- lca_fit(sim_dk$pre, sim_dk$post)
#> 
#> Iter: 1 fn: 937.4302  Pars:  0.3269261279 0.1263752144 0.1924015349 0.1686977128 0.0000008679 0.0375984375 0.1480001047 0.5010433107
#> Iter: 2 fn: 937.4302  Pars:  0.3269269233 0.1263750519 0.1924018014 0.1686977075 0.0000004826 0.0375981817 0.1479998517 0.5010442549
#> solnp--> Completed in 2 iterations

cat("True learning (gk): 0.15\n")
#> True learning (gk): 0.15
cat(sprintf("Estimated gk: %.3f\n", fit_dk$params["gk", 1]))
#> Estimated gk: 0.126
cat(sprintf("\nTrue total learning (gk + kd): %.2f\n", 0.15 + 0.10))
#> 
#> True total learning (gk + kd): 0.25
cat(sprintf("Estimated total: %.3f\n", fit_dk$learning[1]))
#> Estimated total: 0.164

Using validate_recovery()

The package provides a convenience function for Monte Carlo validation:

results <- validate_recovery(
  true_params = c(gg = 0.35, gk = 0.30, kk = 0.35, gamma = 0.25),
  n = 500,
  n_items = 2,
  n_sims = 100,
  seed = 789
)

print(results)

Individual-Level Learning Recovery

Beyond aggregate parameter recovery, we can assess how well the LCA model recovers which specific individuals learned. This is important because the posterior P(learned | data) provides individual-level diagnostic information.

The Key Insight

The LCA model leverages the joint transition structure across all items:

  • A person with (pre=0, post=1) on one item could be: truly learned OR lucky guess
  • The LCA uses ALL items’ transition patterns to separate these cases
  • Cross-sectional methods treat each timepoint independently, losing this information

Computing Posterior Class Probabilities

For each individual with response vector Y = {(y_pre_j, y_post_j)}, Bayes’ rule gives:

\[P(\text{class} = gk \mid Y) \propto P(\text{class} = gk) \times \prod_j P(y_{\text{pre},j}, y_{\text{post},j} \mid \text{class} = gk, \gamma_j)\]

The package provides posterior_class_probs() to compute these:

sim <- simulate_lca(
  n = 500, n_items = 5, gk = 0.30, gamma = 0.25,
  seed = 123, return_classes = TRUE
)

fit <- lca_fit(sim$pre, sim$post)
#> 
#> Iter: 1 fn: 611.2387  Pars:  0.36626 0.27469 0.35905 0.25735
#> Iter: 2 fn: 611.2387  Pars:  0.36626 0.27469 0.35905 0.25735
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5039  Pars:  0.35230 0.29013 0.35756 0.22794
#> Iter: 2 fn: 609.5039  Pars:  0.35230 0.29013 0.35756 0.22794
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2976  Pars:  0.34503 0.29798 0.35699 0.23485
#> Iter: 2 fn: 607.2976  Pars:  0.34503 0.29798 0.35699 0.23485
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.8218  Pars:  0.39929 0.27556 0.32515 0.28873
#> Iter: 2 fn: 622.8218  Pars:  0.39929 0.27556 0.32515 0.28873
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.5954  Pars:  0.35735 0.29287 0.34978 0.25564
#> Iter: 2 fn: 610.5954  Pars:  0.35735 0.29287 0.34978 0.25564
#> solnp--> Completed in 2 iterations

posteriors <- posterior_class_probs(fit, sim$pre, sim$post)
head(posteriors)
#>           P_gg          P_gk      P_kk
#> 1 1.000000e+00 6.677908e-299 0.0000000
#> 2 1.291563e-03  9.987084e-01 0.0000000
#> 3 1.075516e-06  8.316492e-04 0.9991673
#> 4 1.291563e-03  9.987084e-01 0.0000000
#> 5 1.291563e-03  9.987084e-01 0.0000000
#> 6 1.000000e+00  0.000000e+00 0.0000000

The key estimand is P(gk | data) = P(learned | data):

p_learned_lca <- posterior_learned(fit, sim$pre, sim$post)

cor_with_truth <- cor(p_learned_lca, as.numeric(sim$learned))
cat(sprintf("LCA correlation with true learning: %.3f\n", cor_with_truth))
#> LCA correlation with true learning: 1.000

Comparison with Cross-Sectional IRT

Cross-sectional IRT estimates ability at each timepoint independently, then computes learning as the difference:

p_learned_cs <- cross_sectional_irt(sim$pre, sim$post)

cor_cs <- cor(p_learned_cs, as.numeric(sim$learned))
cat(sprintf("Cross-sectional correlation: %.3f\n", cor_cs))
#> Cross-sectional correlation: 0.758

cat(sprintf("\nLCA advantage: %.3f\n", cor_with_truth - cor_cs))
#> 
#> LCA advantage: 0.242

Monte Carlo Comparison

We can systematically compare the two approaches:

comparison <- compare_learning_recovery(
  n = 500, n_items = 5, gk = 0.30, gamma = 0.25,
  n_sims = 50, seed = 456
)
#> 
#> Iter: 1 fn: 603.5070  Pars:  0.33833 0.28963 0.37204 0.21970
#> Iter: 2 fn: 603.5070  Pars:  0.33833 0.28963 0.37204 0.21970
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.4860  Pars:  0.32190 0.33760 0.34051 0.23578
#> Iter: 2 fn: 602.4860  Pars:  0.32189 0.33760 0.34051 0.23577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.1841  Pars:  0.35451 0.32391 0.32158 0.21583
#> Iter: 2 fn: 615.1841  Pars:  0.35451 0.32391 0.32158 0.21583
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0190  Pars:  0.32816 0.33573 0.33612 0.20769
#> Iter: 2 fn: 606.0190  Pars:  0.32816 0.33573 0.33612 0.20769
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.7326  Pars:  0.33961 0.32645 0.33394 0.24031
#> Iter: 2 fn: 608.7326  Pars:  0.33961 0.32645 0.33394 0.24031
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.2553  Pars:  0.36739 0.31935 0.31326 0.29231
#> Iter: 2 fn: 615.2553  Pars:  0.36739 0.31935 0.31326 0.29231
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.1072  Pars:  0.35234 0.32207 0.32559 0.27344
#> Iter: 2 fn: 611.1072  Pars:  0.35234 0.32206 0.32559 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.8467  Pars:  0.35735 0.32559 0.31706 0.24444
#> Iter: 2 fn: 615.8467  Pars:  0.35735 0.32559 0.31706 0.24444
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.0999  Pars:  0.37711 0.29240 0.33050 0.26812
#> Iter: 2 fn: 618.0999  Pars:  0.37711 0.29240 0.33050 0.26812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.7121  Pars:  0.32551 0.33376 0.34073 0.26889
#> Iter: 2 fn: 600.7121  Pars:  0.32555 0.33375 0.34071 0.26891
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.7017  Pars:  0.38982 0.21012 0.40006 0.27660
#> Iter: 2 fn: 605.7017  Pars:  0.38982 0.21012 0.40006 0.27660
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.6148  Pars:  0.33440 0.26257 0.40303 0.19259
#> Iter: 2 fn: 596.6148  Pars:  0.33440 0.26257 0.40303 0.19259
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.1207  Pars:  0.34133 0.26133 0.39733 0.25000
#> Iter: 2 fn: 597.1207  Pars:  0.34133 0.26133 0.39733 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.2436  Pars:  0.34946 0.27900 0.37155 0.29032
#> Iter: 2 fn: 600.2436  Pars:  0.34945 0.27900 0.37155 0.29032
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.6686  Pars:  0.36682 0.25288 0.38029 0.28030
#> Iter: 2 fn: 604.6686  Pars:  0.36682 0.25288 0.38029 0.28030
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.4350  Pars:  0.36179 0.31219 0.32602 0.31452
#> Iter: 2 fn: 608.4350  Pars:  0.36179 0.31219 0.32602 0.31452
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8198  Pars:  0.35617 0.28939 0.35444 0.28125
#> Iter: 2 fn: 606.8198  Pars:  0.35617 0.28939 0.35443 0.28125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.8222  Pars:  0.36739 0.30239 0.33022 0.29231
#> Iter: 2 fn: 612.8222  Pars:  0.36739 0.30239 0.33022 0.29231
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4018  Pars:  0.36245 0.27397 0.36358 0.29922
#> Iter: 2 fn: 604.4018  Pars:  0.36245 0.27398 0.36357 0.29921
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3742  Pars:  0.36009 0.33477 0.30514 0.28906
#> Iter: 2 fn: 614.3742  Pars:  0.36009 0.33477 0.30514 0.28906
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.4628  Pars:  0.30942 0.30680 0.38378 0.23729
#> Iter: 2 fn: 591.4628  Pars:  0.30942 0.30680 0.38378 0.23729
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.9741  Pars:  0.31508 0.27815 0.40677 0.18750
#> Iter: 2 fn: 590.9741  Pars:  0.31508 0.27815 0.40677 0.18750
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.5051  Pars:  0.32073 0.28511 0.39416 0.21429
#> Iter: 2 fn: 594.5051  Pars:  0.32073 0.28509 0.39418 0.21428
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.9568  Pars:  0.32734 0.30136 0.37130 0.23016
#> Iter: 2 fn: 599.9568  Pars:  0.32734 0.30136 0.37130 0.23016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.7541  Pars:  0.32184 0.30832 0.36984 0.26050
#> Iter: 2 fn: 595.7541  Pars:  0.32184 0.30832 0.36984 0.26050
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 627.8913  Pars:  0.41151 0.29269 0.29580 0.30986
#> Iter: 2 fn: 627.8913  Pars:  0.41151 0.29269 0.29580 0.30986
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.6975  Pars:  0.34757 0.28922 0.36320 0.21168
#> Iter: 2 fn: 607.6975  Pars:  0.34757 0.28922 0.36320 0.21168
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.1044  Pars:  0.37577 0.29784 0.32639 0.28148
#> Iter: 2 fn: 617.1044  Pars:  0.37577 0.29784 0.32639 0.28148
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.5341  Pars:  0.31625 0.32373 0.36002 0.19685
#> Iter: 2 fn: 599.5341  Pars:  0.31625 0.32373 0.36002 0.19685
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4972  Pars:  0.31250 0.31500 0.37250 0.20000
#> Iter: 2 fn: 596.4972  Pars:  0.31250 0.31500 0.37250 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.5080  Pars:  0.37366 0.30772 0.31863 0.27206
#> Iter: 2 fn: 618.5080  Pars:  0.37366 0.30772 0.31863 0.27206
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 627.1805  Pars:  0.42007 0.24596 0.33396 0.27632
#> Iter: 2 fn: 627.1805  Pars:  0.42007 0.24596 0.33396 0.27632
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.2673  Pars:  0.35636 0.31818 0.32545 0.21429
#> Iter: 2 fn: 615.2673  Pars:  0.35636 0.31818 0.32545 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.2704  Pars:  0.35230 0.30826 0.33944 0.22794
#> Iter: 2 fn: 612.2704  Pars:  0.35230 0.30827 0.33943 0.22794
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.2501  Pars:  0.39929 0.25026 0.35046 0.28873
#> Iter: 2 fn: 618.2501  Pars:  0.39929 0.25026 0.35046 0.28873
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.9585  Pars:  0.28632 0.32085 0.39283 0.18968
#> Iter: 2 fn: 584.9585  Pars:  0.28630 0.32085 0.39285 0.18966
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.2643  Pars:  0.32554 0.30091 0.37355 0.26890
#> Iter: 2 fn: 595.2643  Pars:  0.32554 0.30092 0.37354 0.26891
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.2088  Pars:  0.38604 0.27652 0.33744 0.26950
#> Iter: 2 fn: 619.2088  Pars:  0.38604 0.27652 0.33744 0.26950
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.4728  Pars:  0.32554 0.25715 0.41731 0.26891
#> Iter: 2 fn: 585.4728  Pars:  0.32554 0.25715 0.41731 0.26891
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.2276  Pars:  0.33618 0.27624 0.38758 0.23256
#> Iter: 2 fn: 599.2276  Pars:  0.33618 0.27624 0.38758 0.23256
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.3731  Pars:  0.37556 0.30911 0.31533 0.30769
#> Iter: 2 fn: 615.3731  Pars:  0.37556 0.30911 0.31533 0.30769
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.1192  Pars:  0.34142 0.33600 0.32258 0.26190
#> Iter: 2 fn: 609.1192  Pars:  0.34142 0.33600 0.32258 0.26190
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.4957  Pars:  0.35556 0.31311 0.33133 0.24627
#> Iter: 2 fn: 613.4957  Pars:  0.35556 0.31311 0.33133 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.3444  Pars:  0.38851 0.30184 0.30965 0.33077
#> Iter: 2 fn: 616.3444  Pars:  0.38851 0.30184 0.30966 0.33077
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6238  Pars:  0.33256 0.32470 0.34274 0.23622
#> Iter: 2 fn: 605.6238  Pars:  0.33256 0.32470 0.34274 0.23622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.1831  Pars:  0.35787 0.28019 0.36194 0.27907
#> Iter: 2 fn: 606.1831  Pars:  0.35787 0.28019 0.36194 0.27907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4865  Pars:  0.32500 0.28250 0.39250 0.20000
#> Iter: 2 fn: 596.4865  Pars:  0.32500 0.28250 0.39250 0.20000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4496  Pars:  0.36818 0.26463 0.36719 0.30469
#> Iter: 2 fn: 604.4496  Pars:  0.36818 0.26463 0.36719 0.30469
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.4705  Pars:  0.32953 0.26566 0.40481 0.21706
#> Iter: 2 fn: 594.4705  Pars:  0.32952 0.26566 0.40481 0.21705
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.8201  Pars:  0.29574 0.31101 0.39326 0.21547
#> Iter: 2 fn: 586.8201  Pars:  0.29574 0.31104 0.39322 0.21551
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.0554  Pars:  0.37517 0.31579 0.30905 0.25899
#> Iter: 2 fn: 621.0554  Pars:  0.37517 0.31579 0.30905 0.25899
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.4438  Pars:  0.38939 0.32926 0.28135 0.30147
#> Iter: 2 fn: 624.4438  Pars:  0.38939 0.32926 0.28135 0.30147
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.5445  Pars:  0.36496 0.35048 0.28456 0.30952
#> Iter: 2 fn: 615.5445  Pars:  0.36497 0.35048 0.28455 0.30952
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.7489  Pars:  0.34252 0.31733 0.34015 0.20588
#> Iter: 2 fn: 609.7489  Pars:  0.34252 0.31733 0.34015 0.20588
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.3465  Pars:  0.30968 0.35355 0.33677 0.22500
#> Iter: 2 fn: 599.3465  Pars:  0.30968 0.35355 0.33677 0.22500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.5611  Pars:  0.36852 0.26600 0.36548 0.27820
#> Iter: 2 fn: 608.5611  Pars:  0.36852 0.26600 0.36548 0.27820
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.4800  Pars:  0.33426 0.31001 0.35573 0.25807
#> Iter: 2 fn: 602.4800  Pars:  0.33426 0.31000 0.35574 0.25806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.3721  Pars:  0.35448 0.28749 0.35802 0.28346
#> Iter: 2 fn: 605.3721  Pars:  0.35448 0.28749 0.35802 0.28346
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9872  Pars:  0.35034 0.30689 0.34277 0.26357
#> Iter: 2 fn: 608.9872  Pars:  0.35034 0.30688 0.34278 0.26357
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.0876  Pars:  0.36100 0.29586 0.34314 0.26316
#> Iter: 2 fn: 612.0876  Pars:  0.36100 0.29586 0.34314 0.26316
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.9996  Pars:  0.35579 0.30105 0.34316 0.26923
#> Iter: 2 fn: 609.9996  Pars:  0.35579 0.30105 0.34316 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.7446  Pars:  0.31703 0.30169 0.38128 0.21774
#> Iter: 2 fn: 595.7446  Pars:  0.31703 0.30169 0.38128 0.21774
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.7548  Pars:  0.36472 0.27697 0.35831 0.27068
#> Iter: 2 fn: 609.7548  Pars:  0.36472 0.27697 0.35831 0.27068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.1189  Pars:  0.35378 0.27930 0.36692 0.24812
#> Iter: 2 fn: 607.1189  Pars:  0.35378 0.27930 0.36692 0.24812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.9345  Pars:  0.37161 0.30308 0.32531 0.24113
#> Iter: 2 fn: 618.9345  Pars:  0.37161 0.30308 0.32531 0.24113
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.3694  Pars:  0.29665 0.31594 0.38742 0.17073
#> Iter: 2 fn: 589.3694  Pars:  0.29665 0.31594 0.38741 0.17073
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.2935  Pars:  0.34252 0.28207 0.37541 0.20588
#> Iter: 2 fn: 604.2935  Pars:  0.34252 0.28207 0.37541 0.20588
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.7383  Pars:  0.38533 0.29750 0.31717 0.29412
#> Iter: 2 fn: 619.7383  Pars:  0.38533 0.29750 0.31717 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.2779  Pars:  0.37395 0.31598 0.31007 0.31008
#> Iter: 2 fn: 615.2779  Pars:  0.37396 0.31598 0.31007 0.31008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.8334  Pars:  0.33779 0.30562 0.35660 0.25397
#> Iter: 2 fn: 603.8334  Pars:  0.33779 0.30562 0.35660 0.25397
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.5997  Pars:  0.32000 0.31200 0.36800 0.25000
#> Iter: 2 fn: 596.5997  Pars:  0.32000 0.31200 0.36800 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.3606  Pars:  0.30722 0.33141 0.36137 0.17323
#> Iter: 2 fn: 596.3606  Pars:  0.30722 0.33141 0.36137 0.17323
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.4839  Pars:  0.31290 0.31819 0.36891 0.24577
#> Iter: 2 fn: 594.4839  Pars:  0.31290 0.31820 0.36890 0.24576
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.1162  Pars:  0.38564 0.32676 0.28760 0.32061
#> Iter: 2 fn: 620.1162  Pars:  0.38564 0.32676 0.28760 0.32061
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3874  Pars:  0.33099 0.34133 0.32768 0.22656
#> Iter: 2 fn: 607.3874  Pars:  0.33099 0.34133 0.32768 0.22656
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.5738  Pars:  0.33426 0.28843 0.37730 0.25806
#> Iter: 2 fn: 598.5738  Pars:  0.33426 0.28843 0.37730 0.25806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.0983  Pars:  0.35787 0.30239 0.33974 0.27907
#> Iter: 2 fn: 610.0983  Pars:  0.35787 0.30239 0.33974 0.27907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.6121  Pars:  0.35209 0.29250 0.35541 0.26154
#> Iter: 2 fn: 607.6121  Pars:  0.35208 0.29250 0.35542 0.26154
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.1084  Pars:  0.37716 0.28791 0.33492 0.30534
#> Iter: 2 fn: 613.1084  Pars:  0.37716 0.28791 0.33492 0.30534
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.6434  Pars:  0.35511 0.31534 0.32955 0.29600
#> Iter: 2 fn: 608.6434  Pars:  0.35511 0.31534 0.32955 0.29600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.1637  Pars:  0.35963 0.26972 0.37064 0.22143
#> Iter: 2 fn: 609.1637  Pars:  0.35963 0.26972 0.37064 0.22143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.8864  Pars:  0.31152 0.28321 0.40527 0.22316
#> Iter: 2 fn: 588.8864  Pars:  0.31151 0.28320 0.40530 0.22314
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.0333  Pars:  0.35388 0.25165 0.39447 0.23704
#> Iter: 2 fn: 602.0333  Pars:  0.35388 0.25165 0.39447 0.23704
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.5457  Pars:  0.33256 0.29852 0.36893 0.23622
#> Iter: 2 fn: 601.5457  Pars:  0.33256 0.29852 0.36893 0.23622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.3747  Pars:  0.33818 0.25425 0.40757 0.18978
#> Iter: 2 fn: 596.3747  Pars:  0.33818 0.25425 0.40757 0.18978
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.8748  Pars:  0.35750 0.29227 0.35023 0.23358
#> Iter: 2 fn: 611.8748  Pars:  0.35750 0.29227 0.35023 0.23358
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.1559  Pars:  0.40351 0.27703 0.31946 0.33582
#> Iter: 2 fn: 618.1559  Pars:  0.40351 0.27703 0.31946 0.33582
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5299  Pars:  0.35752 0.28110 0.36138 0.26718
#> Iter: 2 fn: 607.5299  Pars:  0.35752 0.28110 0.36138 0.26718
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.1540  Pars:  0.32400 0.27771 0.39829 0.22222
#> Iter: 2 fn: 594.1540  Pars:  0.32400 0.27771 0.39829 0.22222
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.3365  Pars:  0.39467 0.23200 0.37333 0.25000
#> Iter: 2 fn: 615.3365  Pars:  0.39467 0.23200 0.37333 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.0311  Pars:  0.33426 0.30730 0.35843 0.25807
#> Iter: 2 fn: 602.0311  Pars:  0.33426 0.30730 0.35844 0.25806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4428  Pars:  0.34810 0.31860 0.33330 0.32203
#> Iter: 2 fn: 601.4428  Pars:  0.34810 0.31860 0.33330 0.32203
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.3103  Pars:  0.36089 0.27000 0.36911 0.25185
#> Iter: 2 fn: 608.3103  Pars:  0.36089 0.27000 0.36911 0.25185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.1072  Pars:  0.33251 0.30818 0.35932 0.26016
#> Iter: 2 fn: 601.1072  Pars:  0.33251 0.30818 0.35932 0.26016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6420  Pars:  0.35787 0.27742 0.36471 0.27907
#> Iter: 2 fn: 605.6420  Pars:  0.35787 0.27742 0.36471 0.27907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.7850  Pars:  0.41390 0.25515 0.33095 0.29452
#> Iter: 2 fn: 624.7850  Pars:  0.41390 0.25515 0.33095 0.29452
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.5912  Pars:  0.36979 0.31887 0.31134 0.25362
#> Iter: 2 fn: 619.5912  Pars:  0.36979 0.31887 0.31134 0.25362
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.4297  Pars:  0.39497 0.27429 0.33074 0.27083
#> Iter: 2 fn: 622.4297  Pars:  0.39497 0.27429 0.33074 0.27083
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3390  Pars:  0.33982 0.31129 0.34889 0.22901
#> Iter: 2 fn: 607.3390  Pars:  0.33982 0.31129 0.34889 0.22901
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 629.8561  Pars:  0.41263 0.31832 0.26905 0.32143
#> Iter: 2 fn: 629.8561  Pars:  0.41263 0.31832 0.26905 0.32143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.7649  Pars:  0.29689 0.34504 0.35807 0.25225
#> Iter: 2 fn: 589.7649  Pars:  0.29689 0.34504 0.35807 0.25225
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.3473  Pars:  0.32381 0.33205 0.34414 0.27119
#> Iter: 2 fn: 599.3473  Pars:  0.32381 0.33205 0.34414 0.27119
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.3350  Pars:  0.29020 0.34671 0.36309 0.22124
#> Iter: 2 fn: 589.3350  Pars:  0.29020 0.34670 0.36309 0.22124
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.1005  Pars:  0.31939 0.26657 0.41404 0.20472
#> Iter: 2 fn: 590.1005  Pars:  0.31939 0.26657 0.41404 0.20472
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.3943  Pars:  0.35184 0.30321 0.34495 0.30081
#> Iter: 2 fn: 604.3943  Pars:  0.35184 0.30321 0.34495 0.30081
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2990  Pars:  0.35842 0.29351 0.34807 0.29134
#> Iter: 2 fn: 607.2990  Pars:  0.35842 0.29351 0.34807 0.29134
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.6278  Pars:  0.36128 0.26200 0.37672 0.27481
#> Iter: 2 fn: 604.6278  Pars:  0.36128 0.26200 0.37672 0.27481
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9213  Pars:  0.35557 0.28392 0.36051 0.24627
#> Iter: 2 fn: 608.9213  Pars:  0.35556 0.28392 0.36051 0.24627
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.5294  Pars:  0.35735 0.26600 0.37665 0.25564
#> Iter: 2 fn: 605.5294  Pars:  0.35735 0.26600 0.37665 0.25564
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.7626  Pars:  0.33275 0.30250 0.36475 0.27273
#> Iter: 2 fn: 598.7626  Pars:  0.33275 0.30250 0.36475 0.27273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.0773  Pars:  0.41160 0.24640 0.34200 0.28571
#> Iter: 2 fn: 623.0773  Pars:  0.41160 0.24640 0.34200 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.7908  Pars:  0.36565 0.26478 0.36957 0.20690
#> Iter: 2 fn: 610.7908  Pars:  0.36565 0.26478 0.36957 0.20690
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 629.2119  Pars:  0.41959 0.27117 0.30924 0.29932
#> Iter: 2 fn: 629.2119  Pars:  0.41959 0.27117 0.30924 0.29932
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.9656  Pars:  0.40264 0.26004 0.33732 0.28472
#> Iter: 2 fn: 621.9656  Pars:  0.40264 0.26004 0.33732 0.28472
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 629.3677  Pars:  0.41285 0.27523 0.31192 0.27333
#> Iter: 2 fn: 629.3677  Pars:  0.41284 0.27523 0.31193 0.27333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.8528  Pars:  0.33602 0.34140 0.32258 0.25600
#> Iter: 2 fn: 607.8528  Pars:  0.33602 0.34140 0.32258 0.25600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9116  Pars:  0.34684 0.30251 0.35065 0.23308
#> Iter: 2 fn: 608.9116  Pars:  0.34684 0.30251 0.35065 0.23308
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.7662  Pars:  0.34690 0.27504 0.37805 0.19286
#> Iter: 2 fn: 604.7662  Pars:  0.34690 0.27504 0.37805 0.19286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.8185  Pars:  0.38222 0.29669 0.32108 0.25175
#> Iter: 2 fn: 621.8185  Pars:  0.38222 0.29669 0.32108 0.25175
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.9040  Pars:  0.34757 0.27400 0.37843 0.21168
#> Iter: 2 fn: 604.9040  Pars:  0.34757 0.27400 0.37843 0.21168
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.9972  Pars:  0.29569 0.32431 0.38000 0.16129
#> Iter: 2 fn: 589.9972  Pars:  0.29569 0.32431 0.38000 0.16129
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.9697  Pars:  0.36450 0.25380 0.38170 0.25926
#> Iter: 2 fn: 605.9697  Pars:  0.36450 0.25380 0.38170 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.1530  Pars:  0.33982 0.30351 0.35667 0.22901
#> Iter: 2 fn: 606.1530  Pars:  0.33982 0.30351 0.35667 0.22901
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1992  Pars:  0.33793 0.32158 0.34048 0.26613
#> Iter: 2 fn: 605.1992  Pars:  0.33793 0.32158 0.34048 0.26613
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.6675  Pars:  0.34322 0.28820 0.36858 0.23664
#> Iter: 2 fn: 604.6675  Pars:  0.34322 0.28820 0.36858 0.23664
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.7631  Pars:  0.33982 0.32166 0.33851 0.22901
#> Iter: 2 fn: 608.7631  Pars:  0.33982 0.32166 0.33851 0.22901
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.4192  Pars:  0.34503 0.27184 0.38313 0.23485
#> Iter: 2 fn: 602.4192  Pars:  0.34503 0.27184 0.38313 0.23485
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9286  Pars:  0.34503 0.30844 0.34653 0.23485
#> Iter: 2 fn: 608.9286  Pars:  0.34503 0.30844 0.34653 0.23485
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.8773  Pars:  0.38368 0.32116 0.29516 0.29629
#> Iter: 2 fn: 621.8773  Pars:  0.38368 0.32116 0.29516 0.29630
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.7471  Pars:  0.33602 0.29369 0.37029 0.24409
#> Iter: 2 fn: 601.7471  Pars:  0.33602 0.29369 0.37029 0.24409
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3354  Pars:  0.34165 0.30542 0.35294 0.22727
#> Iter: 2 fn: 607.3354  Pars:  0.34165 0.30541 0.35294 0.22727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.1318  Pars:  0.29664 0.32077 0.38259 0.17073
#> Iter: 2 fn: 590.1318  Pars:  0.29665 0.32076 0.38259 0.17073
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.8735  Pars:  0.37396 0.31308 0.31296 0.31008
#> Iter: 2 fn: 614.8735  Pars:  0.37395 0.31308 0.31297 0.31008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.3467  Pars:  0.32033 0.31000 0.36967 0.22581
#> Iter: 2 fn: 598.3467  Pars:  0.32033 0.31000 0.36967 0.22581
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.7574  Pars:  0.36100 0.28229 0.35672 0.26316
#> Iter: 2 fn: 609.7574  Pars:  0.36100 0.28229 0.35671 0.26316
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.6810  Pars:  0.40048 0.24857 0.35095 0.27586
#> Iter: 2 fn: 619.6810  Pars:  0.40048 0.24857 0.35095 0.27586
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.5032  Pars:  0.35875 0.29102 0.35023 0.20280
#> Iter: 2 fn: 612.5032  Pars:  0.35875 0.29102 0.35023 0.20280
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.5247  Pars:  0.37341 0.28137 0.34522 0.23944
#> Iter: 2 fn: 616.5247  Pars:  0.37341 0.28137 0.34522 0.23944
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.3640  Pars:  0.37765 0.28069 0.34166 0.21621
#> Iter: 2 fn: 618.3640  Pars:  0.37766 0.28069 0.34165 0.21622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.5659  Pars:  0.40048 0.27619 0.32333 0.27586
#> Iter: 2 fn: 624.5659  Pars:  0.40048 0.27619 0.32333 0.27586
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.4447  Pars:  0.36176 0.35615 0.28209 0.28682
#> Iter: 2 fn: 617.4447  Pars:  0.36176 0.35615 0.28209 0.28682
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.7738  Pars:  0.34845 0.34577 0.30577 0.25385
#> Iter: 2 fn: 613.7738  Pars:  0.34845 0.34577 0.30577 0.25385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.2349  Pars:  0.37820 0.36648 0.25532 0.31783
#> Iter: 2 fn: 621.2349  Pars:  0.37820 0.36648 0.25532 0.31783
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.9249  Pars:  0.39125 0.30702 0.30174 0.26389
#> Iter: 2 fn: 625.9249  Pars:  0.39125 0.30702 0.30174 0.26389
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1949  Pars:  0.32688 0.32438 0.34874 0.19847
#> Iter: 2 fn: 604.1949  Pars:  0.32688 0.32438 0.34874 0.19847
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.9494  Pars:  0.31828 0.30776 0.37396 0.23967
#> Iter: 2 fn: 595.9494  Pars:  0.31828 0.30776 0.37396 0.23967
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.6339  Pars:  0.33002 0.28719 0.38279 0.20611
#> Iter: 2 fn: 599.6339  Pars:  0.33002 0.28719 0.38279 0.20611
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.9617  Pars:  0.35752 0.29475 0.34773 0.26718
#> Iter: 2 fn: 609.9617  Pars:  0.35752 0.29475 0.34773 0.26718
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.6999  Pars:  0.37884 0.26710 0.35406 0.26619
#> Iter: 2 fn: 614.6999  Pars:  0.37884 0.26710 0.35406 0.26619
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2040  Pars:  0.34531 0.29377 0.36092 0.22388
#> Iter: 2 fn: 607.2040  Pars:  0.34531 0.29377 0.36092 0.22388
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.9929  Pars:  0.35200 0.32267 0.32533 0.25000
#> Iter: 2 fn: 612.9929  Pars:  0.35200 0.32267 0.32533 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3195  Pars:  0.37969 0.27563 0.34469 0.28889
#> Iter: 2 fn: 614.3195  Pars:  0.37969 0.27563 0.34469 0.28889
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.9079  Pars:  0.38431 0.25804 0.35765 0.27143
#> Iter: 2 fn: 614.9079  Pars:  0.38431 0.25804 0.35765 0.27143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.4405  Pars:  0.37511 0.25274 0.37215 0.24823
#> Iter: 2 fn: 611.4405  Pars:  0.37511 0.25274 0.37215 0.24823
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.3548  Pars:  0.36274 0.31806 0.31920 0.23913
#> Iter: 2 fn: 617.3548  Pars:  0.36274 0.31806 0.31920 0.23913
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.3010  Pars:  0.30048 0.31731 0.38221 0.16799
#> Iter: 2 fn: 591.3010  Pars:  0.30048 0.31731 0.38221 0.16800
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1280  Pars:  0.31703 0.36816 0.31481 0.21774
#> Iter: 2 fn: 604.1280  Pars:  0.31703 0.36817 0.31480 0.21774
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.9209  Pars:  0.33938 0.28198 0.37864 0.19853
#> Iter: 2 fn: 602.9209  Pars:  0.33938 0.28198 0.37864 0.19853
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.7738  Pars:  0.31592 0.37000 0.31408 0.29730
#> Iter: 2 fn: 596.7738  Pars:  0.31592 0.37000 0.31408 0.29730
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.0051  Pars:  0.37073 0.30331 0.32596 0.28788
#> Iter: 2 fn: 615.0051  Pars:  0.37072 0.30332 0.32596 0.28788
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.0662  Pars:  0.29282 0.30734 0.39984 0.17355
#> Iter: 2 fn: 586.0662  Pars:  0.29282 0.30734 0.39984 0.17355
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.3291  Pars:  0.31151 0.31666 0.37183 0.22314
#> Iter: 2 fn: 595.3291  Pars:  0.31151 0.31666 0.37183 0.22314
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.6200  Pars:  0.33251 0.28925 0.37824 0.26016
#> Iter: 2 fn: 597.6200  Pars:  0.33251 0.28925 0.37824 0.26016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.1219  Pars:  0.32584 0.28222 0.39194 0.22047
#> Iter: 2 fn: 596.1219  Pars:  0.32584 0.28222 0.39194 0.22047
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.7028  Pars:  0.36449 0.29430 0.34120 0.25925
#> Iter: 2 fn: 613.7028  Pars:  0.36450 0.29430 0.34120 0.25926
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.0984  Pars:  0.31888 0.28317 0.39795 0.21600
#> Iter: 2 fn: 593.0984  Pars:  0.31888 0.28316 0.39796 0.21600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.8247  Pars:  0.31336 0.28255 0.40409 0.22133
#> Iter: 2 fn: 589.8247  Pars:  0.31334 0.28253 0.40413 0.22131
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.8685  Pars:  0.28837 0.31412 0.39752 0.22321
#> Iter: 2 fn: 582.8685  Pars:  0.28837 0.31411 0.39752 0.22321
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6621  Pars:  0.34216 0.32814 0.32970 0.28688
#> Iter: 2 fn: 605.6621  Pars:  0.34216 0.32814 0.32970 0.28689
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 579.5301  Pars:  0.28509 0.30291 0.41200 0.21429
#> Iter: 2 fn: 579.5301  Pars:  0.28509 0.30291 0.41200 0.21429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.8382  Pars:  0.33075 0.27037 0.39888 0.23810
#> Iter: 2 fn: 594.8382  Pars:  0.33075 0.27037 0.39888 0.23810
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.0459  Pars:  0.32552 0.32031 0.35417 0.23200
#> Iter: 2 fn: 602.0459  Pars:  0.32552 0.32031 0.35417 0.23200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.6314  Pars:  0.30942 0.32515 0.36542 0.23729
#> Iter: 2 fn: 594.6314  Pars:  0.30942 0.32516 0.36542 0.23729
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.6272  Pars:  0.32313 0.31060 0.36627 0.20155
#> Iter: 2 fn: 600.6272  Pars:  0.32313 0.31060 0.36627 0.20155
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9522  Pars:  0.34317 0.32696 0.32987 0.25984
#> Iter: 2 fn: 608.9522  Pars:  0.34317 0.32696 0.32987 0.25984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.2846  Pars:  0.33552 0.34405 0.32043 0.29661
#> Iter: 2 fn: 603.2846  Pars:  0.33552 0.34405 0.32043 0.29661
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.7399  Pars:  0.32371 0.28977 0.38653 0.23387
#> Iter: 2 fn: 595.7399  Pars:  0.32371 0.28977 0.38653 0.23387
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.4692  Pars:  0.32184 0.27316 0.40500 0.26050
#> Iter: 2 fn: 588.4692  Pars:  0.32184 0.27316 0.40500 0.26050
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.0574  Pars:  0.35920 0.31322 0.32759 0.30400
#> Iter: 2 fn: 609.0574  Pars:  0.35920 0.31322 0.32759 0.30400
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.8928  Pars:  0.32952 0.30909 0.36139 0.21705
#> Iter: 2 fn: 602.8928  Pars:  0.32952 0.30909 0.36139 0.21705
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.8575  Pars:  0.32379 0.28177 0.39443 0.19084
#> Iter: 2 fn: 595.8575  Pars:  0.32379 0.28177 0.39443 0.19084
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.0521  Pars:  0.29537 0.33682 0.36782 0.22808
#> Iter: 2 fn: 590.0521  Pars:  0.29536 0.33682 0.36782 0.22807
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.8532  Pars:  0.39765 0.26306 0.33929 0.34615
#> Iter: 2 fn: 610.8532  Pars:  0.39765 0.26306 0.33929 0.34615
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.5621  Pars:  0.32584 0.25400 0.42016 0.22047
#> Iter: 2 fn: 589.5621  Pars:  0.32584 0.25400 0.42016 0.22047
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.9085  Pars:  0.31129 0.28659 0.40212 0.19048
#> Iter: 2 fn: 590.9085  Pars:  0.31129 0.28659 0.40212 0.19048
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.5371  Pars:  0.38793 0.24310 0.36897 0.22666
#> Iter: 2 fn: 615.5371  Pars:  0.38793 0.24310 0.36896 0.22667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.8484  Pars:  0.37883 0.29523 0.32595 0.23448
#> Iter: 2 fn: 620.8484  Pars:  0.37883 0.29523 0.32595 0.23448
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.6434  Pars:  0.38597 0.21119 0.40284 0.17610
#> Iter: 2 fn: 604.6434  Pars:  0.38597 0.21119 0.40284 0.17610
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.0116  Pars:  0.41068 0.22256 0.36675 0.24516
#> Iter: 2 fn: 620.0116  Pars:  0.41068 0.22256 0.36675 0.24516
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.6848  Pars:  0.43918 0.20533 0.35548 0.29870
#> Iter: 2 fn: 624.6848  Pars:  0.43919 0.20533 0.35548 0.29870
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.3975  Pars:  0.28106 0.35132 0.36762 0.23149
#> Iter: 2 fn: 584.3975  Pars:  0.28106 0.35133 0.36761 0.23148
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.8633  Pars:  0.32010 0.34179 0.33811 0.26272
#> Iter: 2 fn: 599.8633  Pars:  0.32009 0.34179 0.33812 0.26271
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.0324  Pars:  0.31955 0.38761 0.29285 0.32407
#> Iter: 2 fn: 596.0324  Pars:  0.31956 0.38762 0.29282 0.32407
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 576.8414  Pars:  0.26380 0.35259 0.38361 0.21154
#> Iter: 2 fn: 576.8414  Pars:  0.26380 0.35259 0.38361 0.21154
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.2946  Pars:  0.29877 0.32049 0.38074 0.26364
#> Iter: 2 fn: 585.2946  Pars:  0.29877 0.32049 0.38074 0.26364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.3813  Pars:  0.37711 0.30879 0.31410 0.26812
#> Iter: 2 fn: 620.3813  Pars:  0.37711 0.30879 0.31410 0.26812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.2055  Pars:  0.38064 0.27896 0.34039 0.23288
#> Iter: 2 fn: 619.2055  Pars:  0.38064 0.27896 0.34039 0.23288
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.1661  Pars:  0.36905 0.32680 0.30415 0.29007
#> Iter: 2 fn: 617.1661  Pars:  0.36905 0.32680 0.30415 0.29008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.2316  Pars:  0.35384 0.31602 0.33014 0.25954
#> Iter: 2 fn: 612.2316  Pars:  0.35384 0.31602 0.33014 0.25954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5327  Pars:  0.35932 0.30464 0.33604 0.23188
#> Iter: 2 fn: 614.5327  Pars:  0.35932 0.30464 0.33604 0.23188
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.3220  Pars:  0.36739 0.37304 0.25957 0.29231
#> Iter: 2 fn: 620.3220  Pars:  0.36739 0.37304 0.25957 0.29231
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.5710  Pars:  0.40942 0.29600 0.29458 0.27702
#> Iter: 2 fn: 630.5710  Pars:  0.40942 0.29600 0.29458 0.27703
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 631.1485  Pars:  0.40833 0.34125 0.25042 0.31429
#> Iter: 2 fn: 631.1485  Pars:  0.40833 0.34125 0.25042 0.31429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5724  Pars:  0.32947 0.35160 0.31893 0.18657
#> Iter: 2 fn: 607.5724  Pars:  0.32947 0.35160 0.31894 0.18657
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 628.5612  Pars:  0.38812 0.37149 0.24040 0.27857
#> Iter: 2 fn: 628.5612  Pars:  0.38812 0.37149 0.24040 0.27857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.5384  Pars:  0.38578 0.25009 0.36413 0.24828
#> Iter: 2 fn: 615.5384  Pars:  0.38578 0.25009 0.36413 0.24828
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.1023  Pars:  0.39928 0.24463 0.35608 0.28873
#> Iter: 2 fn: 617.1023  Pars:  0.39929 0.24463 0.35608 0.28873
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.9068  Pars:  0.35267 0.27856 0.36878 0.21739
#> Iter: 2 fn: 607.9068  Pars:  0.35267 0.27856 0.36878 0.21739
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3982  Pars:  0.36802 0.28743 0.34455 0.25547
#> Iter: 2 fn: 614.3982  Pars:  0.36802 0.28743 0.34455 0.25547
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.7698  Pars:  0.37079 0.30071 0.32850 0.31496
#> Iter: 2 fn: 610.7698  Pars:  0.37078 0.30071 0.32851 0.31496
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4304  Pars:  0.33968 0.30978 0.35054 0.26401
#> Iter: 2 fn: 604.4304  Pars:  0.33967 0.30978 0.35054 0.26400
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.5180  Pars:  0.28090 0.38955 0.32955 0.24528
#> Iter: 2 fn: 587.5180  Pars:  0.28090 0.38955 0.32955 0.24528
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.3159  Pars:  0.30696 0.36947 0.32358 0.29629
#> Iter: 2 fn: 592.3159  Pars:  0.30695 0.36947 0.32358 0.29630
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.4233  Pars:  0.30942 0.31204 0.37853 0.23729
#> Iter: 2 fn: 592.4233  Pars:  0.30942 0.31204 0.37853 0.23729
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.9857  Pars:  0.31823 0.32089 0.36088 0.25212
#> Iter: 2 fn: 596.9857  Pars:  0.31822 0.32090 0.36088 0.25210
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.2850  Pars:  0.34165 0.27694 0.38141 0.22727
#> Iter: 2 fn: 602.2850  Pars:  0.34165 0.27694 0.38141 0.22727
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7049  Pars:  0.36701 0.24722 0.38577 0.21528
#> Iter: 2 fn: 607.7049  Pars:  0.36701 0.24722 0.38577 0.21528
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6488  Pars:  0.33658 0.34214 0.32129 0.28099
#> Iter: 2 fn: 605.6488  Pars:  0.33657 0.34214 0.32129 0.28099
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3719  Pars:  0.39620 0.25826 0.34554 0.31852
#> Iter: 2 fn: 614.3719  Pars:  0.39620 0.25826 0.34554 0.31852
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.5603  Pars:  0.40519 0.27600 0.31881 0.31884
#> Iter: 2 fn: 621.5603  Pars:  0.40519 0.27600 0.31881 0.31884
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.3621  Pars:  0.32916 0.28251 0.38833 0.22835
#> Iter: 2 fn: 597.3621  Pars:  0.32916 0.28251 0.38833 0.22835
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.3405  Pars:  0.30638 0.29106 0.40255 0.21667
#> Iter: 2 fn: 588.3405  Pars:  0.30638 0.29106 0.40255 0.21667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7716  Pars:  0.36089 0.26733 0.37179 0.25185
#> Iter: 2 fn: 607.7716  Pars:  0.36089 0.26733 0.37178 0.25185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.9234  Pars:  0.38409 0.31023 0.30568 0.32308
#> Iter: 2 fn: 616.9234  Pars:  0.38409 0.31023 0.30568 0.32308
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.2784  Pars:  0.33602 0.31485 0.34913 0.24409
#> Iter: 2 fn: 605.2784  Pars:  0.33602 0.31485 0.34913 0.24409
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.0680  Pars:  0.34341 0.30219 0.35440 0.27200
#> Iter: 2 fn: 604.0680  Pars:  0.34341 0.30220 0.35440 0.27200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.6212  Pars:  0.37911 0.27852 0.34237 0.22449
#> Iter: 2 fn: 618.6212  Pars:  0.37911 0.27853 0.34237 0.22449
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.5284  Pars:  0.31508 0.29046 0.39446 0.18750
#> Iter: 2 fn: 593.5284  Pars:  0.31508 0.29046 0.39446 0.18750
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.5772  Pars:  0.36331 0.26865 0.36804 0.21831
#> Iter: 2 fn: 610.5772  Pars:  0.36332 0.26865 0.36804 0.21831
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8433  Pars:  0.32875 0.29638 0.37487 0.19697
#> Iter: 2 fn: 600.8433  Pars:  0.32875 0.29638 0.37487 0.19697
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.2964  Pars:  0.31438 0.31438 0.37125 0.19841
#> Iter: 2 fn: 597.2964  Pars:  0.31438 0.31438 0.37125 0.19841
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.7469  Pars:  0.33076 0.32533 0.34391 0.26230
#> Iter: 2 fn: 602.7469  Pars:  0.33076 0.32533 0.34391 0.26230
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.5190  Pars:  0.30941 0.29951 0.39109 0.19200
#> Iter: 2 fn: 592.5190  Pars:  0.30941 0.29950 0.39109 0.19200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4462  Pars:  0.34860 0.36588 0.28552 0.30579
#> Iter: 2 fn: 610.4462  Pars:  0.34860 0.36588 0.28552 0.30578
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.8763  Pars:  0.33602 0.31221 0.35177 0.24409
#> Iter: 2 fn: 604.8763  Pars:  0.33602 0.31221 0.35177 0.24409
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.7921  Pars:  0.36445 0.31922 0.31633 0.24818
#> Iter: 2 fn: 617.7921  Pars:  0.36445 0.31922 0.31633 0.24818
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.2520  Pars:  0.35388 0.34078 0.30534 0.23704
#> Iter: 2 fn: 616.2520  Pars:  0.35388 0.34078 0.30534 0.23704
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.4761  Pars:  0.33649 0.31337 0.35014 0.22138
#> Iter: 2 fn: 606.4761  Pars:  0.33649 0.31337 0.35014 0.22137
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.1324  Pars:  0.34493 0.32876 0.32632 0.25781
#> Iter: 2 fn: 610.1324  Pars:  0.34493 0.32876 0.32632 0.25781
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.2334  Pars:  0.36472 0.31810 0.31718 0.27068
#> Iter: 2 fn: 616.2334  Pars:  0.36472 0.31810 0.31718 0.27068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1324  Pars:  0.33465 0.30376 0.36158 0.22308
#> Iter: 2 fn: 604.1324  Pars:  0.33465 0.30376 0.36158 0.22308
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.6788  Pars:  0.34380 0.31758 0.33862 0.31356
#> Iter: 2 fn: 600.6788  Pars:  0.34380 0.31758 0.33862 0.31356
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.8821  Pars:  0.29354 0.35848 0.34798 0.23009
#> Iter: 2 fn: 591.8821  Pars:  0.29354 0.35848 0.34798 0.23009
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1604  Pars:  0.33137 0.31863 0.35000 0.21539
#> Iter: 2 fn: 605.1604  Pars:  0.33137 0.31863 0.35000 0.21538
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.6456  Pars:  0.33099 0.29995 0.36906 0.22656
#> Iter: 2 fn: 601.6456  Pars:  0.33099 0.29996 0.36905 0.22656
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.2614  Pars:  0.30762 0.32339 0.36899 0.23931
#> Iter: 2 fn: 593.2614  Pars:  0.30762 0.32339 0.36899 0.23932
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.9809  Pars:  0.36739 0.28544 0.34717 0.29231
#> Iter: 2 fn: 609.9809  Pars:  0.36739 0.28543 0.34717 0.29231
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.5950  Pars:  0.33465 0.26515 0.40020 0.22306
#> Iter: 2 fn: 596.5950  Pars:  0.33465 0.26515 0.40020 0.22308
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.4460  Pars:  0.37692 0.26654 0.35654 0.25714
#> Iter: 2 fn: 614.4460  Pars:  0.37692 0.26654 0.35654 0.25714
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.1644  Pars:  0.39368 0.25966 0.34666 0.28368
#> Iter: 2 fn: 618.1644  Pars:  0.39368 0.25966 0.34665 0.28369
#> solnp--> Completed in 2 iterations

summary_stats <- summarize_learning_comparison(comparison)
knitr::kable(summary_stats, digits = 3,
             caption = "LCA vs. Cross-Sectional Learning Recovery")
LCA vs. Cross-Sectional Learning Recovery
metric mean sd
cor_lca 0.999 0.002
cor_cs 0.756 0.018
lca_advantage 0.243 0.018

Effect of Gamma (Guessing Rate)

The LCA advantage should be largest when gamma is high (more guessing to filter out):

set.seed(789)

gammas <- c(0.15, 0.25, 0.35)
results_by_gamma <- data.frame()

for (g in gammas) {
  res <- compare_learning_recovery(
    n = 500, n_items = 5, gk = 0.30, gamma = g,
    n_sims = 30, seed = NULL
  )
  res$gamma <- g
  results_by_gamma <- rbind(results_by_gamma, res)
}
#> 
#> Iter: 1 fn: 607.5939  Pars:  0.34381 0.32497 0.33123 0.15069
#> Iter: 2 fn: 607.5939  Pars:  0.34381 0.32497 0.33123 0.15068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.9197  Pars:  0.34484 0.32896 0.32621 0.11842
#> Iter: 2 fn: 602.9197  Pars:  0.34484 0.32896 0.32621 0.11842
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.6032  Pars:  0.37260 0.28770 0.33970 0.15190
#> Iter: 2 fn: 612.6032  Pars:  0.37260 0.28770 0.33970 0.15190
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.5160  Pars:  0.33333 0.34000 0.32667 0.10000
#> Iter: 2 fn: 596.5160  Pars:  0.33333 0.34000 0.32667 0.10000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.6275  Pars:  0.34944 0.33508 0.31548 0.16438
#> Iter: 2 fn: 611.6275  Pars:  0.34944 0.33508 0.31548 0.16438
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.2166  Pars:  0.30769 0.32790 0.36441 0.10949
#> Iter: 2 fn: 590.2166  Pars:  0.30769 0.32790 0.36441 0.10949
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.0281  Pars:  0.30124 0.31909 0.37967 0.10371
#> Iter: 2 fn: 586.0281  Pars:  0.30124 0.31909 0.37967 0.10370
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.0203  Pars:  0.32327 0.31639 0.36034 0.12766
#> Iter: 2 fn: 597.0203  Pars:  0.32327 0.31639 0.36034 0.12766
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.9958  Pars:  0.32202 0.31043 0.36755 0.13669
#> Iter: 2 fn: 596.9958  Pars:  0.32202 0.31043 0.36755 0.13669
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.6007  Pars:  0.31502 0.33618 0.34881 0.14925
#> Iter: 2 fn: 598.6007  Pars:  0.31502 0.33618 0.34881 0.14925
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.4037  Pars:  0.33896 0.30726 0.35377 0.17986
#> Iter: 2 fn: 606.4037  Pars:  0.33896 0.30726 0.35377 0.17986
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.7883  Pars:  0.34278 0.31603 0.34119 0.17730
#> Iter: 2 fn: 608.7883  Pars:  0.34278 0.31603 0.34119 0.17730
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8156  Pars:  0.32941 0.30824 0.36235 0.15000
#> Iter: 2 fn: 600.8156  Pars:  0.32941 0.30824 0.36235 0.15000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.0143  Pars:  0.32400 0.29025 0.38575 0.11111
#> Iter: 2 fn: 591.0143  Pars:  0.32400 0.29025 0.38575 0.11111
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3477  Pars:  0.35451 0.31625 0.32923 0.21583
#> Iter: 2 fn: 614.3477  Pars:  0.35451 0.31626 0.32923 0.21583
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.7863  Pars:  0.35825 0.29200 0.34975 0.18493
#> Iter: 2 fn: 611.7863  Pars:  0.35825 0.29200 0.34975 0.18493
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5185  Pars:  0.36585 0.26342 0.37073 0.18000
#> Iter: 2 fn: 609.5185  Pars:  0.36585 0.26341 0.37073 0.18000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5138  Pars:  0.38119 0.27938 0.33943 0.15528
#> Iter: 2 fn: 614.5138  Pars:  0.38119 0.27938 0.33943 0.15528
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0034  Pars:  0.35522 0.27416 0.37062 0.16107
#> Iter: 2 fn: 606.0034  Pars:  0.35522 0.27416 0.37062 0.16107
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.0175  Pars:  0.37265 0.27948 0.34787 0.18421
#> Iter: 2 fn: 615.0175  Pars:  0.37265 0.27948 0.34787 0.18421
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.5011  Pars:  0.43702 0.22342 0.33956 0.18539
#> Iter: 2 fn: 625.5011  Pars:  0.43702 0.22342 0.33956 0.18539
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.6232  Pars:  0.37185 0.25384 0.37431 0.10180
#> Iter: 2 fn: 596.6232  Pars:  0.37185 0.25384 0.37431 0.10180
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.4350  Pars:  0.36508 0.28119 0.35373 0.11802
#> Iter: 2 fn: 603.4350  Pars:  0.36508 0.28118 0.35373 0.11801
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.9351  Pars:  0.37435 0.24434 0.38131 0.10778
#> Iter: 2 fn: 596.9351  Pars:  0.37435 0.24434 0.38132 0.10778
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.9617  Pars:  0.40067 0.27453 0.32479 0.19136
#> Iter: 2 fn: 623.9617  Pars:  0.40067 0.27453 0.32479 0.19136
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.5533  Pars:  0.36486 0.23455 0.40058 0.15584
#> Iter: 2 fn: 600.5533  Pars:  0.36486 0.23455 0.40058 0.15584
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1268  Pars:  0.33569 0.27361 0.39071 0.13014
#> Iter: 2 fn: 595.1268  Pars:  0.33569 0.27361 0.39071 0.13014
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.5253  Pars:  0.35714 0.27381 0.36905 0.16000
#> Iter: 2 fn: 606.5253  Pars:  0.35714 0.27381 0.36905 0.16000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.7878  Pars:  0.33800 0.29073 0.37127 0.15385
#> Iter: 2 fn: 601.7878  Pars:  0.33800 0.29073 0.37127 0.15385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.9615  Pars:  0.32736 0.29848 0.37416 0.16912
#> Iter: 2 fn: 599.9615  Pars:  0.32736 0.29848 0.37416 0.16912
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.0096  Pars:  0.30764 0.29607 0.39630 0.13534
#> Iter: 2 fn: 589.0096  Pars:  0.30763 0.29607 0.39630 0.13534
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.5624  Pars:  0.31009 0.31248 0.37743 0.16154
#> Iter: 2 fn: 594.5624  Pars:  0.31009 0.31248 0.37743 0.16154
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.3961  Pars:  0.31228 0.30762 0.38010 0.14179
#> Iter: 2 fn: 593.3961  Pars:  0.31228 0.30762 0.38010 0.14179
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.9767  Pars:  0.31502 0.28916 0.39583 0.14925
#> Iter: 2 fn: 591.9767  Pars:  0.31502 0.28916 0.39582 0.14925
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.5611  Pars:  0.33818 0.30115 0.36067 0.18978
#> Iter: 2 fn: 605.5611  Pars:  0.33818 0.30115 0.36067 0.18978
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.5181  Pars:  0.31308 0.31309 0.37383 0.09929
#> Iter: 2 fn: 588.5181  Pars:  0.31309 0.31309 0.37383 0.09929
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.3988  Pars:  0.32006 0.30654 0.37339 0.11268
#> Iter: 2 fn: 592.3988  Pars:  0.32006 0.30654 0.37340 0.11268
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.7382  Pars:  0.35156 0.29063 0.35781 0.14667
#> Iter: 2 fn: 605.7382  Pars:  0.35156 0.29063 0.35781 0.14667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.3576  Pars:  0.36000 0.28080 0.35920 0.16667
#> Iter: 2 fn: 609.3576  Pars:  0.36000 0.28080 0.35920 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.4790  Pars:  0.32667 0.31967 0.35367 0.14286
#> Iter: 2 fn: 600.4790  Pars:  0.32667 0.31967 0.35367 0.14286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.6397  Pars:  0.36696 0.27583 0.35721 0.18792
#> Iter: 2 fn: 612.6397  Pars:  0.36696 0.27583 0.35721 0.18792
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.7274  Pars:  0.37454 0.24725 0.37821 0.18301
#> Iter: 2 fn: 609.7274  Pars:  0.37454 0.24725 0.37821 0.18301
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8273  Pars:  0.36679 0.26031 0.37290 0.15484
#> Iter: 2 fn: 606.8273  Pars:  0.36679 0.26031 0.37290 0.15484
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.3321  Pars:  0.36322 0.25845 0.37833 0.14103
#> Iter: 2 fn: 603.3321  Pars:  0.36322 0.25845 0.37833 0.14103
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2539  Pars:  0.33441 0.28470 0.38089 0.11486
#> Iter: 2 fn: 594.2539  Pars:  0.33441 0.28470 0.38089 0.11486
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.2466  Pars:  0.32991 0.25809 0.41200 0.10884
#> Iter: 2 fn: 586.2466  Pars:  0.32991 0.25809 0.41200 0.10884
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.9913  Pars:  0.37688 0.24959 0.37354 0.19868
#> Iter: 2 fn: 611.9913  Pars:  0.37688 0.24959 0.37354 0.19868
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.1831  Pars:  0.34087 0.28243 0.37670 0.17857
#> Iter: 2 fn: 603.1831  Pars:  0.34087 0.28243 0.37670 0.17857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6757  Pars:  0.35527 0.26523 0.37950 0.17808
#> Iter: 2 fn: 605.6757  Pars:  0.35527 0.26523 0.37950 0.17808
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 580.9911  Pars:  0.29588 0.29136 0.41276 0.11450
#> Iter: 2 fn: 580.9911  Pars:  0.29588 0.29136 0.41276 0.11450
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.8010  Pars:  0.36053 0.27733 0.36213 0.13462
#> Iter: 2 fn: 604.8010  Pars:  0.36053 0.27733 0.36213 0.13462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.8791  Pars:  0.35508 0.27568 0.36923 0.09317
#> Iter: 2 fn: 593.8791  Pars:  0.35508 0.27568 0.36923 0.09317
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3261  Pars:  0.35240 0.29327 0.35433 0.15436
#> Iter: 2 fn: 607.3261  Pars:  0.35240 0.29327 0.35433 0.15436
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.7865  Pars:  0.36769 0.30800 0.32431 0.16234
#> Iter: 2 fn: 614.7865  Pars:  0.36769 0.30800 0.32431 0.16234
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.2006  Pars:  0.33441 0.31408 0.35151 0.11487
#> Iter: 2 fn: 598.2006  Pars:  0.33441 0.31408 0.35151 0.11486
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.0378  Pars:  0.33640 0.30160 0.36200 0.13793
#> Iter: 2 fn: 601.0378  Pars:  0.33640 0.30160 0.36200 0.13793
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.3227  Pars:  0.35522 0.28846 0.35632 0.16107
#> Iter: 2 fn: 608.3227  Pars:  0.35522 0.28846 0.35632 0.16107
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.9150  Pars:  0.33441 0.30278 0.36281 0.11486
#> Iter: 2 fn: 596.9150  Pars:  0.33441 0.30278 0.36281 0.11486
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.0210  Pars:  0.35820 0.29457 0.34722 0.15132
#> Iter: 2 fn: 609.0210  Pars:  0.35820 0.29457 0.34722 0.15132
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.2992  Pars:  0.37248 0.29318 0.33434 0.16774
#> Iter: 2 fn: 615.2992  Pars:  0.37248 0.29318 0.33434 0.16774
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.7079  Pars:  0.37841 0.29615 0.32545 0.14907
#> Iter: 2 fn: 614.7079  Pars:  0.37841 0.29615 0.32545 0.14907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.7723  Pars:  0.36053 0.29120 0.34827 0.13462
#> Iter: 2 fn: 606.7723  Pars:  0.36053 0.29120 0.34827 0.13462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.6217  Pars:  0.36208 0.31035 0.32757 0.14935
#> Iter: 2 fn: 611.6217  Pars:  0.36208 0.31035 0.32757 0.14935
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.5238  Pars:  0.38113 0.30635 0.31252 0.17089
#> Iter: 2 fn: 619.5238  Pars:  0.38113 0.30635 0.31252 0.17089
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.9335  Pars:  0.33993 0.34466 0.31541 0.15278
#> Iter: 2 fn: 607.9335  Pars:  0.33993 0.34466 0.31541 0.15278
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.0913  Pars:  0.32203 0.34005 0.33792 0.11189
#> Iter: 2 fn: 596.0913  Pars:  0.32203 0.34005 0.33792 0.11189
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1313  Pars:  0.35331 0.31684 0.32985 0.12258
#> Iter: 2 fn: 605.1313  Pars:  0.35331 0.31684 0.32985 0.12258
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6037  Pars:  0.33413 0.33176 0.33410 0.15603
#> Iter: 2 fn: 605.6037  Pars:  0.33413 0.33176 0.33410 0.15603
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5594  Pars:  0.35616 0.34413 0.29971 0.16892
#> Iter: 2 fn: 614.5593  Pars:  0.35616 0.34413 0.29971 0.16892
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.2681  Pars:  0.32642 0.36216 0.31143 0.16058
#> Iter: 2 fn: 605.2681  Pars:  0.32642 0.36216 0.31143 0.16058
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.9439  Pars:  0.35446 0.32000 0.32554 0.18750
#> Iter: 2 fn: 613.9439  Pars:  0.35446 0.32000 0.32554 0.18750
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.3457  Pars:  0.32597 0.31923 0.35480 0.11034
#> Iter: 2 fn: 595.3457  Pars:  0.32597 0.31922 0.35481 0.11034
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.9390  Pars:  0.32914 0.32000 0.35086 0.12500
#> Iter: 2 fn: 598.9389  Pars:  0.32914 0.32000 0.35086 0.12500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.0284  Pars:  0.35046 0.28179 0.36774 0.15541
#> Iter: 2 fn: 605.0284  Pars:  0.35046 0.28179 0.36774 0.15541
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.4024  Pars:  0.33413 0.32940 0.33647 0.15603
#> Iter: 2 fn: 605.4024  Pars:  0.33413 0.32939 0.33647 0.15603
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8469  Pars:  0.35663 0.29874 0.34463 0.13636
#> Iter: 2 fn: 606.8469  Pars:  0.35663 0.29874 0.34463 0.13636
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.7542  Pars:  0.36100 0.31350 0.32550 0.15789
#> Iter: 2 fn: 612.7542  Pars:  0.36100 0.31350 0.32550 0.15789
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.7812  Pars:  0.34381 0.29906 0.35713 0.15069
#> Iter: 2 fn: 604.7812  Pars:  0.34381 0.29906 0.35713 0.15069
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.4491  Pars:  0.35933 0.33600 0.30467 0.14286
#> Iter: 2 fn: 611.4491  Pars:  0.35933 0.33600 0.30467 0.14286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.3564  Pars:  0.33638 0.33864 0.32498 0.11410
#> Iter: 2 fn: 600.3564  Pars:  0.33638 0.33864 0.32498 0.11409
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.1620  Pars:  0.34768 0.31010 0.34222 0.14865
#> Iter: 2 fn: 607.1620  Pars:  0.34768 0.31010 0.34222 0.14865
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.2571  Pars:  0.35425 0.29882 0.34693 0.17007
#> Iter: 2 fn: 610.2571  Pars:  0.35425 0.29882 0.34693 0.17007
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.7466  Pars:  0.32991 0.32542 0.34467 0.10884
#> Iter: 2 fn: 596.7466  Pars:  0.32991 0.32542 0.34467 0.10884
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.0618  Pars:  0.33088 0.29338 0.37574 0.09333
#> Iter: 2 fn: 590.0618  Pars:  0.33088 0.29338 0.37574 0.09333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.2708  Pars:  0.35788 0.27988 0.36224 0.12821
#> Iter: 2 fn: 603.2708  Pars:  0.35788 0.27988 0.36224 0.12821
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.8527  Pars:  0.39264 0.25139 0.35597 0.16463
#> Iter: 2 fn: 614.8527  Pars:  0.39264 0.25139 0.35597 0.16463
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.6479  Pars:  0.35240 0.29564 0.35197 0.15436
#> Iter: 2 fn: 607.6479  Pars:  0.35240 0.29564 0.35197 0.15436
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.9210  Pars:  0.39006 0.29378 0.31616 0.18987
#> Iter: 2 fn: 622.9210  Pars:  0.39006 0.29378 0.31616 0.18987
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.5302  Pars:  0.37154 0.28104 0.34742 0.16026
#> Iter: 2 fn: 612.5302  Pars:  0.37154 0.28104 0.34742 0.16026
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.9137  Pars:  0.37190 0.30744 0.32066 0.19333
#> Iter: 2 fn: 618.9137  Pars:  0.37190 0.30744 0.32066 0.19333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.3985  Pars:  0.31890 0.28372 0.39738 0.14706
#> Iter: 2 fn: 592.3985  Pars:  0.31890 0.28372 0.39738 0.14706
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.2819  Pars:  0.36000 0.24480 0.39520 0.16667
#> Iter: 2 fn: 602.2819  Pars:  0.36000 0.24480 0.39520 0.16667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1703  Pars:  0.35527 0.25793 0.38680 0.17808
#> Iter: 2 fn: 604.1703  Pars:  0.35527 0.25793 0.38680 0.17808
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.5649  Pars:  0.31557 0.28648 0.39795 0.10638
#> Iter: 2 fn: 586.5649  Pars:  0.31557 0.28648 0.39795 0.10638
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.0725  Pars:  0.32132 0.25475 0.42393 0.12858
#> Iter: 2 fn: 585.0725  Pars:  0.32131 0.25475 0.42393 0.12857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.9380  Pars:  0.30727 0.33563 0.35709 0.15385
#> Iter: 2 fn: 595.9380  Pars:  0.30727 0.33564 0.35709 0.15385
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.9371  Pars:  0.28545 0.33651 0.37804 0.13821
#> Iter: 2 fn: 585.9371  Pars:  0.28545 0.33651 0.37804 0.13821
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.9451  Pars:  0.30638 0.35784 0.33579 0.18400
#> Iter: 2 fn: 598.9451  Pars:  0.30637 0.35784 0.33578 0.18400
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.6415  Pars:  0.30531 0.33196 0.36273 0.17460
#> Iter: 2 fn: 595.6415  Pars:  0.30531 0.33196 0.36273 0.17460
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.3787  Pars:  0.30062 0.33116 0.36822 0.14844
#> Iter: 2 fn: 592.3787  Pars:  0.30062 0.33116 0.36822 0.14844
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.9395  Pars:  0.34547 0.32030 0.33423 0.12583
#> Iter: 2 fn: 603.9395  Pars:  0.34547 0.32030 0.33423 0.12583
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6007  Pars:  0.35527 0.31883 0.32590 0.12179
#> Iter: 2 fn: 605.6007  Pars:  0.35527 0.31883 0.32590 0.12179
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.1273  Pars:  0.39084 0.30290 0.30626 0.18125
#> Iter: 2 fn: 623.1273  Pars:  0.39084 0.30290 0.30626 0.18125
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.9491  Pars:  0.35397 0.30800 0.33803 0.12987
#> Iter: 2 fn: 605.9491  Pars:  0.35397 0.30800 0.33803 0.12987
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.4324  Pars:  0.35627 0.31144 0.33230 0.15232
#> Iter: 2 fn: 610.4324  Pars:  0.35627 0.31144 0.33230 0.15232
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.2046  Pars:  0.33698 0.30511 0.35791 0.12162
#> Iter: 2 fn: 599.2046  Pars:  0.33698 0.30511 0.35791 0.12162
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4319  Pars:  0.32788 0.33940 0.33272 0.13380
#> Iter: 2 fn: 601.4319  Pars:  0.32787 0.33941 0.33272 0.13380
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.9484  Pars:  0.38025 0.28519 0.33456 0.17949
#> Iter: 2 fn: 617.9484  Pars:  0.38025 0.28519 0.33456 0.17949
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.2170  Pars:  0.34087 0.31652 0.34261 0.17857
#> Iter: 2 fn: 608.2170  Pars:  0.34087 0.31652 0.34261 0.17857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.6395  Pars:  0.33640 0.30624 0.35736 0.13793
#> Iter: 2 fn: 601.6395  Pars:  0.33640 0.30624 0.35736 0.13793
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4820  Pars:  0.31617 0.32082 0.36301 0.13970
#> Iter: 2 fn: 596.4820  Pars:  0.31617 0.32082 0.36301 0.13971
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.7899  Pars:  0.32007 0.33166 0.34827 0.13768
#> Iter: 2 fn: 598.7899  Pars:  0.32007 0.33166 0.34827 0.13768
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.3804  Pars:  0.33896 0.34872 0.31232 0.17986
#> Iter: 2 fn: 610.3804  Pars:  0.33896 0.34872 0.31232 0.17986
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.1198  Pars:  0.34381 0.29435 0.36184 0.15068
#> Iter: 2 fn: 604.1198  Pars:  0.34381 0.29435 0.36184 0.15068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.4523  Pars:  0.36205 0.30334 0.33461 0.18243
#> Iter: 2 fn: 614.4523  Pars:  0.36205 0.30334 0.33461 0.18243
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.6803  Pars:  0.31613 0.28452 0.39935 0.11429
#> Iter: 2 fn: 587.6803  Pars:  0.31613 0.28452 0.39935 0.11429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.8993  Pars:  0.32861 0.30997 0.36142 0.14184
#> Iter: 2 fn: 599.8993  Pars:  0.32861 0.30997 0.36142 0.14184
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.0913  Pars:  0.32982 0.30906 0.36111 0.13287
#> Iter: 2 fn: 599.0913  Pars:  0.32982 0.30906 0.36111 0.13287
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5825  Pars:  0.36384 0.27528 0.36088 0.16447
#> Iter: 2 fn: 609.5825  Pars:  0.36384 0.27528 0.36088 0.16447
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3645  Pars:  0.34576 0.29426 0.35998 0.18440
#> Iter: 2 fn: 607.3645  Pars:  0.34576 0.29426 0.35998 0.18440
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.5858  Pars:  0.34574 0.30106 0.35320 0.14966
#> Iter: 2 fn: 605.5858  Pars:  0.34574 0.30106 0.35320 0.14966
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.3330  Pars:  0.36015 0.29890 0.34095 0.18367
#> Iter: 2 fn: 613.3330  Pars:  0.36015 0.29890 0.34095 0.18367
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3607  Pars:  0.35336 0.27781 0.36882 0.17931
#> Iter: 2 fn: 607.3607  Pars:  0.35336 0.27782 0.36882 0.17931
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.7398  Pars:  0.31613 0.30258 0.38129 0.11429
#> Iter: 2 fn: 590.7398  Pars:  0.31613 0.30258 0.38129 0.11429
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.7927  Pars:  0.32007 0.30615 0.37378 0.13768
#> Iter: 2 fn: 595.7927  Pars:  0.32007 0.30615 0.37378 0.13768
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.4221  Pars:  0.35078 0.30665 0.34257 0.13907
#> Iter: 2 fn: 606.4221  Pars:  0.35078 0.30665 0.34257 0.13907
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.7421  Pars:  0.40445 0.27374 0.32180 0.18902
#> Iter: 2 fn: 624.7421  Pars:  0.40445 0.27374 0.32180 0.18902
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.8606  Pars:  0.37688 0.27758 0.34554 0.11377
#> Iter: 2 fn: 604.8606  Pars:  0.37688 0.27758 0.34554 0.11377
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.0631  Pars:  0.36790 0.30228 0.32982 0.14650
#> Iter: 2 fn: 612.0631  Pars:  0.36790 0.30228 0.32982 0.14650
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.1197  Pars:  0.35808 0.30521 0.33671 0.16779
#> Iter: 2 fn: 612.1197  Pars:  0.35808 0.30521 0.33671 0.16779
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.3304  Pars:  0.36639 0.25578 0.37783 0.13208
#> Iter: 2 fn: 602.3304  Pars:  0.36639 0.25578 0.37783 0.13208
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.4505  Pars:  0.35329 0.30077 0.34594 0.16216
#> Iter: 2 fn: 609.4505  Pars:  0.35329 0.30077 0.34594 0.16216
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.0524  Pars:  0.34811 0.30200 0.34989 0.13245
#> Iter: 2 fn: 604.0524  Pars:  0.34811 0.30200 0.34989 0.13245
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1014  Pars:  0.32655 0.30387 0.36957 0.11806
#> Iter: 2 fn: 595.1014  Pars:  0.32655 0.30387 0.36957 0.11806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0888  Pars:  0.36790 0.27182 0.36028 0.14650
#> Iter: 2 fn: 608.0888  Pars:  0.36790 0.27182 0.36028 0.14650
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.4858  Pars:  0.35908 0.27902 0.36190 0.17568
#> Iter: 2 fn: 609.4858  Pars:  0.35908 0.27902 0.36190 0.17568
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.3873  Pars:  0.32262 0.28173 0.39565 0.11972
#> Iter: 2 fn: 590.3873  Pars:  0.32262 0.28173 0.39565 0.11972
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.7652  Pars:  0.31812 0.29721 0.38466 0.13869
#> Iter: 2 fn: 593.7652  Pars:  0.31812 0.29722 0.38466 0.13869
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.5795  Pars:  0.32257 0.28673 0.39071 0.16296
#> Iter: 2 fn: 595.5795  Pars:  0.32257 0.28673 0.39071 0.16296
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5072  Pars:  0.35616 0.27675 0.36709 0.16892
#> Iter: 2 fn: 607.5072  Pars:  0.35616 0.27675 0.36709 0.16892
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.0447  Pars:  0.31815 0.29636 0.38549 0.08219
#> Iter: 2 fn: 584.0447  Pars:  0.31815 0.29636 0.38549 0.08219
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.5311  Pars:  0.36100 0.27313 0.36587 0.15789
#> Iter: 2 fn: 607.5311  Pars:  0.36100 0.27312 0.36588 0.15789
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.5817  Pars:  0.33411 0.30989 0.35600 0.17391
#> Iter: 2 fn: 604.5817  Pars:  0.33411 0.30989 0.35600 0.17391
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8221  Pars:  0.33889 0.27923 0.38188 0.16197
#> Iter: 2 fn: 600.8221  Pars:  0.33889 0.27923 0.38188 0.16197
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.1309  Pars:  0.33373 0.27159 0.39468 0.13103
#> Iter: 2 fn: 594.1309  Pars:  0.33373 0.27159 0.39468 0.13103
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.1180  Pars:  0.33835 0.30590 0.35575 0.13699
#> Iter: 2 fn: 602.1180  Pars:  0.33835 0.30590 0.35575 0.13699
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.3952  Pars:  0.35446 0.32492 0.32062 0.18750
#> Iter: 2 fn: 614.3952  Pars:  0.35446 0.32492 0.32062 0.18750
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.8330  Pars:  0.32741 0.30736 0.36523 0.10204
#> Iter: 2 fn: 592.8330  Pars:  0.32741 0.30736 0.36523 0.10204
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.3851  Pars:  0.33895 0.31165 0.34940 0.12081
#> Iter: 2 fn: 600.3851  Pars:  0.33895 0.31165 0.34940 0.12081
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.9462  Pars:  0.36208 0.28684 0.35108 0.14935
#> Iter: 2 fn: 608.9462  Pars:  0.36208 0.28684 0.35108 0.14935
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 625.3407  Pars:  0.39762 0.29892 0.30346 0.29078
#> Iter: 2 fn: 625.3407  Pars:  0.39762 0.29892 0.30346 0.29078
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.5300  Pars:  0.38407 0.27359 0.34234 0.23973
#> Iter: 2 fn: 619.5300  Pars:  0.38407 0.27359 0.34234 0.23973
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.4257  Pars:  0.36979 0.29476 0.33546 0.25362
#> Iter: 2 fn: 616.4257  Pars:  0.36979 0.29476 0.33546 0.25362
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.9488  Pars:  0.32009 0.33321 0.34671 0.23771
#> Iter: 2 fn: 600.9488  Pars:  0.32009 0.33320 0.34671 0.23770
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.2073  Pars:  0.37471 0.32929 0.29600 0.29545
#> Iter: 2 fn: 619.2073  Pars:  0.37471 0.32929 0.29600 0.29545
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.4120  Pars:  0.31823 0.32358 0.35820 0.25210
#> Iter: 2 fn: 597.4120  Pars:  0.31822 0.32357 0.35820 0.25210
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.4736  Pars:  0.30762 0.30236 0.39002 0.23932
#> Iter: 2 fn: 589.4736  Pars:  0.30762 0.30236 0.39002 0.23932
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.6612  Pars:  0.36245 0.29681 0.34074 0.29921
#> Iter: 2 fn: 608.6612  Pars:  0.36245 0.29681 0.34074 0.29921
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.3615  Pars:  0.35234 0.29178 0.35587 0.27344
#> Iter: 2 fn: 606.3615  Pars:  0.35234 0.29178 0.35587 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.2104  Pars:  0.33827 0.29946 0.36227 0.27869
#> Iter: 2 fn: 600.2104  Pars:  0.33827 0.29945 0.36227 0.27869
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.2508  Pars:  0.33064 0.28837 0.38099 0.19549
#> Iter: 2 fn: 600.2508  Pars:  0.33064 0.28837 0.38099 0.19549
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.8198  Pars:  0.39194 0.27000 0.33806 0.31111
#> Iter: 2 fn: 615.8198  Pars:  0.39194 0.27000 0.33806 0.31111
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.3363  Pars:  0.36662 0.26593 0.36745 0.22535
#> Iter: 2 fn: 611.3363  Pars:  0.36662 0.26593 0.36745 0.22535
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.0552  Pars:  0.35579 0.31474 0.32947 0.26924
#> Iter: 2 fn: 612.0552  Pars:  0.35579 0.31474 0.32947 0.26923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.0830  Pars:  0.35735 0.30899 0.33366 0.25564
#> Iter: 2 fn: 613.0830  Pars:  0.35735 0.30899 0.33366 0.25564
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.8979  Pars:  0.39032 0.28642 0.32325 0.28777
#> Iter: 2 fn: 620.8979  Pars:  0.39032 0.28642 0.32325 0.28777
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.6058  Pars:  0.35208 0.29427 0.35365 0.23881
#> Iter: 2 fn: 609.6058  Pars:  0.35208 0.29427 0.35365 0.23881
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.1047  Pars:  0.33137 0.29314 0.37549 0.21538
#> Iter: 2 fn: 601.1047  Pars:  0.33137 0.29314 0.37549 0.21538
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.8902  Pars:  0.37341 0.27329 0.35329 0.26087
#> Iter: 2 fn: 613.8902  Pars:  0.37341 0.27329 0.35329 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.0284  Pars:  0.35046 0.28179 0.36774 0.15541
#> Iter: 2 fn: 605.0284  Pars:  0.35046 0.28179 0.36774 0.15541
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.2232  Pars:  0.36472 0.32633 0.30895 0.27068
#> Iter: 2 fn: 617.2232  Pars:  0.36472 0.32633 0.30895 0.27068
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.5608  Pars:  0.37161 0.32680 0.30159 0.24113
#> Iter: 2 fn: 621.5608  Pars:  0.37161 0.32680 0.30159 0.24113
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.1495  Pars:  0.32568 0.31335 0.36097 0.18939
#> Iter: 2 fn: 602.1495  Pars:  0.32568 0.31335 0.36097 0.18939
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.5951  Pars:  0.31703 0.35027 0.33270 0.21774
#> Iter: 2 fn: 602.5951  Pars:  0.31703 0.35027 0.33270 0.21774
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.7539  Pars:  0.40048 0.25410 0.34543 0.27586
#> Iter: 2 fn: 620.7539  Pars:  0.40048 0.25410 0.34543 0.27586
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7572  Pars:  0.36007 0.26118 0.37875 0.21127
#> Iter: 2 fn: 607.7572  Pars:  0.36007 0.26118 0.37875 0.21127
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.0147  Pars:  0.37306 0.30472 0.32222 0.29772
#> Iter: 2 fn: 615.0147  Pars:  0.37307 0.30472 0.32222 0.29771
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.8652  Pars:  0.36114 0.30138 0.33748 0.23022
#> Iter: 2 fn: 614.8652  Pars:  0.36114 0.30138 0.33748 0.23022
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1961  Pars:  0.33322 0.31288 0.35390 0.21375
#> Iter: 2 fn: 605.1961  Pars:  0.33322 0.31287 0.35390 0.21374
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.6668  Pars:  0.36516 0.27579 0.35905 0.21678
#> Iter: 2 fn: 612.6668  Pars:  0.36516 0.27579 0.35905 0.21678
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.5060  Pars:  0.33618 0.33358 0.33024 0.23256
#> Iter: 2 fn: 608.5060  Pars:  0.33618 0.33358 0.33024 0.23256
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.2866  Pars:  0.37029 0.28543 0.34429 0.22222
#> Iter: 2 fn: 616.2866  Pars:  0.37029 0.28543 0.34429 0.22222
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0643  Pars:  0.32933 0.37360 0.29707 0.27731
#> Iter: 2 fn: 606.0643  Pars:  0.32933 0.37360 0.29707 0.27731
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.8828  Pars:  0.39124 0.29072 0.31804 0.26389
#> Iter: 2 fn: 623.8828  Pars:  0.39125 0.29072 0.31804 0.26389
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.8450  Pars:  0.36802 0.30355 0.32843 0.25547
#> Iter: 2 fn: 616.8450  Pars:  0.36802 0.30355 0.32843 0.25547
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.0066  Pars:  0.35384 0.25930 0.38687 0.25954
#> Iter: 2 fn: 602.0066  Pars:  0.35384 0.25930 0.38687 0.25954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.1321  Pars:  0.40772 0.21911 0.37317 0.27891
#> Iter: 2 fn: 616.1321  Pars:  0.40772 0.21911 0.37317 0.27891
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.4306  Pars:  0.37917 0.26016 0.36067 0.27737
#> Iter: 2 fn: 612.4306  Pars:  0.37917 0.26016 0.36067 0.27737
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.0817  Pars:  0.37869 0.26746 0.35385 0.24475
#> Iter: 2 fn: 616.0817  Pars:  0.37869 0.26746 0.35385 0.24476
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.8612  Pars:  0.39124 0.27713 0.33162 0.26389
#> Iter: 2 fn: 621.8612  Pars:  0.39125 0.27713 0.33162 0.26389
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7655  Pars:  0.35511 0.30966 0.33523 0.29600
#> Iter: 2 fn: 607.7655  Pars:  0.35511 0.30966 0.33523 0.29600
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0220  Pars:  0.36179 0.29760 0.34061 0.31451
#> Iter: 2 fn: 606.0220  Pars:  0.36179 0.29760 0.34061 0.31452
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.7001  Pars:  0.34169 0.33342 0.32489 0.27419
#> Iter: 2 fn: 607.7001  Pars:  0.34169 0.33342 0.32489 0.27419
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.6901  Pars:  0.30086 0.32657 0.37257 0.22222
#> Iter: 2 fn: 591.6901  Pars:  0.30086 0.32657 0.37257 0.22222
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8735  Pars:  0.32381 0.34302 0.33316 0.27119
#> Iter: 2 fn: 600.8735  Pars:  0.32381 0.34302 0.33316 0.27119
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8483  Pars:  0.32734 0.30656 0.36610 0.23016
#> Iter: 2 fn: 600.8483  Pars:  0.32734 0.30656 0.36610 0.23016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4113  Pars:  0.31831 0.31039 0.37130 0.23970
#> Iter: 2 fn: 596.4113  Pars:  0.31828 0.31039 0.37133 0.23967
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.6024  Pars:  0.31318 0.27619 0.41062 0.18898
#> Iter: 2 fn: 589.6024  Pars:  0.31318 0.27619 0.41062 0.18898
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.5864  Pars:  0.29759 0.33319 0.36922 0.21367
#> Iter: 2 fn: 591.5864  Pars:  0.29759 0.33320 0.36922 0.21368
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.4436  Pars:  0.36802 0.24714 0.38484 0.25547
#> Iter: 2 fn: 606.4436  Pars:  0.36802 0.24714 0.38484 0.25547
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.9526  Pars:  0.36245 0.31108 0.32647 0.29921
#> Iter: 2 fn: 610.9526  Pars:  0.36245 0.31108 0.32647 0.29921
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.3776  Pars:  0.37517 0.30229 0.32254 0.25899
#> Iter: 2 fn: 619.3776  Pars:  0.37516 0.30229 0.32254 0.25899
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.6335  Pars:  0.36089 0.29406 0.34505 0.25185
#> Iter: 2 fn: 612.6335  Pars:  0.36089 0.29406 0.34505 0.25185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.8139  Pars:  0.41891 0.25018 0.33091 0.31250
#> Iter: 2 fn: 623.8139  Pars:  0.41891 0.25018 0.33091 0.31250
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.8324  Pars:  0.38699 0.28530 0.32771 0.29197
#> Iter: 2 fn: 618.8324  Pars:  0.38699 0.28530 0.32771 0.29197
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.1506  Pars:  0.34614 0.32627 0.32759 0.29508
#> Iter: 2 fn: 606.1506  Pars:  0.34614 0.32628 0.32758 0.29508
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.6280  Pars:  0.29536 0.31092 0.39372 0.22812
#> Iter: 2 fn: 585.6280  Pars:  0.29537 0.31090 0.39373 0.22808
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.8037  Pars:  0.30823 0.30314 0.38863 0.21488
#> Iter: 2 fn: 591.8037  Pars:  0.30823 0.30314 0.38863 0.21488
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.2232  Pars:  0.35758 0.30279 0.33963 0.30645
#> Iter: 2 fn: 606.2232  Pars:  0.35758 0.30279 0.33963 0.30645
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.8748  Pars:  0.29198 0.30915 0.39887 0.18487
#> Iter: 2 fn: 585.8748  Pars:  0.29198 0.30915 0.39887 0.18487
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.6093  Pars:  0.35048 0.29596 0.35356 0.22963
#> Iter: 2 fn: 609.6093  Pars:  0.35048 0.29596 0.35356 0.22963
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.6164  Pars:  0.37702 0.25658 0.36640 0.23611
#> Iter: 2 fn: 613.6164  Pars:  0.37702 0.25658 0.36640 0.23611
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.0954  Pars:  0.34348 0.27633 0.38019 0.22556
#> Iter: 2 fn: 603.0954  Pars:  0.34348 0.27633 0.38019 0.22556
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.9573  Pars:  0.39843 0.26744 0.33413 0.26712
#> Iter: 2 fn: 622.9573  Pars:  0.39843 0.26744 0.33413 0.26712
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.8409  Pars:  0.34531 0.27057 0.38412 0.22388
#> Iter: 2 fn: 602.8409  Pars:  0.34531 0.27058 0.38412 0.22388
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.9378  Pars:  0.37156 0.29938 0.32906 0.25180
#> Iter: 2 fn: 617.9378  Pars:  0.37156 0.29938 0.32906 0.25180
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.1476  Pars:  0.40209 0.30748 0.29043 0.32353
#> Iter: 2 fn: 624.1476  Pars:  0.40209 0.30748 0.29043 0.32353
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.0549  Pars:  0.38428 0.27523 0.34049 0.22973
#> Iter: 2 fn: 620.0549  Pars:  0.38428 0.27523 0.34049 0.22973
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0468  Pars:  0.34531 0.29892 0.35577 0.22388
#> Iter: 2 fn: 608.0468  Pars:  0.34531 0.29892 0.35577 0.22388
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.9682  Pars:  0.42050 0.29000 0.28950 0.31034
#> Iter: 2 fn: 630.9682  Pars:  0.42050 0.29000 0.28950 0.31034
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.3147  Pars:  0.33251 0.36494 0.30255 0.26016
#> Iter: 2 fn: 608.3147  Pars:  0.33251 0.36495 0.30255 0.26016
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8736  Pars:  0.34066 0.38765 0.27170 0.31897
#> Iter: 2 fn: 606.8736  Pars:  0.34066 0.38765 0.27170 0.31897
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 627.2076  Pars:  0.40517 0.31712 0.27771 0.31883
#> Iter: 2 fn: 627.2076  Pars:  0.40519 0.31711 0.27770 0.31884
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.2951  Pars:  0.32357 0.35274 0.32370 0.24590
#> Iter: 2 fn: 604.2951  Pars:  0.32357 0.35274 0.32370 0.24590
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.8290  Pars:  0.30149 0.32337 0.37514 0.17742
#> Iter: 2 fn: 592.8290  Pars:  0.30149 0.32337 0.37514 0.17742
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.7094  Pars:  0.33602 0.28310 0.38088 0.24409
#> Iter: 2 fn: 599.7094  Pars:  0.33602 0.28310 0.38087 0.24409
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5844  Pars:  0.36445 0.29528 0.34027 0.24818
#> Iter: 2 fn: 614.5844  Pars:  0.36445 0.29528 0.34027 0.24818
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.4990  Pars:  0.38642 0.25576 0.35782 0.28058
#> Iter: 2 fn: 614.4990  Pars:  0.38642 0.25576 0.35782 0.28058
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.1349  Pars:  0.34511 0.33693 0.31795 0.26982
#> Iter: 2 fn: 610.1349  Pars:  0.34513 0.33691 0.31796 0.26984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 624.9112  Pars:  0.41837 0.23828 0.34336 0.27815
#> Iter: 2 fn: 624.9112  Pars:  0.41837 0.23828 0.34336 0.27815
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 631.5739  Pars:  0.44288 0.31451 0.24261 0.37681
#> Iter: 2 fn: 631.5739  Pars:  0.44288 0.31451 0.24260 0.37681
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.5681  Pars:  0.35963 0.29541 0.34495 0.22143
#> Iter: 2 fn: 613.5681  Pars:  0.35963 0.29541 0.34495 0.22143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.9221  Pars:  0.36852 0.30202 0.32946 0.27820
#> Iter: 2 fn: 614.9221  Pars:  0.36852 0.30202 0.32946 0.27820
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.2993  Pars:  0.36818 0.29182 0.34000 0.26666
#> Iter: 2 fn: 614.2993  Pars:  0.36818 0.29182 0.34000 0.26667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 615.4591  Pars:  0.36573 0.32888 0.30539 0.29457
#> Iter: 2 fn: 615.4591  Pars:  0.36574 0.32888 0.30538 0.29457
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.5429  Pars:  0.36114 0.31437 0.32449 0.23022
#> Iter: 2 fn: 616.5429  Pars:  0.36114 0.31437 0.32449 0.23022
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 628.4349  Pars:  0.40942 0.27940 0.31118 0.27703
#> Iter: 2 fn: 628.4349  Pars:  0.40942 0.27940 0.31118 0.27703
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.5478  Pars:  0.38304 0.31035 0.30661 0.28467
#> Iter: 2 fn: 621.5478  Pars:  0.38304 0.31035 0.30661 0.28467
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.6999  Pars:  0.37884 0.26710 0.35406 0.26619
#> Iter: 2 fn: 614.6999  Pars:  0.37884 0.26710 0.35406 0.26619
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.0672  Pars:  0.36978 0.25456 0.37565 0.25362
#> Iter: 2 fn: 609.0672  Pars:  0.36979 0.25456 0.37565 0.25362
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.8772  Pars:  0.36147 0.26918 0.36935 0.21986
#> Iter: 2 fn: 609.8772  Pars:  0.36147 0.26918 0.36935 0.21986
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.2707  Pars:  0.38088 0.25947 0.35966 0.27537
#> Iter: 2 fn: 613.2707  Pars:  0.38088 0.25944 0.35968 0.27536
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0516  Pars:  0.34615 0.34047 0.31339 0.29509
#> Iter: 2 fn: 608.0516  Pars:  0.34614 0.34046 0.31340 0.29508
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.7837  Pars:  0.30188 0.31685 0.38127 0.19835
#> Iter: 2 fn: 591.7837  Pars:  0.30188 0.31684 0.38128 0.19835
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.8076  Pars:  0.31814 0.30074 0.38113 0.19531
#> Iter: 2 fn: 596.8076  Pars:  0.31814 0.30074 0.38113 0.19531
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.4465  Pars:  0.31668 0.31668 0.36664 0.22951
#> Iter: 2 fn: 597.4465  Pars:  0.31668 0.31668 0.36664 0.22951
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.0077  Pars:  0.34531 0.25769 0.39700 0.22388
#> Iter: 2 fn: 600.0077  Pars:  0.34531 0.25769 0.39700 0.22388
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.6288  Pars:  0.32178 0.30050 0.37772 0.24793
#> Iter: 2 fn: 595.6288  Pars:  0.32178 0.30051 0.37771 0.24793
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.2893  Pars:  0.32712 0.32176 0.35112 0.25410
#> Iter: 2 fn: 601.2893  Pars:  0.32712 0.32176 0.35112 0.25410
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.9448  Pars:  0.36636 0.28262 0.35103 0.23571
#> Iter: 2 fn: 613.9448  Pars:  0.36636 0.28262 0.35103 0.23571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.7792  Pars:  0.29503 0.31237 0.39260 0.19329
#> Iter: 2 fn: 587.7792  Pars:  0.29502 0.31238 0.39260 0.19328
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.2591  Pars:  0.31318 0.31072 0.37610 0.18898
#> Iter: 2 fn: 596.2591  Pars:  0.31318 0.31072 0.37610 0.18898
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.0053  Pars:  0.27848 0.33276 0.38876 0.15254
#> Iter: 2 fn: 583.0053  Pars:  0.27848 0.33276 0.38876 0.15254
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.2890  Pars:  0.36818 0.30777 0.32405 0.30468
#> Iter: 2 fn: 612.2890  Pars:  0.36818 0.30778 0.32404 0.30469
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.9990  Pars:  0.30502 0.29998 0.39500 0.20661
#> Iter: 2 fn: 589.9990  Pars:  0.30502 0.29998 0.39500 0.20661
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.6373  Pars:  0.33322 0.30270 0.36408 0.21374
#> Iter: 2 fn: 603.6373  Pars:  0.33322 0.30270 0.36408 0.21374
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.7786  Pars:  0.33411 0.28568 0.38021 0.17391
#> Iter: 2 fn: 600.7786  Pars:  0.33411 0.28568 0.38021 0.17391
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.2657  Pars:  0.38583 0.26172 0.35245 0.25874
#> Iter: 2 fn: 617.2657  Pars:  0.38583 0.26172 0.35245 0.25874
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.0756  Pars:  0.34866 0.28621 0.36513 0.23134
#> Iter: 2 fn: 607.0756  Pars:  0.34866 0.28621 0.36513 0.23134
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.0799  Pars:  0.35209 0.29521 0.35270 0.26155
#> Iter: 2 fn: 608.0799  Pars:  0.35208 0.29521 0.35271 0.26154
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.1973  Pars:  0.31469 0.31200 0.37331 0.25641
#> Iter: 2 fn: 593.1973  Pars:  0.31469 0.31200 0.37331 0.25641
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.5425  Pars:  0.37023 0.27076 0.35901 0.27612
#> Iter: 2 fn: 610.5425  Pars:  0.37023 0.27076 0.35901 0.27612
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.3191  Pars:  0.39467 0.25600 0.34933 0.25000
#> Iter: 2 fn: 620.3191  Pars:  0.39467 0.25600 0.34933 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.1837  Pars:  0.38812 0.24950 0.36238 0.27857
#> Iter: 2 fn: 614.1837  Pars:  0.38812 0.24950 0.36238 0.27857
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 621.8059  Pars:  0.40002 0.25167 0.34831 0.24503
#> Iter: 2 fn: 621.8059  Pars:  0.40002 0.25167 0.34832 0.24503
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.7074  Pars:  0.29481 0.32783 0.37736 0.15200
#> Iter: 2 fn: 589.7074  Pars:  0.29481 0.32783 0.37736 0.15200
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.0298  Pars:  0.38615 0.29393 0.31991 0.30597
#> Iter: 2 fn: 618.0298  Pars:  0.38615 0.29394 0.31991 0.30597
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.9850  Pars:  0.41220 0.30122 0.28659 0.36923
#> Iter: 2 fn: 618.9850  Pars:  0.41220 0.30122 0.28659 0.36923
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 620.5305  Pars:  0.38409 0.33977 0.27614 0.32308
#> Iter: 2 fn: 620.5305  Pars:  0.38409 0.33977 0.27614 0.32308
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.7751  Pars:  0.32009 0.31222 0.36770 0.23770
#> Iter: 2 fn: 597.7751  Pars:  0.32009 0.31222 0.36770 0.23770
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.8771  Pars:  0.36128 0.31440 0.32432 0.27481
#> Iter: 2 fn: 613.8771  Pars:  0.36128 0.31440 0.32432 0.27481
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.8584  Pars:  0.36094 0.29771 0.34135 0.24088
#> Iter: 2 fn: 613.8584  Pars:  0.36094 0.29771 0.34135 0.24088
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 623.8172  Pars:  0.39596 0.29414 0.30990 0.29286
#> Iter: 2 fn: 623.8172  Pars:  0.39596 0.29414 0.30990 0.29286
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.1867  Pars:  0.35048 0.29337 0.35615 0.22963
#> Iter: 2 fn: 609.1867  Pars:  0.35048 0.29337 0.35615 0.22963
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.9987  Pars:  0.36114 0.25721 0.38164 0.23022
#> Iter: 2 fn: 606.9987  Pars:  0.36114 0.25721 0.38164 0.23022
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.3756  Pars:  0.31360 0.32760 0.35880 0.28571
#> Iter: 2 fn: 591.3756  Pars:  0.31360 0.32760 0.35880 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.1074  Pars:  0.30056 0.29271 0.40672 0.23477
#> Iter: 2 fn: 584.1074  Pars:  0.30057 0.29273 0.40671 0.23478
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 575.0277  Pars:  0.27075 0.32183 0.40742 0.21698
#> Iter: 2 fn: 575.0277  Pars:  0.27075 0.32183 0.40742 0.21698
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.6531  Pars:  0.32762 0.28042 0.39195 0.27966
#> Iter: 2 fn: 590.6531  Pars:  0.32762 0.28042 0.39195 0.27966
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 568.9092  Pars:  0.25600 0.35733 0.38667 0.24999
#> Iter: 2 fn: 568.9092  Pars:  0.25600 0.35733 0.38667 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.8834  Pars:  0.37341 0.29765 0.32894 0.26087
#> Iter: 2 fn: 617.8834  Pars:  0.37341 0.29765 0.32894 0.26087
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 630.4963  Pars:  0.42464 0.31466 0.26070 0.34532
#> Iter: 2 fn: 630.4963  Pars:  0.42464 0.31466 0.26070 0.34532
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.6630  Pars:  0.36275 0.32214 0.31511 0.26119
#> Iter: 2 fn: 616.6630  Pars:  0.36275 0.32214 0.31511 0.26119
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.6408  Pars:  0.32457 0.30749 0.36794 0.18045
#> Iter: 2 fn: 600.6408  Pars:  0.32457 0.30749 0.36794 0.18045
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 626.4721  Pars:  0.38400 0.33600 0.28000 0.25000
#> Iter: 2 fn: 626.4721  Pars:  0.38400 0.33600 0.28000 0.25000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8135  Pars:  0.34945 0.31564 0.33491 0.29032
#> Iter: 2 fn: 606.8135  Pars:  0.34945 0.31564 0.33491 0.29032
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2467  Pars:  0.30602 0.32936 0.36462 0.22881
#> Iter: 2 fn: 594.2467  Pars:  0.30602 0.32936 0.36462 0.22881
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.3008  Pars:  0.30051 0.36549 0.33400 0.26126
#> Iter: 2 fn: 593.3008  Pars:  0.30051 0.36549 0.33400 0.26126
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.0848  Pars:  0.34493 0.30720 0.34787 0.25781
#> Iter: 2 fn: 607.0848  Pars:  0.34493 0.30720 0.34787 0.25781
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.8801  Pars:  0.33074 0.31241 0.35685 0.23810
#> Iter: 2 fn: 602.8801  Pars:  0.33075 0.31237 0.35687 0.23810
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.5006  Pars:  0.37408 0.28754 0.33837 0.28358
#> Iter: 2 fn: 614.5006  Pars:  0.37408 0.28754 0.33837 0.28358
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.1189  Pars:  0.35234 0.30830 0.33936 0.27344
#> Iter: 2 fn: 609.1189  Pars:  0.35234 0.30830 0.33935 0.27344
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.9177  Pars:  0.33426 0.31270 0.35304 0.25807
#> Iter: 2 fn: 602.9177  Pars:  0.33426 0.31270 0.35304 0.25806
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.8038  Pars:  0.37711 0.28420 0.33869 0.26812
#> Iter: 2 fn: 616.8038  Pars:  0.37711 0.28420 0.33869 0.26812
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.3568  Pars:  0.35184 0.30893 0.33923 0.30081
#> Iter: 2 fn: 605.3568  Pars:  0.35184 0.30893 0.33923 0.30081
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.4719  Pars:  0.30968 0.34581 0.34451 0.22500
#> Iter: 2 fn: 598.4719  Pars:  0.30968 0.34581 0.34452 0.22500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.1573  Pars:  0.31486 0.32788 0.35726 0.23141
#> Iter: 2 fn: 598.1573  Pars:  0.31486 0.32787 0.35727 0.23141
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 598.8304  Pars:  0.32895 0.29474 0.37632 0.24000
#> Iter: 2 fn: 598.8304  Pars:  0.32895 0.29474 0.37632 0.24000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.2408  Pars:  0.29377 0.32482 0.38142 0.16260
#> Iter: 2 fn: 589.2408  Pars:  0.29377 0.32482 0.38142 0.16260
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.3651  Pars:  0.30130 0.34687 0.35183 0.21008
#> Iter: 2 fn: 595.3651  Pars:  0.30130 0.34687 0.35183 0.21008
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.1246  Pars:  0.39961 0.27472 0.32567 0.35936
#> Iter: 2 fn: 611.1246  Pars:  0.39961 0.27473 0.32566 0.35937
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.8713  Pars:  0.42711 0.28589 0.28700 0.41936
#> Iter: 2 fn: 609.8713  Pars:  0.42711 0.28589 0.28700 0.41935
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.3789  Pars:  0.36751 0.31328 0.31921 0.33607
#> Iter: 2 fn: 607.3789  Pars:  0.36751 0.31328 0.31921 0.33607
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.3603  Pars:  0.41893 0.24740 0.33366 0.39370
#> Iter: 2 fn: 606.3603  Pars:  0.41893 0.24740 0.33366 0.39370
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 617.4769  Pars:  0.39302 0.30535 0.30163 0.33846
#> Iter: 2 fn: 617.4769  Pars:  0.39302 0.30535 0.30163 0.33846
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 565.0120  Pars:  0.28071 0.36400 0.35529 0.35165
#> Iter: 2 fn: 565.0120  Pars:  0.28071 0.36400 0.35529 0.35165
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 568.5718  Pars:  0.32787 0.29508 0.37705 0.39000
#> Iter: 2 fn: 568.5718  Pars:  0.32787 0.29508 0.37705 0.39000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.2654  Pars:  0.31616 0.33213 0.35171 0.37374
#> Iter: 2 fn: 574.2654  Pars:  0.31616 0.33213 0.35171 0.37374
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 572.8750  Pars:  0.32134 0.32459 0.35407 0.38383
#> Iter: 2 fn: 572.8750  Pars:  0.32134 0.32459 0.35407 0.38384
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 558.0068  Pars:  0.34847 0.27664 0.37489 0.44329
#> Iter: 2 fn: 558.0068  Pars:  0.34848 0.27663 0.37489 0.44330
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.6725  Pars:  0.33280 0.35840 0.30880 0.37500
#> Iter: 2 fn: 587.6725  Pars:  0.33280 0.35840 0.30880 0.37500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 579.9340  Pars:  0.28843 0.33557 0.37600 0.27885
#> Iter: 2 fn: 579.9340  Pars:  0.28843 0.33557 0.37600 0.27885
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 577.7947  Pars:  0.30633 0.27848 0.41519 0.28182
#> Iter: 2 fn: 577.7947  Pars:  0.30633 0.27848 0.41519 0.28182
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 573.8380  Pars:  0.34112 0.30098 0.35790 0.40196
#> Iter: 2 fn: 573.8380  Pars:  0.34111 0.30098 0.35790 0.40196
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.3500  Pars:  0.28985 0.33590 0.37425 0.26169
#> Iter: 2 fn: 583.3500  Pars:  0.28985 0.33590 0.37425 0.26168
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.5697  Pars:  0.36000 0.30900 0.33100 0.33333
#> Iter: 2 fn: 603.5697  Pars:  0.36000 0.30900 0.33100 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.4010  Pars:  0.31593 0.29031 0.39376 0.29730
#> Iter: 2 fn: 583.4010  Pars:  0.31592 0.29031 0.39377 0.29730
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.3540  Pars:  0.31056 0.34310 0.34634 0.32381
#> Iter: 2 fn: 585.3540  Pars:  0.31056 0.34310 0.34634 0.32381
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.8395  Pars:  0.39988 0.27360 0.32652 0.42982
#> Iter: 2 fn: 590.8395  Pars:  0.39988 0.27360 0.32652 0.42982
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.5629  Pars:  0.36024 0.29558 0.34418 0.35043
#> Iter: 2 fn: 597.5629  Pars:  0.36024 0.29558 0.34418 0.35043
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.0860  Pars:  0.28446 0.34081 0.37473 0.25472
#> Iter: 2 fn: 582.0860  Pars:  0.28446 0.34081 0.37473 0.25472
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.4558  Pars:  0.34065 0.28779 0.37156 0.31896
#> Iter: 2 fn: 592.4558  Pars:  0.34066 0.28780 0.37155 0.31896
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.0890  Pars:  0.33151 0.33151 0.33699 0.33636
#> Iter: 2 fn: 592.0890  Pars:  0.33151 0.33151 0.33699 0.33636
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.7365  Pars:  0.39168 0.29537 0.31295 0.37705
#> Iter: 2 fn: 606.7365  Pars:  0.39168 0.29537 0.31295 0.37705
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.1833  Pars:  0.35099 0.27899 0.37002 0.33332
#> Iter: 2 fn: 593.1833  Pars:  0.35100 0.27900 0.37000 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.8448  Pars:  0.36173 0.24678 0.39148 0.28684
#> Iter: 2 fn: 599.8448  Pars:  0.36174 0.24678 0.39148 0.28680
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 611.2054  Pars:  0.38256 0.28170 0.33574 0.32556
#> Iter: 2 fn: 611.2054  Pars:  0.38254 0.28173 0.33573 0.32557
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8717  Pars:  0.36024 0.31405 0.32571 0.35043
#> Iter: 2 fn: 600.8717  Pars:  0.36024 0.31405 0.32571 0.35043
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.1308  Pars:  0.37556 0.33900 0.28545 0.39822
#> Iter: 2 fn: 600.1308  Pars:  0.37556 0.33900 0.28544 0.39823
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.0550  Pars:  0.37131 0.30208 0.32661 0.36441
#> Iter: 2 fn: 601.0550  Pars:  0.37131 0.30208 0.32661 0.36441
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 622.9638  Pars:  0.42117 0.30083 0.27800 0.36842
#> Iter: 2 fn: 622.9638  Pars:  0.42117 0.30083 0.27800 0.36842
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6220  Pars:  0.38028 0.30171 0.31800 0.36364
#> Iter: 2 fn: 605.6220  Pars:  0.38029 0.30171 0.31800 0.36364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.4007  Pars:  0.36021 0.28993 0.34986 0.31707
#> Iter: 2 fn: 603.4007  Pars:  0.36021 0.28993 0.34986 0.31707
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.7835  Pars:  0.37966 0.33373 0.28662 0.34679
#> Iter: 2 fn: 613.7835  Pars:  0.37965 0.33373 0.28662 0.34677
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 609.5930  Pars:  0.39302 0.26000 0.34698 0.33846
#> Iter: 2 fn: 609.5930  Pars:  0.39302 0.26000 0.34698 0.33846
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 565.3880  Pars:  0.30784 0.24975 0.44241 0.31132
#> Iter: 2 fn: 565.3880  Pars:  0.30784 0.24975 0.44241 0.31132
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.1503  Pars:  0.41191 0.24058 0.34752 0.45133
#> Iter: 2 fn: 582.1503  Pars:  0.41190 0.24058 0.34752 0.45133
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 579.9693  Pars:  0.35072 0.26465 0.38464 0.37273
#> Iter: 2 fn: 579.9693  Pars:  0.35072 0.26464 0.38464 0.37273
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 566.1359  Pars:  0.31360 0.22400 0.46240 0.28572
#> Iter: 2 fn: 566.1359  Pars:  0.31360 0.22400 0.46240 0.28571
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 561.7532  Pars:  0.28843 0.25791 0.45365 0.27886
#> Iter: 2 fn: 561.7532  Pars:  0.28843 0.25792 0.45365 0.27885
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.9707  Pars:  0.35122 0.24585 0.40293 0.31667
#> Iter: 2 fn: 588.9707  Pars:  0.35122 0.24585 0.40293 0.31667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.9720  Pars:  0.37763 0.27608 0.34629 0.36975
#> Iter: 2 fn: 597.9720  Pars:  0.37763 0.27608 0.34629 0.36975
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.1844  Pars:  0.35466 0.29934 0.34600 0.38532
#> Iter: 2 fn: 586.1844  Pars:  0.35466 0.29934 0.34600 0.38532
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.3644  Pars:  0.31193 0.29787 0.39021 0.28829
#> Iter: 2 fn: 584.3644  Pars:  0.31192 0.29787 0.39020 0.28829
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.1975  Pars:  0.37504 0.27247 0.35249 0.37607
#> Iter: 2 fn: 594.1975  Pars:  0.37504 0.27247 0.35249 0.37607
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.3701  Pars:  0.34066 0.21732 0.44203 0.31897
#> Iter: 2 fn: 574.3701  Pars:  0.34066 0.21732 0.44203 0.31897
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 575.1560  Pars:  0.28986 0.33623 0.37391 0.31000
#> Iter: 2 fn: 575.1560  Pars:  0.28985 0.33623 0.37391 0.31000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 578.2183  Pars:  0.32384 0.33346 0.34270 0.37624
#> Iter: 2 fn: 578.2183  Pars:  0.32384 0.33346 0.34270 0.37624
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 570.6496  Pars:  0.29568 0.30446 0.39986 0.31683
#> Iter: 2 fn: 570.6496  Pars:  0.29568 0.30446 0.39986 0.31683
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 581.0481  Pars:  0.31104 0.29952 0.38944 0.30555
#> Iter: 2 fn: 581.0481  Pars:  0.31104 0.29952 0.38944 0.30556
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 569.2092  Pars:  0.35363 0.27123 0.37513 0.41748
#> Iter: 2 fn: 569.2092  Pars:  0.35363 0.27123 0.37513 0.41748
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.3881  Pars:  0.34571 0.27657 0.37771 0.36364
#> Iter: 2 fn: 582.3881  Pars:  0.34571 0.27657 0.37771 0.36364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 569.8037  Pars:  0.28324 0.26793 0.44883 0.21622
#> Iter: 2 fn: 569.8037  Pars:  0.28324 0.26793 0.44883 0.21622
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 571.7298  Pars:  0.31616 0.31935 0.36449 0.37374
#> Iter: 2 fn: 571.7298  Pars:  0.31616 0.31935 0.36448 0.37374
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 571.9001  Pars:  0.30044 0.28889 0.41067 0.30769
#> Iter: 2 fn: 571.9001  Pars:  0.30044 0.28889 0.41067 0.30769
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 591.3997  Pars:  0.34225 0.31450 0.34325 0.35135
#> Iter: 2 fn: 591.3997  Pars:  0.34225 0.31450 0.34325 0.35135
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.8621  Pars:  0.30468 0.33983 0.35549 0.31731
#> Iter: 2 fn: 582.8621  Pars:  0.30468 0.33983 0.35549 0.31731
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.5726  Pars:  0.32327 0.30324 0.37349 0.30088
#> Iter: 2 fn: 589.5726  Pars:  0.32327 0.30324 0.37349 0.30088
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.4782  Pars:  0.40397 0.34209 0.25395 0.45046
#> Iter: 2 fn: 597.4782  Pars:  0.40397 0.34210 0.25394 0.45045
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.9153  Pars:  0.36997 0.28776 0.34227 0.36752
#> Iter: 2 fn: 596.9153  Pars:  0.36997 0.28776 0.34227 0.36752
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 559.3025  Pars:  0.27188 0.31237 0.41575 0.30851
#> Iter: 2 fn: 559.3025  Pars:  0.27188 0.31237 0.41575 0.30851
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 567.9762  Pars:  0.30303 0.29697 0.40000 0.34000
#> Iter: 2 fn: 567.9762  Pars:  0.30303 0.29697 0.40000 0.34000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 573.3646  Pars:  0.31388 0.31077 0.37535 0.35644
#> Iter: 2 fn: 573.3646  Pars:  0.31388 0.31077 0.37535 0.35644
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 558.1896  Pars:  0.25146 0.35317 0.39537 0.29213
#> Iter: 2 fn: 558.1896  Pars:  0.25146 0.35317 0.39537 0.29213
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 563.0361  Pars:  0.28213 0.34347 0.37440 0.34783
#> Iter: 2 fn: 563.0361  Pars:  0.28213 0.34347 0.37440 0.34783
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.3603  Pars:  0.29797 0.29514 0.40689 0.29524
#> Iter: 2 fn: 574.3603  Pars:  0.29797 0.29513 0.40689 0.29524
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 575.0628  Pars:  0.31922 0.24579 0.43500 0.29203
#> Iter: 2 fn: 575.0628  Pars:  0.31923 0.24577 0.43500 0.29204
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.4632  Pars:  0.40536 0.31927 0.27537 0.44248
#> Iter: 2 fn: 597.4632  Pars:  0.40536 0.31927 0.27537 0.44248
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 587.0173  Pars:  0.33326 0.31783 0.34891 0.35186
#> Iter: 2 fn: 587.0173  Pars:  0.33326 0.31783 0.34891 0.35185
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.5208  Pars:  0.31192 0.34284 0.34524 0.28829
#> Iter: 2 fn: 592.5208  Pars:  0.31192 0.34284 0.34524 0.28829
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.9467  Pars:  0.34169 0.31413 0.34418 0.27419
#> Iter: 2 fn: 604.9467  Pars:  0.34169 0.31413 0.34418 0.27419
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.7318  Pars:  0.31683 0.36915 0.31403 0.31193
#> Iter: 2 fn: 594.7318  Pars:  0.31683 0.36915 0.31403 0.31193
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.1828  Pars:  0.35883 0.35264 0.28853 0.35345
#> Iter: 2 fn: 605.1828  Pars:  0.35883 0.35264 0.28853 0.35345
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 618.2391  Pars:  0.41344 0.37617 0.21039 0.40984
#> Iter: 2 fn: 618.2391  Pars:  0.41344 0.37617 0.21039 0.40984
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.6478  Pars:  0.38700 0.24600 0.36700 0.33333
#> Iter: 2 fn: 604.6478  Pars:  0.38700 0.24600 0.36700 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.8943  Pars:  0.38273 0.32483 0.29244 0.37814
#> Iter: 2 fn: 606.8943  Pars:  0.38273 0.32484 0.29243 0.37815
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 606.0096  Pars:  0.43406 0.34426 0.22169 0.46551
#> Iter: 2 fn: 606.0096  Pars:  0.43406 0.34426 0.22168 0.46552
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 604.4238  Pars:  0.35852 0.32236 0.31912 0.33615
#> Iter: 2 fn: 604.4238  Pars:  0.35850 0.32235 0.31914 0.33613
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.7547  Pars:  0.32933 0.30996 0.36072 0.27731
#> Iter: 2 fn: 597.7547  Pars:  0.32933 0.30995 0.36072 0.27731
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.7225  Pars:  0.44678 0.24030 0.31292 0.40910
#> Iter: 2 fn: 613.7225  Pars:  0.44677 0.24031 0.31292 0.40909
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.9624  Pars:  0.33451 0.29867 0.36682 0.33036
#> Iter: 2 fn: 588.9624  Pars:  0.33451 0.29867 0.36683 0.33036
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 613.6714  Pars:  0.41352 0.26200 0.32448 0.36641
#> Iter: 2 fn: 613.6714  Pars:  0.41352 0.26200 0.32448 0.36641
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.7075  Pars:  0.41478 0.27544 0.30977 0.38281
#> Iter: 2 fn: 612.7075  Pars:  0.41478 0.27544 0.30977 0.38281
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.0022  Pars:  0.38025 0.26975 0.35000 0.38462
#> Iter: 2 fn: 594.0022  Pars:  0.38025 0.26975 0.35000 0.38462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 619.3668  Pars:  0.40802 0.26507 0.32691 0.32847
#> Iter: 2 fn: 619.3668  Pars:  0.40802 0.26507 0.32691 0.32847
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.3334  Pars:  0.38660 0.25034 0.36306 0.36886
#> Iter: 2 fn: 597.3334  Pars:  0.38660 0.25034 0.36306 0.36885
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 608.7222  Pars:  0.37143 0.27428 0.35429 0.30000
#> Iter: 2 fn: 608.7222  Pars:  0.37143 0.27429 0.35429 0.30000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.6041  Pars:  0.38440 0.27900 0.33660 0.35484
#> Iter: 2 fn: 605.6041  Pars:  0.38440 0.27900 0.33660 0.35484
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 610.8407  Pars:  0.41557 0.29492 0.28951 0.40323
#> Iter: 2 fn: 610.8407  Pars:  0.41557 0.29492 0.28951 0.40323
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2411  Pars:  0.34066 0.29661 0.36273 0.31897
#> Iter: 2 fn: 594.2411  Pars:  0.34066 0.29661 0.36273 0.31897
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.4509  Pars:  0.31746 0.32381 0.35873 0.37000
#> Iter: 2 fn: 574.4509  Pars:  0.31746 0.32381 0.35873 0.37000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 578.6366  Pars:  0.32818 0.40764 0.26418 0.42105
#> Iter: 2 fn: 578.6366  Pars:  0.32818 0.40764 0.26418 0.42105
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 555.6794  Pars:  0.27656 0.34572 0.37772 0.36363
#> Iter: 2 fn: 555.6794  Pars:  0.27657 0.34571 0.37772 0.36364
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 577.7465  Pars:  0.31004 0.41228 0.27768 0.39362
#> Iter: 2 fn: 577.7465  Pars:  0.31003 0.41228 0.27768 0.39362
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 564.0929  Pars:  0.28421 0.36947 0.34632 0.36666
#> Iter: 2 fn: 564.0929  Pars:  0.28421 0.36947 0.34632 0.36667
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 577.9711  Pars:  0.37128 0.25887 0.36985 0.41284
#> Iter: 2 fn: 577.9711  Pars:  0.37128 0.25888 0.36984 0.41284
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 575.9621  Pars:  0.32134 0.34082 0.33784 0.38384
#> Iter: 2 fn: 575.9621  Pars:  0.32134 0.34082 0.33784 0.38384
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 571.7966  Pars:  0.32287 0.27940 0.39773 0.35577
#> Iter: 2 fn: 571.7966  Pars:  0.32287 0.27940 0.39773 0.35577
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 584.6104  Pars:  0.33717 0.24367 0.41917 0.29412
#> Iter: 2 fn: 584.6104  Pars:  0.33717 0.24367 0.41917 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.0138  Pars:  0.32551 0.28967 0.38482 0.33028
#> Iter: 2 fn: 582.0138  Pars:  0.32551 0.28967 0.38482 0.33027
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 586.9543  Pars:  0.35335 0.28079 0.36586 0.36607
#> Iter: 2 fn: 586.9543  Pars:  0.35335 0.28079 0.36586 0.36607
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 577.8144  Pars:  0.31193 0.26977 0.41830 0.28829
#> Iter: 2 fn: 577.8144  Pars:  0.31192 0.26977 0.41830 0.28829
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.3262  Pars:  0.32258 0.32258 0.35484 0.38000
#> Iter: 2 fn: 574.3262  Pars:  0.32258 0.32258 0.35484 0.38000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.0553  Pars:  0.28900 0.31733 0.39367 0.29412
#> Iter: 2 fn: 574.0553  Pars:  0.28900 0.31733 0.39367 0.29412
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.7280  Pars:  0.32818 0.38000 0.29182 0.42105
#> Iter: 2 fn: 574.7280  Pars:  0.32818 0.38000 0.29182 0.42105
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.4868  Pars:  0.38446 0.28834 0.32720 0.39655
#> Iter: 2 fn: 596.4868  Pars:  0.38446 0.28834 0.32720 0.39655
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 571.3019  Pars:  0.30903 0.28229 0.40869 0.32692
#> Iter: 2 fn: 571.3019  Pars:  0.30903 0.28229 0.40869 0.32692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.3338  Pars:  0.36866 0.26378 0.36756 0.37069
#> Iter: 2 fn: 590.3338  Pars:  0.36866 0.26378 0.36756 0.37069
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 585.7410  Pars:  0.37717 0.29413 0.32870 0.42202
#> Iter: 2 fn: 585.7410  Pars:  0.37717 0.29413 0.32870 0.42202
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 594.2687  Pars:  0.38794 0.29266 0.31940 0.41228
#> Iter: 2 fn: 594.2687  Pars:  0.38794 0.29266 0.31940 0.41228
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 568.3998  Pars:  0.28669 0.31887 0.39445 0.31633
#> Iter: 2 fn: 568.3998  Pars:  0.28669 0.31887 0.39445 0.31633
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 569.6584  Pars:  0.29319 0.36885 0.33797 0.36559
#> Iter: 2 fn: 569.6584  Pars:  0.29319 0.36885 0.33797 0.36559
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.3455  Pars:  0.33468 0.29169 0.37363 0.34862
#> Iter: 2 fn: 583.3455  Pars:  0.33468 0.29169 0.37363 0.34862
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.4506  Pars:  0.33409 0.31818 0.34773 0.37143
#> Iter: 2 fn: 582.4506  Pars:  0.33409 0.31818 0.34773 0.37143
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 564.7524  Pars:  0.28971 0.33285 0.37744 0.35106
#> Iter: 2 fn: 564.7524  Pars:  0.28970 0.33285 0.37744 0.35106
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 563.8385  Pars:  0.27900 0.33900 0.38200 0.33333
#> Iter: 2 fn: 563.8385  Pars:  0.27900 0.33900 0.38200 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 557.2604  Pars:  0.24711 0.32417 0.42871 0.24731
#> Iter: 2 fn: 557.2604  Pars:  0.24711 0.32417 0.42871 0.24731
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.2977  Pars:  0.33809 0.29739 0.36452 0.36111
#> Iter: 2 fn: 583.2977  Pars:  0.33809 0.29739 0.36452 0.36111
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 573.0218  Pars:  0.32258 0.31613 0.36129 0.38000
#> Iter: 2 fn: 573.0218  Pars:  0.32258 0.31613 0.36129 0.38000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 574.7752  Pars:  0.31057 0.31057 0.37887 0.34314
#> Iter: 2 fn: 574.7752  Pars:  0.31057 0.31057 0.37887 0.34314
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 612.4053  Pars:  0.40344 0.31816 0.27840 0.39024
#> Iter: 2 fn: 612.4053  Pars:  0.40344 0.31816 0.27840 0.39024
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.3484  Pars:  0.36024 0.31097 0.32879 0.35042
#> Iter: 2 fn: 600.3484  Pars:  0.36024 0.31097 0.32879 0.35043
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.4004  Pars:  0.35438 0.25271 0.39292 0.31147
#> Iter: 2 fn: 593.4004  Pars:  0.35438 0.25272 0.39290 0.31148
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 600.8834  Pars:  0.38025 0.30550 0.31425 0.38461
#> Iter: 2 fn: 600.8834  Pars:  0.38025 0.30550 0.31425 0.38462
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 601.4209  Pars:  0.38678 0.29828 0.31495 0.38983
#> Iter: 2 fn: 601.4209  Pars:  0.38678 0.29828 0.31494 0.38983
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 572.0083  Pars:  0.31104 0.26209 0.42687 0.30556
#> Iter: 2 fn: 572.0083  Pars:  0.31104 0.26208 0.42688 0.30556
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.0913  Pars:  0.34844 0.30800 0.34356 0.35714
#> Iter: 2 fn: 592.0913  Pars:  0.34844 0.30800 0.34356 0.35714
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 596.6079  Pars:  0.36245 0.23973 0.39782 0.29921
#> Iter: 2 fn: 596.6079  Pars:  0.36245 0.23973 0.39782 0.29921
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.1912  Pars:  0.32551 0.33148 0.34301 0.33028
#> Iter: 2 fn: 590.1912  Pars:  0.32551 0.33148 0.34301 0.33028
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 582.0138  Pars:  0.32551 0.28967 0.38482 0.33028
#> Iter: 2 fn: 582.0138  Pars:  0.32551 0.28967 0.38482 0.33027
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 583.4556  Pars:  0.33280 0.33280 0.33440 0.37500
#> Iter: 2 fn: 583.4556  Pars:  0.33280 0.33280 0.33440 0.37500
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 571.3292  Pars:  0.33192 0.40047 0.26760 0.44566
#> Iter: 2 fn: 571.3292  Pars:  0.33192 0.40047 0.26761 0.44565
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 568.4087  Pars:  0.27751 0.37404 0.34846 0.33696
#> Iter: 2 fn: 568.4087  Pars:  0.27751 0.37403 0.34846 0.33696
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.0873  Pars:  0.36667 0.31998 0.31335 0.39998
#> Iter: 2 fn: 592.0873  Pars:  0.36667 0.32000 0.31333 0.40000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 575.3868  Pars:  0.30296 0.28052 0.41652 0.28704
#> Iter: 2 fn: 575.3868  Pars:  0.30296 0.28052 0.41652 0.28704
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 599.3892  Pars:  0.33481 0.33772 0.32747 0.31304
#> Iter: 2 fn: 599.3892  Pars:  0.33481 0.33772 0.32747 0.31304
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.5058  Pars:  0.36932 0.33480 0.29589 0.42057
#> Iter: 2 fn: 589.5058  Pars:  0.36932 0.33481 0.29587 0.42056
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.8213  Pars:  0.35345 0.33382 0.31273 0.38889
#> Iter: 2 fn: 590.8213  Pars:  0.35345 0.33382 0.31273 0.38889
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.1337  Pars:  0.39539 0.36245 0.24216 0.45370
#> Iter: 2 fn: 595.1337  Pars:  0.39539 0.36244 0.24217 0.45370
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 593.5479  Pars:  0.33151 0.34055 0.32795 0.33636
#> Iter: 2 fn: 593.5479  Pars:  0.33151 0.34055 0.32795 0.33636
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 589.1667  Pars:  0.39603 0.31247 0.29150 0.44954
#> Iter: 2 fn: 589.1667  Pars:  0.39603 0.31247 0.29150 0.44954
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 581.3521  Pars:  0.33003 0.28461 0.38537 0.33945
#> Iter: 2 fn: 581.3521  Pars:  0.33003 0.28461 0.38536 0.33945
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 590.2134  Pars:  0.34200 0.28800 0.37000 0.33333
#> Iter: 2 fn: 590.2134  Pars:  0.34200 0.28800 0.37000 0.33333
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 577.4793  Pars:  0.33897 0.33899 0.32204 0.40998
#> Iter: 2 fn: 577.4793  Pars:  0.33898 0.33898 0.32204 0.41000
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 588.7630  Pars:  0.33003 0.32094 0.34903 0.33945
#> Iter: 2 fn: 588.7630  Pars:  0.33003 0.32094 0.34903 0.33945
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 605.8964  Pars:  0.35743 0.36986 0.27270 0.35652
#> Iter: 2 fn: 605.8964  Pars:  0.35743 0.36986 0.27270 0.35652
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 592.0165  Pars:  0.32424 0.29908 0.37667 0.28448
#> Iter: 2 fn: 592.0165  Pars:  0.32424 0.29908 0.37667 0.28448
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 603.1891  Pars:  0.38596 0.37218 0.24186 0.41963
#> Iter: 2 fn: 603.1891  Pars:  0.38597 0.37219 0.24185 0.41964
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 597.5492  Pars:  0.38224 0.31182 0.30594 0.40351
#> Iter: 2 fn: 597.5492  Pars:  0.38224 0.31182 0.30594 0.40351
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 614.6252  Pars:  0.40889 0.33243 0.25868 0.39837
#> Iter: 2 fn: 614.6252  Pars:  0.40889 0.33243 0.25868 0.39837
#> solnp--> Completed in 2 iterations

agg <- aggregate(lca_advantage ~ gamma, data = results_by_gamma,
                 FUN = function(x) c(mean = mean(x), se = sd(x)/sqrt(length(x))))
agg <- do.call(data.frame, agg)
names(agg) <- c("gamma", "mean", "se")

barplot(agg$mean, names.arg = agg$gamma,
        main = "LCA Advantage by Guessing Rate",
        xlab = "Gamma (guessing probability)",
        ylab = "Correlation advantage (LCA - CS)",
        col = "steelblue")
LCA advantage by gamma level

LCA advantage by gamma level

Interpreting Posterior Probabilities

The posterior probabilities provide actionable individual-level information:

sim <- simulate_lca(
  n = 500, n_items = 5, gk = 0.30, gamma = 0.25,
  seed = 101, return_classes = TRUE
)
fit <- lca_fit(sim$pre, sim$post)
#> 
#> Iter: 1 fn: 615.4418  Pars:  0.35957 0.33468 0.30574 0.27692
#> Iter: 2 fn: 615.4418  Pars:  0.35957 0.33468 0.30574 0.27692
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 602.2486  Pars:  0.32258 0.32512 0.35230 0.21260
#> Iter: 2 fn: 602.2486  Pars:  0.32258 0.32512 0.35230 0.21260
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 595.6830  Pars:  0.31670 0.30630 0.37700 0.22955
#> Iter: 2 fn: 595.6830  Pars:  0.31668 0.30629 0.37703 0.22951
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 607.2976  Pars:  0.34503 0.29798 0.35699 0.23485
#> Iter: 2 fn: 607.2976  Pars:  0.34503 0.29798 0.35699 0.23485
#> solnp--> Completed in 2 iterations
#> 
#> Iter: 1 fn: 616.9452  Pars:  0.39155 0.30960 0.29885 0.34109
#> Iter: 2 fn: 616.9452  Pars:  0.39155 0.30960 0.29885 0.34109
#> solnp--> Completed in 2 iterations
posteriors <- posterior_class_probs(fit, sim$pre, sim$post)

posteriors$true_class <- sim$true_class

kk_subset <- posteriors[posteriors$true_class == "kk", ]
gk_subset <- posteriors[posteriors$true_class == "gk", ]
gg_subset <- posteriors[posteriors$true_class == "gg", ]

cat("Mean posteriors by true class:\n")
#> Mean posteriors by true class:
cat(sprintf("  kk class: P_kk=%.3f, P_gk=%.3f, P_gg=%.3f\n",
            mean(kk_subset$P_kk), mean(kk_subset$P_gk), mean(kk_subset$P_gg)))
#>   kk class: P_kk=0.999, P_gk=0.001, P_gg=0.000
cat(sprintf("  gk class: P_kk=%.3f, P_gk=%.3f, P_gg=%.3f\n",
            mean(gk_subset$P_kk), mean(gk_subset$P_gk), mean(gk_subset$P_gg)))
#>   gk class: P_kk=0.000, P_gk=0.999, P_gg=0.001
cat(sprintf("  gg class: P_kk=%.3f, P_gk=%.3f, P_gg=%.3f\n",
            mean(gg_subset$P_kk), mean(gg_subset$P_gk), mean(gg_subset$P_gg)))
#>   gg class: P_kk=0.000, P_gk=0.011, P_gg=0.989

Conclusion

This vignette demonstrates that the guess package implementation: 1. Correctly implements the cell probability formulas from the latent class model 2. Produces unbiased parameter estimates 3. Has valid standard errors with proper coverage 4. Shows the expected \(1/\sqrt{n}\) efficiency gains

The latent class model provides a principled way to adjust estimates of learning for guessing bias, recovering the true proportion who learned from pre-post test data.

References

Cor, K. and Sood, G. (2018). Measuring Learning. Working paper. https://gsood.com/research/papers/k_gains.pdf

Cor, K. and Sood, G. (2016). Adjusting for Guessing. Working paper. https://gsood.com/research/papers/guess.pdf

Session Info

sessionInfo()
#> R version 4.6.0 (2026-04-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] guess_0.5.0    rmarkdown_2.31
#> 
#> loaded via a namespace (and not attached):
#>  [1] cli_3.6.6           knitr_1.51          rlang_1.2.0        
#>  [4] xfun_0.58           otel_0.2.0          jsonlite_2.0.0     
#>  [7] backports_1.5.1     listenv_0.10.1      future.apply_1.20.2
#> [10] buildtools_1.0.0    htmltools_0.5.9     maketools_1.3.2    
#> [13] sys_3.4.3           sass_0.4.10         evaluate_1.0.5     
#> [16] jquerylib_0.1.4     fastmap_1.2.0       numDeriv_2016.8-1.1
#> [19] yaml_2.3.12         lifecycle_1.0.5     compiler_4.6.0     
#> [22] codetools_0.2-20    Rsolnp_2.0.1        Rcpp_1.1.1-1.1     
#> [25] future_1.70.0       truncnorm_1.0-9     digest_0.6.39      
#> [28] R6_2.6.1            parallelly_1.47.0   parallel_4.6.0     
#> [31] checkmate_2.3.4     bslib_0.11.0        tools_4.6.0        
#> [34] globals_0.19.1      cachem_1.1.0