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guess: Adjust Estimates of Learning for Guessing

Over informative processes, naive estimator of learning—difference between post and pre process scores—underestimates actual learning. A heuristic account for why the naive estimator is negatively biased is as follows: people know as much or more after exposed to an informative process than before it. And the less people know, the larger the number of items they don’t know. And greater the opportunity to guess.

Guessing, even when random, only increases the proportion correct. Thus, bias due to guessing for naive measures of knowledge is always positive. On average, thus, there is more positive bias in the pre-process scores than post-process scores. And naturally, subtracting pre-process scores from post-process provides an attenuated estimate of actual learning. For a more complete treatment of the issue, read this paper by Ken Cor and Gaurav Sood.

We provide a few different ways to adjust estimates of learning for guessing. For now, we limit our attention to cases where the same battery of knowledge questions has been asked in both the pre- and the post-process wave. And to cases where closed-ended questions have been asked. (Guessing is not a serious issue on open-ended items. See more evidence for that in DK Means DK by Robert Luskin and John Bullock.) More generally, the package implements the methods to adjust learning for guessing discussed in this paper.

Measuring Learning:

Estimand

Proportion of people who learned a particular piece of information over the course of an informative process.

Other Issues

Measurement of knowledge is fundamentally reactive – we must probe to learn. But probing is not without its problems. For instance, people who don’t know the answer try to triangulate based on the cues in the question itself. For another, people are remarkably averse to confessing to their ignorance. So on a closed ended question, lots of people who don’t know the right answer, guess. Here are some pertinent issues that relate to how we analyze the data:

  1. Dealing with Missing Data
    If you assume that the data are missing completely at random, you can simply ignore them. Generally, however, respondents tend to skip items they don’t know. So missing responses on knowledge questions typically indicate ignorance. (Of course, it is important to investigate other potential reasons behind missing data. And we encourage researchers to take all precautions.) In our treatment, however, for simplicity sake, we treat missing as indicators of ignorance.

  2. Dealing with Don’t Know
    We now know a little bit about Don’t Know. One generally strategy is to treat Don’t Know responses as ignorance. But research suggests that on average there is approximately 3% hidden knowledge behind Don’t Know responses. See DK Means DK by Robert Luskin and John Bullock. Thus one can also choose to replace Don’t Know responses with .03.

  3. Related Knowledge
    People either know a particular piece of information or they don’t. On an open-ended question, they may struggle to remember it but those kinds of concerns don’t apply to closed-ended questions where the task is simply to identify the correct answer. What does on occassion happen on closed-ended questions is that people have related cognitions. So for instance, asked to identify the prime minister of France, the respondents sometimes know that one of the options is the king of Sudan and may guess randomly between the remaining options. But that isn’t the same as knowing the prime minister of France.

Standard Correction for Guessing

The standard correction for guessing assumes that people guess randomly. And that people either know or don’t know. Using this assumption, it then uses total number of incorrect answers to estimate the total number of items that the person guessed on. For instance, let us assume there are 4 options on a multiple choice question. Say we have data from 100 respondents. Say there are 70 incorrect answers and 30 correct. Incorrect answers reflect attempts of guessing. (We also assume that people aren’t misinformed.) This means we can triangulat the total number of questions respondents guessed on – 70*(4/3). This means that the proportion of people who know the piece of information is roughly .067. Do it for the pre and the post wave and you have estimate of learning adjusted for guessing using the standard correction.

Latent Class Correction for Guessing

See the paper for details.


Installation

To get the current development version from github:

# install.packages("devtools")
library(devtools)
#devtools::install_github("soodoku/guess")

Usage

Standard Correction for Guessing

To adjust estimates of learning for standard correction of guessing, use stndcor. The function requires takes pre test and post test data frames containing responses to the items on the pre- and the post-test, and a lucky vector that contains the probability of getting an item correct when guessing randomly. Under standard guessing correction, it is taken to be inverse of total number of options.

Structure of the Input Data:

  1. For current purposes, we assume missing responses to indicate ignorance. Thus functions internally code missing responses as 0.
  2. If the items offer an option to mark Don't know, code all Don't Know responses as ‘d’.
# Load library
library(guess)

# Generate some data without DK
pre_test <- data.frame(item1=c(1,0,0,1,0), item2=c(1,NA,0,1,0)) 
pst_test <-  pre_test + cbind(c(0,1,1,0,0), c(0,1,0,0,1))
lucky <- rep(.25, 2)

# Unadjusted Effect
# Treating Don't Know as ignorance
colMeans(nona(pst_test) - nona(pre_test))
## item1 item2 
##   0.4   0.2
# MCAR
colMeans(pst_test - pre_test, na.rm=T)
## item1 item2 
##  0.40  0.25
# Adjusted Effect
stndcor(pre_test, pst_test, lucky)
## $pre
##     item1     item2 
## 0.2000000 0.2666667 
## 
## $pst
##     item1     item2 
## 0.7333333 0.5333333 
## 
## $learn
##     item1     item2 
## 0.5333333 0.2666667

Transition Matrix

# Without Don't Know
pre_test_var <- c(1,0,0,1,0,1,0) 
pst_test_var <- c(1,0,1,1,0,1,1)
print(transmat(pre_test_var, pst_test_var))
## x00 x01 x10 x11 
##   2   2   0   3
# With Don't Know
pre_test_var <- c(1,0,NA,1,"d","d",0,1,0)
pst_test_var <- c(1,0,1,"d",1,0,1,1,"d")
print(transmat(pre_test_var, pst_test_var))
## x00 x01 x0d x10 x11 x1d xd0 xd1 xdd 
##   1   2   1   0   2   1   1   1   0

Adjusting Using the Latent Class Model

# load(system.file("data/alldat.rda", package = "guess"))
load("../data/alldat.rda")

# nitems
nitems <- length(alldat)/400

# Vectors of Names
t1 <- paste0("guess.t1", 1:nitems)
t2 <- paste0("guess.t2", 1:nitems)

transmatrix <- multi_transmat(alldat[,t1], alldat[,t2])

res <- guesstimate(transmatrix)
## 
## Iter: 1 fn: 134.6419  Pars:  0.07656179909 0.00000002922 0.92343817140 0.54285573349
## Iter: 2 fn: 134.6419  Pars:  0.076564035243 0.000000009896 0.923435954861 0.542859555980
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 150.0954  Pars:  0.05000 0.02000 0.93000 0.20000
## Iter: 2 fn: 150.0954  Pars:  0.05000 0.02000 0.93000 0.20000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 100.8425  Pars:  0.04000 0.01600 0.94400 0.49999
## Iter: 2 fn: 100.8425  Pars:  0.04000 0.01600 0.94400 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## Iter: 2 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.2764  Pars:  0.04114 0.03086 0.92800 0.41667
## Iter: 2 fn: 128.2764  Pars:  0.04114 0.03086 0.92800 0.41667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 131.8840  Pars:  0.04247 0.01565 0.94188 0.10525
## Iter: 2 fn: 131.8840  Pars:  0.04247 0.01565 0.94188 0.10527
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.2272  Pars:  0.03756 0.02600 0.93644 0.30770
## Iter: 2 fn: 128.2272  Pars:  0.03756 0.02600 0.93644 0.30769
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 168.8418  Pars:  0.05290 0.02760 0.91950 0.13045
## Iter: 2 fn: 168.8418  Pars:  0.05290 0.02760 0.91950 0.13043
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 178.7014  Pars:  0.05694 0.03365 0.90941 0.22727
## Iter: 2 fn: 178.7014  Pars:  0.05694 0.03365 0.90941 0.22727
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 179.6872  Pars:  0.05408 0.03328 0.91264 0.03845
## Iter: 2 fn: 179.6872  Pars:  0.05408 0.03328 0.91264 0.03846
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1415.6458     Pars:  0.04587 0.02159 0.93254 0.25882
## Iter: 2 fn: 1415.6458     Pars:  0.04587 0.02159 0.93254 0.25882
## solnp--> Completed in 2 iterations
round(res$param.lca[,1:4], 3)
##        [,1] [,2]  [,3]  [,4]
## lgg   0.077 0.05 0.040 0.036
## lgk   0.000 0.02 0.016 0.030
## lkk   0.923 0.93 0.944 0.934
## gamma 0.543 0.20 0.500 0.667
round(res$est.learning[1:4], 3)
## [1] 0.000 0.020 0.016 0.030
# Guesstimate with DK
# load(system.file("data/alldat_dk.rda", package = "guess"))
load("../data/alldat_dk.rda")
transmatrix <- multi_transmat(alldat_dk[,t1], alldat_dk[,t2], force9=T)
res_dk <- guesstimate(transmatrix)
## 
## Iter: 1 fn: 134.6419  Pars:  0.076562252326 0.000000214880 0.000000002369 0.923437523376 0.000000002367 0.000000002367 0.000000002369 0.542856534002
## Iter: 2 fn: 134.6419  Pars:  0.0765622744671 0.0000001894393 0.0000000003812 0.9234375345713 0.0000000003799 0.0000000003799 0.0000000003812 0.5428564920787
## Iter: 3 fn: 134.6419  Pars:  0.0765622761271 0.0000001877334 0.0000000002490 0.9234375351460 0.0000000002477 0.0000000002477 0.0000000002490 0.5428564818674
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 150.0954  Pars:  0.0499999606403 0.0199999635144 0.0000000001635 0.9300000752424 0.0000000001641 0.0000000001641 0.0000000001638 0.1999998619850
## Iter: 2 fn: 150.0954  Pars:  5.000e-02 2.000e-02 4.823e-11 9.300e-01 4.889e-11 4.889e-11 4.861e-11 2.000e-01
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 100.8425  Pars:  0.039999495190 0.015999963656 0.000000007825 0.944000509625 0.000000007967 0.000000007967 0.000000007823 0.499997028567
## Iter: 2 fn: 100.8425  Pars:  0.0399999036867 0.0159999766571 0.0000000007674 0.9440001164614 0.0000000008304 0.0000000008304 0.0000000007666 0.4999991977046
## Iter: 3 fn: 100.8425  Pars:  0.0399999053152 0.0159999767258 0.0000000002108 0.9440001169994 0.0000000002694 0.0000000002694 0.0000000002100 0.4999992149097
## Iter: 4 fn: 100.8425  Pars:  4.000e-02 1.600e-02 3.826e-11 9.440e-01 9.543e-11 9.543e-11 3.748e-11 5.000e-01
## solnp--> Completed in 4 iterations
## 
## Iter: 1 fn: 81.2853   Pars:  3.600e-02 3.000e-02 7.593e-12 9.340e-01 7.618e-12 7.618e-12 7.772e-12 6.667e-01
## Iter: 2 fn: 81.2853   Pars:  3.600e-02 3.000e-02 5.021e-12 9.340e-01 5.045e-12 5.045e-12 5.200e-12 6.667e-01
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.2764  Pars:  0.041142771823 0.030857105168 0.000000002388 0.928000113637 0.000000002323 0.000000002323 0.000000002391 0.416665957602
## Iter: 2 fn: 128.2764  Pars:  0.0411427721306 0.0308571052407 0.0000000003023 0.9280001215177 0.0000000002522 0.0000000002522 0.0000000003044 0.4166659589663
## Iter: 3 fn: 128.2764  Pars:  0.0411427715733 0.0308571049308 0.0000000001650 0.9280001229323 0.0000000001158 0.0000000001158 0.0000000001670 0.4166659551953
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 131.8840  Pars:  0.042470551085 0.015647016225 0.000000002271 0.941882423658 0.000000002271 0.000000002271 0.000000002271 0.105263111226
## Iter: 2 fn: 131.8840  Pars:  0.0424705514907 0.0156470163053 0.0000000002666 0.9418824311377 0.0000000002666 0.0000000002666 0.0000000002666 0.1052631121290
## Iter: 3 fn: 131.8840  Pars:  0.0424705515292 0.0156470163278 0.0000000001336 0.9418824316085 0.0000000001336 0.0000000001336 0.0000000001336 0.1052631119743
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 128.2273  Pars:  0.03755549203 0.02599996372 0.00000001118 0.93644449953 0.00000001121 0.00000001121 0.00000001118 0.30769180979
## Iter: 2 fn: 128.2272  Pars:  0.0375554937072 0.0259999655631 0.0000000001133 0.9364445402695 0.0000000001173 0.0000000001173 0.0000000001122 0.3076918150389
## Iter: 3 fn: 128.2272  Pars:  3.756e-02 2.600e-02 6.863e-11 9.364e-01 7.263e-11 7.263e-11 6.758e-11 3.077e-01
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 168.8418  Pars:  0.0528999584716 0.0275999615252 0.0000000007793 0.9195000769200 0.0000000007879 0.0000000007879 0.0000000007809 0.1304346686963
## Iter: 2 fn: 168.8418  Pars:  0.0528999586042 0.0275999616437 0.0000000004463 0.9195000779488 0.0000000004546 0.0000000004546 0.0000000004479 0.1304346687845
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 178.7014  Pars:  0.0569411277836 0.0336470251744 0.0000000005190 0.9094118450339 0.0000000005122 0.0000000005122 0.0000000005172 0.2272725082730
## Iter: 2 fn: 178.7014  Pars:  0.0569411280763 0.0336470251668 0.0000000002148 0.9094118459123 0.0000000002083 0.0000000002083 0.0000000002131 0.2272725114672
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 179.6872  Pars:  5.408e-02 3.328e-02 4.054e-11 9.126e-01 4.313e-11 4.313e-11 4.125e-11 3.846e-02
## Iter: 2 fn: 179.6872  Pars:  5.408e-02 3.328e-02 8.979e-12 9.126e-01 1.156e-11 1.156e-11 9.684e-12 3.846e-02
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1415.6461     Pars:  0.04587296618 0.02158726744 0.00000001089 0.93253972283 0.00000001091 0.00000001091 0.00000001090 0.25882326898
## Iter: 2 fn: 1415.6459     Pars:  0.0458729682871 0.0215872683764 0.0000000007563 0.9325397603040 0.0000000007589 0.0000000007589 0.0000000007585 0.2588232714950
## Iter: 3 fn: 1415.6458     Pars:  0.0458729684759 0.0215872681847 0.0000000003604 0.9325397618910 0.0000000003628 0.0000000003628 0.0000000003624 0.2588232755429
## solnp--> Completed in 3 iterations
round(res_dk$param.lca[,1:4], 3)
##        [,1] [,2]  [,3]  [,4]
## lgg   0.077 0.05 0.040 0.036
## lgk   0.000 0.02 0.016 0.030
## lgc   0.000 0.00 0.000 0.000
## lkk   0.923 0.93 0.944 0.934
## lcg   0.000 0.00 0.000 0.000
## lck   0.000 0.00 0.000 0.000
## lcc   0.000 0.00 0.000 0.000
## gamma 0.543 0.20 0.500 0.667
round(res_dk$est.learning[1:4], 3)
## [1] 0.000 0.020 0.016 0.030

Standard Errors

# Raw 
# Generate some data without DK
pre_test <- data.frame(item1=c(1,0,0,1,0), item2=c(1,NA,0,1,0)) 
pst_test <-  pre_test + cbind(c(0,1,1,0,0), c(0,1,0,0,1))
diff <- pst_test - pre_test
stnd_err <-  sapply(diff, function(x) sqrt(var(x, na.rm=T)/(length(x)-1)))

# Bootstrapped s.e.

# LCA model
lca_stnd_err <- guess_stnderr(alldat[,t1], alldat[,t2], 10)
## [1] 1
## 
## Iter: 1 fn: 105.3595  Pars:  0.046722577160 0.000000007789 0.953277414759 0.379314763477
## Iter: 2 fn: 105.3595  Pars:  0.046721728967 0.000000004953 0.953278266080 0.379305162713
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 158.6721  Pars:  0.05095 0.02316 0.92589 0.13636
## Iter: 2 fn: 158.6721  Pars:  0.05095 0.02316 0.92589 0.13636
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## Iter: 2 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 87.5072   Pars:  0.054001 0.005998 0.940001 0.666678
## Iter: 2 fn: 87.5072   Pars:  0.05400 0.00600 0.94000 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.5056  Pars:  0.04225 0.01950 0.93825 0.38463
## Iter: 2 fn: 121.5056  Pars:  0.04225 0.01950 0.93825 0.38461
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 126.1123  Pars:  0.03812 0.01694 0.94494 0.05555
## Iter: 2 fn: 126.1123  Pars:  0.03812 0.01694 0.94494 0.05556
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 135.1800  Pars:  0.04114 0.03772 0.92114 0.41662
## Iter: 2 fn: 135.1800  Pars:  0.04114 0.03771 0.92114 0.41667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.3189  Pars:  0.06827 0.02560 0.90613 0.06250
## Iter: 2 fn: 189.3189  Pars:  0.06827 0.02560 0.90613 0.06250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 155.0273  Pars:  0.05120 0.03520 0.91360 0.37500
## Iter: 2 fn: 155.0273  Pars:  0.05120 0.03520 0.91360 0.37500
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 182.5722  Pars:  0.05608 0.03323 0.91069 0.03705
## Iter: 2 fn: 182.5722  Pars:  0.05608 0.03323 0.91069 0.03704
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1390.1695     Pars:  0.04517 0.01969 0.93514 0.23838
## Iter: 2 fn: 1390.1695     Pars:  0.04517 0.01969 0.93514 0.23837
## solnp--> Completed in 2 iterations
## [1] 2
## 
## Iter: 1 fn: 130.7062  Pars:  0.0722518775 0.0000001279 0.9277479943 0.5294248039
## Iter: 2 fn: 130.7062  Pars:  0.07224990984 0.00000001749 0.92775007267 0.52941139466
## Iter: 3 fn: 130.7062  Pars:  0.072249918660 0.000000001945 0.927750079395 0.529411409792
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 154.0044  Pars:  0.04050 0.03150 0.92800 0.11111
## Iter: 2 fn: 154.0044  Pars:  0.04050 0.03150 0.92800 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 73.0666   Pars:  0.03600 0.01800 0.94600 0.66667
## Iter: 2 fn: 73.0666   Pars:  0.03600 0.01800 0.94600 0.66666
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0849   Pars:  0.1620727635 0.0000009363 0.8379262999 0.8889460210
## Iter: 2 fn: 89.0849   Pars:  0.1619965935 0.0000007011 0.8380027054 0.8888886383
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.2376  Pars:  0.049999 0.006667 0.943334 0.399998
## Iter: 2 fn: 118.2376  Pars:  0.050000 0.006667 0.943333 0.400000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 123.7286  Pars:  0.02817 0.02600 0.94583 0.07692
## Iter: 2 fn: 123.7286  Pars:  0.02817 0.02600 0.94583 0.07692
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 135.2690  Pars:  0.03756 0.03178 0.93067 0.30768
## Iter: 2 fn: 135.2690  Pars:  0.03756 0.03178 0.93067 0.30769
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08695
## Iter: 2 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08696
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.3867  Pars:  0.08577 0.01588 0.89835 0.37038
## Iter: 2 fn: 189.3867  Pars:  0.08576 0.01588 0.89835 0.37037
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 166.9102  Pars:  0.04399995993 0.03599995479 0.92000008499 0.00000007538
## Iter: 2 fn: 166.9102  Pars:  0.04399995816 0.03599995511 0.92000008673 0.00000003559
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1382.9524     Pars:  0.04654 0.02003 0.93344 0.29091
## Iter: 2 fn: 1382.9524     Pars:  0.04654 0.02003 0.93344 0.29091
## solnp--> Completed in 2 iterations
## [1] 3
## 
## Iter: 1 fn: 121.0777  Pars:  0.05760 0.02400 0.91840 0.58333
## Iter: 2 fn: 121.0777  Pars:  0.05760 0.02400 0.91840 0.58333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 155.4906  Pars:  0.05236 0.01964 0.92800 0.08333
## Iter: 2 fn: 155.4906  Pars:  0.05236 0.01964 0.92800 0.08333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 79.4208   Pars:  0.02420 0.00660 0.96920 0.09091
## Iter: 2 fn: 79.4208   Pars:  0.02420 0.00660 0.96920 0.09091
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 90.4891   Pars:  0.03267 0.02801 0.93932 0.57152
## Iter: 2 fn: 90.4891   Pars:  0.03267 0.02800 0.93933 0.57145
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 126.4468  Pars:  0.05625 0.01125 0.93250 0.46667
## Iter: 2 fn: 126.4468  Pars:  0.05625 0.01125 0.93250 0.46667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 122.7553  Pars:  0.03612 0.01700 0.94688 0.05880
## Iter: 2 fn: 122.7553  Pars:  0.03613 0.01700 0.94687 0.05883
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 122.8513  Pars:  0.03025 0.03025 0.93950 0.27272
## Iter: 2 fn: 122.8513  Pars:  0.03025 0.03025 0.93950 0.27273
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 169.0715  Pars:  0.05095 0.03011 0.91895 0.13636
## Iter: 2 fn: 169.0715  Pars:  0.05095 0.03011 0.91895 0.13636
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.3149  Pars:  0.02880 0.04080 0.93040 0.16667
## Iter: 2 fn: 142.3149  Pars:  0.02880 0.04080 0.93040 0.16667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 170.2204  Pars:  0.039999967 0.041999957 0.918000075 0.000000283
## Iter: 2 fn: 170.2204  Pars:  0.0399999623 0.0419999567 0.9180000810 0.0000001543
## Iter: 3 fn: 170.2204  Pars:  0.03999995724 0.04199995640 0.91800008636 0.00000002973
## Iter: 4 fn: 170.2204  Pars:  0.039999956124 0.041999956264 0.918000087612 0.000000003726
## solnp--> Completed in 4 iterations
## 
## Iter: 1 fn: 1336.7458     Pars:  0.03768 0.02396 0.93836 0.19867
## Iter: 2 fn: 1336.7458     Pars:  0.03769 0.02396 0.93835 0.19868
## solnp--> Completed in 2 iterations
## [1] 4
## 
## Iter: 1 fn: 150.0779  Pars:  0.0770416027250 0.0000000005341 0.9229583964483 0.4418602409733
## Iter: 2 fn: 150.0779  Pars:  0.0770416051094 0.0000000001822 0.9229583947081 0.4418602369692
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 125.5305  Pars:  0.04654 0.01163 0.94182 0.31249
## Iter: 2 fn: 125.5305  Pars:  0.04655 0.01164 0.94182 0.31250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 91.6741   Pars:  0.02700 0.01500 0.95800 0.33333
## Iter: 2 fn: 91.6741   Pars:  0.02700 0.01500 0.95800 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 76.1239   Pars:  0.07200 0.03601 0.89199 0.83335
## Iter: 2 fn: 76.1239   Pars:  0.07200 0.03600 0.89200 0.83334
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 144.1488  Pars:  0.04655 0.02618 0.92727 0.31250
## Iter: 2 fn: 144.1488  Pars:  0.04655 0.02618 0.92727 0.31250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.5057  Pars:  0.057166618176 0.000000002602 0.942833378930 0.142857098211
## Iter: 2 fn: 128.5057  Pars:  0.0571666209623 0.0000000008003 0.9428333782377 0.1428570621846
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 114.5824  Pars:  0.01829 0.03429 0.94743 0.12500
## Iter: 2 fn: 114.5824  Pars:  0.01829 0.03429 0.94743 0.12500
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 143.7175  Pars:  0.03854 0.02720 0.93427 0.11765
## Iter: 2 fn: 143.7175  Pars:  0.03853 0.02720 0.93427 0.11765
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 192.5972  Pars:  0.06943 0.02828 0.90229 0.22223
## Iter: 2 fn: 192.5972  Pars:  0.06943 0.02829 0.90229 0.22222
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 170.0458  Pars:  0.05208 0.02917 0.91875 0.04000
## Iter: 2 fn: 170.0458  Pars:  0.05208 0.02917 0.91875 0.04000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1381.9339     Pars:  0.04857 0.01619 0.93524 0.27118
## Iter: 2 fn: 1381.9339     Pars:  0.04857 0.01619 0.93524 0.27118
## solnp--> Completed in 2 iterations
## [1] 5
## 
## Iter: 1 fn: 149.6656  Pars:  0.067846 0.006462 0.925692 0.380952
## Iter: 2 fn: 149.6656  Pars:  0.067846 0.006462 0.925692 0.380952
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 173.6807  Pars:  0.06945 0.01666 0.91389 0.28001
## Iter: 2 fn: 173.6807  Pars:  0.06944 0.01667 0.91389 0.28000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 87.4491   Pars:  0.03199 0.01601 0.95199 0.50004
## Iter: 2 fn: 87.4491   Pars:  0.03200 0.01600 0.95200 0.49999
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0477   Pars:  0.03600 0.04200 0.92200 0.66666
## Iter: 2 fn: 89.0477   Pars:  0.03600 0.04200 0.92200 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 108.3869  Pars:  0.03333 0.02333 0.94334 0.40000
## Iter: 2 fn: 108.3869  Pars:  0.03333 0.02333 0.94333 0.40000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 98.9920   Pars:  0.035636 0.005091 0.959273 0.214273
## Iter: 2 fn: 98.9920   Pars:  0.035636 0.005091 0.959273 0.214286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.7326  Pars:  0.02025 0.03375 0.94600 0.11117
## Iter: 2 fn: 118.7326  Pars:  0.02025 0.03375 0.94600 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 183.2884  Pars:  0.06145 0.02836 0.91018 0.15385
## Iter: 2 fn: 183.2884  Pars:  0.06145 0.02836 0.91018 0.15385
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 210.4495  Pars:  0.08182 0.03000 0.88818 0.26667
## Iter: 2 fn: 210.4495  Pars:  0.08182 0.03000 0.88818 0.26667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08695
## Iter: 2 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08696
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1412.9777     Pars:  0.04659 0.02059 0.93283 0.26163
## Iter: 2 fn: 1412.9777     Pars:  0.04659 0.02059 0.93283 0.26163
## solnp--> Completed in 2 iterations
## [1] 6
## 
## Iter: 1 fn: 105.6160  Pars:  0.06250072528 0.00000004976 0.93749922467 0.60000285361
## Iter: 2 fn: 105.6160  Pars:  0.062499894608 0.000000002683 0.937500102709 0.599999479155
## Iter: 3 fn: 105.6160  Pars:  0.062499894566 0.000000001559 0.937500103875 0.599999477922
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 162.5757  Pars:  0.04512 0.03325 0.92163 0.15791
## Iter: 2 fn: 162.5757  Pars:  0.04512 0.03325 0.92163 0.15789
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0477   Pars:  0.01800 0.02700 0.95500 0.33333
## Iter: 2 fn: 89.0477   Pars:  0.01800 0.02700 0.95500 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.2923   Pars:  0.03199 0.08801 0.88000 0.75000
## Iter: 2 fn: 89.2923   Pars:  0.03200 0.08800 0.88000 0.75000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 103.4635  Pars:  0.05400 0.03000 0.91599 0.66669
## Iter: 2 fn: 103.4635  Pars:  0.05400 0.03000 0.91600 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 136.0270  Pars:  0.04266 0.02133 0.93601 0.24998
## Iter: 2 fn: 136.0270  Pars:  0.04267 0.02133 0.93600 0.25000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.2452  Pars:  0.05397452 0.00002533 0.94600015 0.33317637
## Iter: 2 fn: 121.2452  Pars:  0.0539994284 0.0000005199 0.9460000517 0.3333299539
## Iter: 3 fn: 121.2452  Pars:  0.0539995393 0.0000004084 0.9460000522 0.3333306245
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 134.9492  Pars:  0.04610 0.01467 0.93924 0.04545
## Iter: 2 fn: 134.9492  Pars:  0.04610 0.01467 0.93924 0.04545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 169.1859  Pars:  0.04900 0.03267 0.91833 0.14286
## Iter: 2 fn: 169.1859  Pars:  0.04900 0.03267 0.91833 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 157.5158  Pars:  0.04609 0.02724 0.92667 0.04546
## Iter: 2 fn: 157.5158  Pars:  0.04610 0.02724 0.92667 0.04545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1312.1547     Pars:  0.04143 0.02004 0.93853 0.26144
## Iter: 2 fn: 1312.1547     Pars:  0.04143 0.02004 0.93853 0.26144
## solnp--> Completed in 2 iterations
## [1] 7
## 
## Iter: 1 fn: 137.7057  Pars:  0.05254 0.01546 0.93200 0.35291
## Iter: 2 fn: 137.7057  Pars:  0.05255 0.01545 0.93200 0.35294
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 132.8261  Pars:  0.03853 0.02040 0.94107 0.11765
## Iter: 2 fn: 132.8261  Pars:  0.03853 0.02040 0.94107 0.11765
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 109.2359  Pars:  0.04840 0.01760 0.93400 0.54545
## Iter: 2 fn: 109.2359  Pars:  0.04840 0.01760 0.93400 0.54545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 45.5157   Pars:  0.003999955 0.011999960 0.984000085 0.000001027
## Iter: 2 fn: 45.5157   Pars:  0.00399995087 0.01199995234 0.98400009680 0.00000006701
## Iter: 3 fn: 45.5157   Pars:  0.00399995073 0.01199995205 0.98400009722 0.00000003425
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 105.3140  Pars:  0.043555 0.003111 0.953333 0.357141
## Iter: 2 fn: 105.3140  Pars:  0.043556 0.003111 0.953333 0.357143
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 137.9923  Pars:  0.059524 0.002381 0.938095 0.160000
## Iter: 2 fn: 137.9923  Pars:  0.059524 0.002381 0.938095 0.160000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 137.9947  Pars:  0.05689 0.01778 0.92533 0.43750
## Iter: 2 fn: 137.9947  Pars:  0.05689 0.01778 0.92533 0.43750
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 151.8269  Pars:  0.04900 0.02100 0.93000 0.14286
## Iter: 2 fn: 151.8269  Pars:  0.04900 0.02100 0.93000 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 181.8365  Pars:  0.04446 0.05493 0.90061 0.23530
## Iter: 2 fn: 181.8365  Pars:  0.04446 0.05492 0.90061 0.23530
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 186.3808  Pars:  0.05208 0.03958 0.90833 0.04000
## Iter: 2 fn: 186.3808  Pars:  0.05208 0.03958 0.90833 0.04000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1368.8204     Pars:  0.04287 0.02079 0.93634 0.23032
## Iter: 2 fn: 1368.8204     Pars:  0.04287 0.02079 0.93634 0.23030
## solnp--> Completed in 2 iterations
## [1] 8
## 
## Iter: 1 fn: 138.4520  Pars:  0.0691362976 0.0000001194 0.9308635827 0.4358971394
## Iter: 2 fn: 138.4520  Pars:  0.06913626642 0.00000003935 0.93086369423 0.43589705238
## Iter: 3 fn: 138.4520  Pars:  0.0691363056726 0.0000000001597 0.9308636941681 0.4358972032714
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 139.4971  Pars:  0.04629 0.01800 0.93571 0.22222
## Iter: 2 fn: 139.4971  Pars:  0.04629 0.01800 0.93571 0.22222
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 116.8411  Pars:  0.03600 0.02100 0.94300 0.33332
## Iter: 2 fn: 116.8411  Pars:  0.03600 0.02100 0.94300 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 77.7518   Pars:  0.04900 0.01400 0.93700 0.71429
## Iter: 2 fn: 77.7518   Pars:  0.04900 0.01400 0.93700 0.71428
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.4439  Pars:  0.04800 0.03200 0.92000 0.50000
## Iter: 2 fn: 128.4439  Pars:  0.04800 0.03200 0.92000 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 120.3604  Pars:  0.04050 0.01125 0.94825 0.11111
## Iter: 2 fn: 120.3604  Pars:  0.04050 0.01125 0.94825 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 106.8588  Pars:  0.01633 0.03267 0.95100 0.14279
## Iter: 2 fn: 106.8588  Pars:  0.01633 0.03267 0.95100 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 159.1280  Pars:  0.04033 0.07333 0.88633 0.45455
## Iter: 2 fn: 159.1280  Pars:  0.04033 0.07333 0.88633 0.45455
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.4939  Pars:  0.06760 0.02860 0.90380 0.23078
## Iter: 2 fn: 189.4939  Pars:  0.06760 0.02860 0.90380 0.23077
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 174.6289  Pars:  0.06031 0.02369 0.91600 0.07143
## Iter: 2 fn: 174.6289  Pars:  0.06031 0.02369 0.91600 0.07143
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1389.8039     Pars:  0.04397 0.02323 0.93281 0.27672
## Iter: 2 fn: 1389.8038     Pars:  0.04397 0.02323 0.93281 0.27673
## solnp--> Completed in 2 iterations
## [1] 9
## 
## Iter: 1 fn: 105.0705  Pars:  0.07199982872 0.00000006055 0.92800011044 0.66666604994
## Iter: 2 fn: 105.0705  Pars:  0.07199984310 0.00000001874 0.92800013815 0.66666605337
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 129.9523  Pars:  0.05290 0.00460 0.94250 0.13044
## Iter: 2 fn: 129.9523  Pars:  0.05290 0.00460 0.94250 0.13044
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 94.3171   Pars:  0.02450 0.02800 0.94750 0.42856
## Iter: 2 fn: 94.3171   Pars:  0.02450 0.02800 0.94750 0.42857
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 67.6779   Pars:  0.0845099419486 0.0000000006277 0.9154900571318 0.8461720339470
## Iter: 2 fn: 67.6779   Pars:  0.08449785454 0.00000000032 0.91550214514 0.84615043582
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.0349  Pars:  0.03756 0.03756 0.92489 0.30769
## Iter: 2 fn: 142.0349  Pars:  0.03756 0.03756 0.92489 0.30769
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 131.2505  Pars:  0.04813 0.01013 0.94173 0.21052
## Iter: 2 fn: 131.2505  Pars:  0.04813 0.01013 0.94173 0.21053
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 112.3169  Pars:  0.04000 0.02800 0.93200 0.49998
## Iter: 2 fn: 112.3169  Pars:  0.04000 0.02800 0.93200 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 186.6110  Pars:  0.06145 0.03073 0.90782 0.15385
## Iter: 2 fn: 186.6110  Pars:  0.06145 0.03073 0.90782 0.15385
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 180.2304  Pars:  0.0885963414 0.0000001728 0.9114034854 0.3114817103
## Iter: 2 fn: 180.2303  Pars:  0.08859327043 0.00000004167 0.91140668789 0.31146506929
## Iter: 3 fn: 180.2303  Pars:  0.088598103784 0.000000005886 0.911401890330 0.311490911864
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 182.4494  Pars:  0.0439999677 0.0459999574 0.9100000746 0.0000002526
## Iter: 2 fn: 182.4494  Pars:  0.0439999630 0.0459999571 0.9100000799 0.0000001461
## Iter: 3 fn: 182.4494  Pars:  0.04399995802 0.04599995709 0.91000008489 0.00000003035
## Iter: 4 fn: 182.4494  Pars:  0.043999956688 0.045999956823 0.910000086488 0.000000002915
## solnp--> Completed in 4 iterations
## 
## Iter: 1 fn: 1386.4757     Pars:  0.04755 0.01835 0.93410 0.28070
## Iter: 2 fn: 1386.4757     Pars:  0.04755 0.01835 0.93410 0.28070
## solnp--> Completed in 2 iterations
## [1] 10
## 
## Iter: 1 fn: 128.4439  Pars:  0.057142802903 0.000000007229 0.942857189576 0.299999831435
## Iter: 2 fn: 128.4439  Pars:  0.057142806076 0.000000001737 0.942857192187 0.299999844731
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 160.6000  Pars:  0.05188 0.02471 0.92341 0.19047
## Iter: 2 fn: 160.6000  Pars:  0.05188 0.02471 0.92341 0.19048
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 100.0937  Pars:  0.04050 0.02250 0.93700 0.55555
## Iter: 2 fn: 100.0937  Pars:  0.04050 0.02250 0.93700 0.55555
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.2452  Pars:  0.04800 0.02400 0.92800 0.49998
## Iter: 2 fn: 121.2452  Pars:  0.04800 0.02400 0.92800 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.5063  Pars:  0.06424384 0.00004192 0.93571425 0.53318186
## Iter: 2 fn: 118.5062  Pars:  0.0642847581 0.0000008747 0.9357143672 0.5333297539
## Iter: 3 fn: 118.5062  Pars:  0.0642849366 0.0000006959 0.9357143675 0.5333304101
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 114.0325  Pars:  0.03462 0.01385 0.95154 0.13334
## Iter: 2 fn: 114.0325  Pars:  0.03462 0.01385 0.95154 0.13333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.3493  Pars:  0.06453 0.01173 0.92373 0.31818
## Iter: 2 fn: 156.3493  Pars:  0.06453 0.01173 0.92373 0.31818
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.8815  Pars:  0.04444 0.02000 0.93556 0.10000
## Iter: 2 fn: 142.8815  Pars:  0.04444 0.02000 0.93556 0.10000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 220.6438  Pars:  0.08736 0.03382 0.87882 0.29033
## Iter: 2 fn: 220.6438  Pars:  0.08736 0.03382 0.87882 0.29032
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 167.0704  Pars:  0.05009 0.02922 0.92069 0.04168
## Iter: 2 fn: 167.0704  Pars:  0.05009 0.02922 0.92070 0.04167
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1461.9631     Pars:  0.05249 0.01704 0.93047 0.27225
## Iter: 2 fn: 1461.9631     Pars:  0.05249 0.01704 0.93047 0.27225
## solnp--> Completed in 2 iterations
sapply(lca_stnd_err, function(x) round(head(x, 1),3))
## $stnderrs.lca.params
##     [,1]  [,2]  [,3]  [,4]  [,5] [,6]  [,7] [,8]  [,9] [,10]
## lgg 0.01 0.009 0.009 0.043 0.009 0.01 0.017 0.01 0.021 0.006
## 
## $avg.effects
##      [,1] [,2] [,3]  [,4]  [,5]  [,6]  [,7]  [,8] [,9] [,10] [,11]
## lca 0.005 0.02 0.02 0.025 0.019 0.012 0.026 0.029 0.03 0.033  0.02
## 
## $stnderrs.effects
##      [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11]
## lca 0.008 0.009 0.007 0.026 0.013 0.008 0.012 0.016 0.014 0.008 0.002
lca_dk_stnd_err <- guess_stnderr(alldat_dk[,t1], alldat_dk[,t2], 10)
## [1] 1
## 
## Iter: 1 fn: 105.3595  Pars:  0.046722577160 0.000000007789 0.953277414759 0.379314763477
## Iter: 2 fn: 105.3595  Pars:  0.046721728967 0.000000004953 0.953278266080 0.379305162713
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 158.6721  Pars:  0.05095 0.02316 0.92589 0.13636
## Iter: 2 fn: 158.6721  Pars:  0.05095 0.02316 0.92589 0.13636
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## Iter: 2 fn: 81.2853   Pars:  0.03600 0.03000 0.93400 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 87.5072   Pars:  0.054001 0.005998 0.940001 0.666678
## Iter: 2 fn: 87.5072   Pars:  0.05400 0.00600 0.94000 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.5056  Pars:  0.04225 0.01950 0.93825 0.38463
## Iter: 2 fn: 121.5056  Pars:  0.04225 0.01950 0.93825 0.38461
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 126.1123  Pars:  0.03812 0.01694 0.94494 0.05555
## Iter: 2 fn: 126.1123  Pars:  0.03812 0.01694 0.94494 0.05556
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 135.1800  Pars:  0.04114 0.03772 0.92114 0.41662
## Iter: 2 fn: 135.1800  Pars:  0.04114 0.03771 0.92114 0.41667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.3189  Pars:  0.06827 0.02560 0.90613 0.06250
## Iter: 2 fn: 189.3189  Pars:  0.06827 0.02560 0.90613 0.06250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 155.0273  Pars:  0.05120 0.03520 0.91360 0.37500
## Iter: 2 fn: 155.0273  Pars:  0.05120 0.03520 0.91360 0.37500
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 182.5722  Pars:  0.05608 0.03323 0.91069 0.03705
## Iter: 2 fn: 182.5722  Pars:  0.05608 0.03323 0.91069 0.03704
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1390.1695     Pars:  0.04517 0.01969 0.93514 0.23838
## Iter: 2 fn: 1390.1695     Pars:  0.04517 0.01969 0.93514 0.23837
## solnp--> Completed in 2 iterations
## [1] 2
## 
## Iter: 1 fn: 130.7062  Pars:  0.0722518775 0.0000001279 0.9277479943 0.5294248039
## Iter: 2 fn: 130.7062  Pars:  0.07224990984 0.00000001749 0.92775007267 0.52941139466
## Iter: 3 fn: 130.7062  Pars:  0.072249918660 0.000000001945 0.927750079395 0.529411409792
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 154.0044  Pars:  0.04050 0.03150 0.92800 0.11111
## Iter: 2 fn: 154.0044  Pars:  0.04050 0.03150 0.92800 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 73.0666   Pars:  0.03600 0.01800 0.94600 0.66667
## Iter: 2 fn: 73.0666   Pars:  0.03600 0.01800 0.94600 0.66666
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0849   Pars:  0.1620727635 0.0000009363 0.8379262999 0.8889460210
## Iter: 2 fn: 89.0849   Pars:  0.1619965935 0.0000007011 0.8380027054 0.8888886383
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.2376  Pars:  0.049999 0.006667 0.943334 0.399998
## Iter: 2 fn: 118.2376  Pars:  0.050000 0.006667 0.943333 0.400000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 123.7286  Pars:  0.02817 0.02600 0.94583 0.07692
## Iter: 2 fn: 123.7286  Pars:  0.02817 0.02600 0.94583 0.07692
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 135.2690  Pars:  0.03756 0.03178 0.93067 0.30768
## Iter: 2 fn: 135.2690  Pars:  0.03756 0.03178 0.93067 0.30769
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08695
## Iter: 2 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08696
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.3867  Pars:  0.08577 0.01588 0.89835 0.37038
## Iter: 2 fn: 189.3867  Pars:  0.08576 0.01588 0.89835 0.37037
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 166.9102  Pars:  0.04399995993 0.03599995479 0.92000008499 0.00000007538
## Iter: 2 fn: 166.9102  Pars:  0.04399995816 0.03599995511 0.92000008673 0.00000003559
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1382.9524     Pars:  0.04654 0.02003 0.93344 0.29091
## Iter: 2 fn: 1382.9524     Pars:  0.04654 0.02003 0.93344 0.29091
## solnp--> Completed in 2 iterations
## [1] 3
## 
## Iter: 1 fn: 121.0777  Pars:  0.05760 0.02400 0.91840 0.58333
## Iter: 2 fn: 121.0777  Pars:  0.05760 0.02400 0.91840 0.58333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 155.4906  Pars:  0.05236 0.01964 0.92800 0.08333
## Iter: 2 fn: 155.4906  Pars:  0.05236 0.01964 0.92800 0.08333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 79.4208   Pars:  0.02420 0.00660 0.96920 0.09091
## Iter: 2 fn: 79.4208   Pars:  0.02420 0.00660 0.96920 0.09091
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 90.4891   Pars:  0.03267 0.02801 0.93932 0.57152
## Iter: 2 fn: 90.4891   Pars:  0.03267 0.02800 0.93933 0.57145
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 126.4468  Pars:  0.05625 0.01125 0.93250 0.46667
## Iter: 2 fn: 126.4468  Pars:  0.05625 0.01125 0.93250 0.46667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 122.7553  Pars:  0.03612 0.01700 0.94688 0.05880
## Iter: 2 fn: 122.7553  Pars:  0.03613 0.01700 0.94687 0.05883
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 122.8513  Pars:  0.03025 0.03025 0.93950 0.27272
## Iter: 2 fn: 122.8513  Pars:  0.03025 0.03025 0.93950 0.27273
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 169.0715  Pars:  0.05095 0.03011 0.91895 0.13636
## Iter: 2 fn: 169.0715  Pars:  0.05095 0.03011 0.91895 0.13636
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.3149  Pars:  0.02880 0.04080 0.93040 0.16667
## Iter: 2 fn: 142.3149  Pars:  0.02880 0.04080 0.93040 0.16667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 170.2204  Pars:  0.039999967 0.041999957 0.918000075 0.000000283
## Iter: 2 fn: 170.2204  Pars:  0.0399999623 0.0419999567 0.9180000810 0.0000001543
## Iter: 3 fn: 170.2204  Pars:  0.03999995724 0.04199995640 0.91800008636 0.00000002973
## Iter: 4 fn: 170.2204  Pars:  0.039999956124 0.041999956264 0.918000087612 0.000000003726
## solnp--> Completed in 4 iterations
## 
## Iter: 1 fn: 1336.7458     Pars:  0.03768 0.02396 0.93836 0.19867
## Iter: 2 fn: 1336.7458     Pars:  0.03769 0.02396 0.93835 0.19868
## solnp--> Completed in 2 iterations
## [1] 4
## 
## Iter: 1 fn: 150.0779  Pars:  0.0770416027250 0.0000000005341 0.9229583964483 0.4418602409733
## Iter: 2 fn: 150.0779  Pars:  0.0770416051094 0.0000000001822 0.9229583947081 0.4418602369692
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 125.5305  Pars:  0.04654 0.01163 0.94182 0.31249
## Iter: 2 fn: 125.5305  Pars:  0.04655 0.01164 0.94182 0.31250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 91.6741   Pars:  0.02700 0.01500 0.95800 0.33333
## Iter: 2 fn: 91.6741   Pars:  0.02700 0.01500 0.95800 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 76.1239   Pars:  0.07200 0.03601 0.89199 0.83335
## Iter: 2 fn: 76.1239   Pars:  0.07200 0.03600 0.89200 0.83334
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 144.1488  Pars:  0.04655 0.02618 0.92727 0.31250
## Iter: 2 fn: 144.1488  Pars:  0.04655 0.02618 0.92727 0.31250
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.5057  Pars:  0.057166618176 0.000000002602 0.942833378930 0.142857098211
## Iter: 2 fn: 128.5057  Pars:  0.0571666209623 0.0000000008003 0.9428333782377 0.1428570621846
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 114.5824  Pars:  0.01829 0.03429 0.94743 0.12500
## Iter: 2 fn: 114.5824  Pars:  0.01829 0.03429 0.94743 0.12500
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 143.7175  Pars:  0.03854 0.02720 0.93427 0.11765
## Iter: 2 fn: 143.7175  Pars:  0.03853 0.02720 0.93427 0.11765
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 192.5972  Pars:  0.06943 0.02828 0.90229 0.22223
## Iter: 2 fn: 192.5972  Pars:  0.06943 0.02829 0.90229 0.22222
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 170.0458  Pars:  0.05208 0.02917 0.91875 0.04000
## Iter: 2 fn: 170.0458  Pars:  0.05208 0.02917 0.91875 0.04000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1381.9339     Pars:  0.04857 0.01619 0.93524 0.27118
## Iter: 2 fn: 1381.9339     Pars:  0.04857 0.01619 0.93524 0.27118
## solnp--> Completed in 2 iterations
## [1] 5
## 
## Iter: 1 fn: 149.6656  Pars:  0.067846 0.006462 0.925692 0.380952
## Iter: 2 fn: 149.6656  Pars:  0.067846 0.006462 0.925692 0.380952
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 173.6807  Pars:  0.06945 0.01666 0.91389 0.28001
## Iter: 2 fn: 173.6807  Pars:  0.06944 0.01667 0.91389 0.28000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 87.4491   Pars:  0.03199 0.01601 0.95199 0.50004
## Iter: 2 fn: 87.4491   Pars:  0.03200 0.01600 0.95200 0.49999
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0477   Pars:  0.03600 0.04200 0.92200 0.66666
## Iter: 2 fn: 89.0477   Pars:  0.03600 0.04200 0.92200 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 108.3869  Pars:  0.03333 0.02333 0.94334 0.40000
## Iter: 2 fn: 108.3869  Pars:  0.03333 0.02333 0.94333 0.40000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 98.9920   Pars:  0.035636 0.005091 0.959273 0.214273
## Iter: 2 fn: 98.9920   Pars:  0.035636 0.005091 0.959273 0.214286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.7326  Pars:  0.02025 0.03375 0.94600 0.11117
## Iter: 2 fn: 118.7326  Pars:  0.02025 0.03375 0.94600 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 183.2884  Pars:  0.06145 0.02836 0.91018 0.15385
## Iter: 2 fn: 183.2884  Pars:  0.06145 0.02836 0.91018 0.15385
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 210.4495  Pars:  0.08182 0.03000 0.88818 0.26667
## Iter: 2 fn: 210.4495  Pars:  0.08182 0.03000 0.88818 0.26667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08695
## Iter: 2 fn: 156.1165  Pars:  0.05038 0.02190 0.92771 0.08696
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1412.9777     Pars:  0.04659 0.02059 0.93283 0.26163
## Iter: 2 fn: 1412.9777     Pars:  0.04659 0.02059 0.93283 0.26163
## solnp--> Completed in 2 iterations
## [1] 6
## 
## Iter: 1 fn: 105.6160  Pars:  0.06250072528 0.00000004976 0.93749922467 0.60000285361
## Iter: 2 fn: 105.6160  Pars:  0.062499894608 0.000000002683 0.937500102709 0.599999479155
## Iter: 3 fn: 105.6160  Pars:  0.062499894566 0.000000001559 0.937500103875 0.599999477922
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 162.5757  Pars:  0.04512 0.03325 0.92163 0.15791
## Iter: 2 fn: 162.5757  Pars:  0.04512 0.03325 0.92163 0.15789
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.0477   Pars:  0.01800 0.02700 0.95500 0.33333
## Iter: 2 fn: 89.0477   Pars:  0.01800 0.02700 0.95500 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 89.2923   Pars:  0.03199 0.08801 0.88000 0.75000
## Iter: 2 fn: 89.2923   Pars:  0.03200 0.08800 0.88000 0.75000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 103.4635  Pars:  0.05400 0.03000 0.91599 0.66669
## Iter: 2 fn: 103.4635  Pars:  0.05400 0.03000 0.91600 0.66667
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 136.0270  Pars:  0.04266 0.02133 0.93601 0.24998
## Iter: 2 fn: 136.0270  Pars:  0.04267 0.02133 0.93600 0.25000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.2452  Pars:  0.05397452 0.00002533 0.94600015 0.33317637
## Iter: 2 fn: 121.2452  Pars:  0.0539994284 0.0000005199 0.9460000517 0.3333299539
## Iter: 3 fn: 121.2452  Pars:  0.0539995393 0.0000004084 0.9460000522 0.3333306245
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 134.9492  Pars:  0.04610 0.01467 0.93924 0.04545
## Iter: 2 fn: 134.9492  Pars:  0.04610 0.01467 0.93924 0.04545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 169.1859  Pars:  0.04900 0.03267 0.91833 0.14286
## Iter: 2 fn: 169.1859  Pars:  0.04900 0.03267 0.91833 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 157.5158  Pars:  0.04609 0.02724 0.92667 0.04546
## Iter: 2 fn: 157.5158  Pars:  0.04610 0.02724 0.92667 0.04545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1312.1547     Pars:  0.04143 0.02004 0.93853 0.26144
## Iter: 2 fn: 1312.1547     Pars:  0.04143 0.02004 0.93853 0.26144
## solnp--> Completed in 2 iterations
## [1] 7
## 
## Iter: 1 fn: 137.7057  Pars:  0.05254 0.01546 0.93200 0.35291
## Iter: 2 fn: 137.7057  Pars:  0.05255 0.01545 0.93200 0.35294
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 132.8261  Pars:  0.03853 0.02040 0.94107 0.11765
## Iter: 2 fn: 132.8261  Pars:  0.03853 0.02040 0.94107 0.11765
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 109.2359  Pars:  0.04840 0.01760 0.93400 0.54545
## Iter: 2 fn: 109.2359  Pars:  0.04840 0.01760 0.93400 0.54545
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 45.5157   Pars:  0.003999955 0.011999960 0.984000085 0.000001027
## Iter: 2 fn: 45.5157   Pars:  0.00399995087 0.01199995234 0.98400009680 0.00000006701
## Iter: 3 fn: 45.5157   Pars:  0.00399995073 0.01199995205 0.98400009722 0.00000003425
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 105.3140  Pars:  0.043555 0.003111 0.953333 0.357141
## Iter: 2 fn: 105.3140  Pars:  0.043556 0.003111 0.953333 0.357143
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 137.9923  Pars:  0.059524 0.002381 0.938095 0.160000
## Iter: 2 fn: 137.9923  Pars:  0.059524 0.002381 0.938095 0.160000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 137.9947  Pars:  0.05689 0.01778 0.92533 0.43750
## Iter: 2 fn: 137.9947  Pars:  0.05689 0.01778 0.92533 0.43750
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 151.8269  Pars:  0.04900 0.02100 0.93000 0.14286
## Iter: 2 fn: 151.8269  Pars:  0.04900 0.02100 0.93000 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 181.8365  Pars:  0.04446 0.05493 0.90061 0.23530
## Iter: 2 fn: 181.8365  Pars:  0.04446 0.05492 0.90061 0.23530
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 186.3808  Pars:  0.05208 0.03958 0.90833 0.04000
## Iter: 2 fn: 186.3808  Pars:  0.05208 0.03958 0.90833 0.04000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1368.8204     Pars:  0.04287 0.02079 0.93634 0.23032
## Iter: 2 fn: 1368.8204     Pars:  0.04287 0.02079 0.93634 0.23030
## solnp--> Completed in 2 iterations
## [1] 8
## 
## Iter: 1 fn: 138.4520  Pars:  0.0691362976 0.0000001194 0.9308635827 0.4358971394
## Iter: 2 fn: 138.4520  Pars:  0.06913626642 0.00000003935 0.93086369423 0.43589705238
## Iter: 3 fn: 138.4520  Pars:  0.0691363056726 0.0000000001597 0.9308636941681 0.4358972032714
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 139.4971  Pars:  0.04629 0.01800 0.93571 0.22222
## Iter: 2 fn: 139.4971  Pars:  0.04629 0.01800 0.93571 0.22222
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 116.8411  Pars:  0.03600 0.02100 0.94300 0.33332
## Iter: 2 fn: 116.8411  Pars:  0.03600 0.02100 0.94300 0.33333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 77.7518   Pars:  0.04900 0.01400 0.93700 0.71429
## Iter: 2 fn: 77.7518   Pars:  0.04900 0.01400 0.93700 0.71428
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 128.4439  Pars:  0.04800 0.03200 0.92000 0.50000
## Iter: 2 fn: 128.4439  Pars:  0.04800 0.03200 0.92000 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 120.3604  Pars:  0.04050 0.01125 0.94825 0.11111
## Iter: 2 fn: 120.3604  Pars:  0.04050 0.01125 0.94825 0.11111
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 106.8588  Pars:  0.01633 0.03267 0.95100 0.14279
## Iter: 2 fn: 106.8588  Pars:  0.01633 0.03267 0.95100 0.14286
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 159.1280  Pars:  0.04033 0.07333 0.88633 0.45455
## Iter: 2 fn: 159.1280  Pars:  0.04033 0.07333 0.88633 0.45455
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 189.4939  Pars:  0.06760 0.02860 0.90380 0.23078
## Iter: 2 fn: 189.4939  Pars:  0.06760 0.02860 0.90380 0.23077
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 174.6289  Pars:  0.06031 0.02369 0.91600 0.07143
## Iter: 2 fn: 174.6289  Pars:  0.06031 0.02369 0.91600 0.07143
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1389.8039     Pars:  0.04397 0.02323 0.93281 0.27672
## Iter: 2 fn: 1389.8038     Pars:  0.04397 0.02323 0.93281 0.27673
## solnp--> Completed in 2 iterations
## [1] 9
## 
## Iter: 1 fn: 105.0705  Pars:  0.07199982872 0.00000006055 0.92800011044 0.66666604994
## Iter: 2 fn: 105.0705  Pars:  0.07199984310 0.00000001874 0.92800013815 0.66666605337
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 129.9523  Pars:  0.05290 0.00460 0.94250 0.13044
## Iter: 2 fn: 129.9523  Pars:  0.05290 0.00460 0.94250 0.13044
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 94.3171   Pars:  0.02450 0.02800 0.94750 0.42856
## Iter: 2 fn: 94.3171   Pars:  0.02450 0.02800 0.94750 0.42857
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 67.6779   Pars:  0.0845099419486 0.0000000006277 0.9154900571318 0.8461720339470
## Iter: 2 fn: 67.6779   Pars:  0.08449785454 0.00000000032 0.91550214514 0.84615043582
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.0349  Pars:  0.03756 0.03756 0.92489 0.30769
## Iter: 2 fn: 142.0349  Pars:  0.03756 0.03756 0.92489 0.30769
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 131.2505  Pars:  0.04813 0.01013 0.94173 0.21052
## Iter: 2 fn: 131.2505  Pars:  0.04813 0.01013 0.94173 0.21053
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 112.3169  Pars:  0.04000 0.02800 0.93200 0.49998
## Iter: 2 fn: 112.3169  Pars:  0.04000 0.02800 0.93200 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 186.6110  Pars:  0.06145 0.03073 0.90782 0.15385
## Iter: 2 fn: 186.6110  Pars:  0.06145 0.03073 0.90782 0.15385
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 180.2304  Pars:  0.0885963414 0.0000001728 0.9114034854 0.3114817103
## Iter: 2 fn: 180.2303  Pars:  0.08859327043 0.00000004167 0.91140668789 0.31146506929
## Iter: 3 fn: 180.2303  Pars:  0.088598103784 0.000000005886 0.911401890330 0.311490911864
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 182.4494  Pars:  0.0439999677 0.0459999574 0.9100000746 0.0000002526
## Iter: 2 fn: 182.4494  Pars:  0.0439999630 0.0459999571 0.9100000799 0.0000001461
## Iter: 3 fn: 182.4494  Pars:  0.04399995802 0.04599995709 0.91000008489 0.00000003035
## Iter: 4 fn: 182.4494  Pars:  0.043999956688 0.045999956823 0.910000086488 0.000000002915
## solnp--> Completed in 4 iterations
## 
## Iter: 1 fn: 1386.4757     Pars:  0.04755 0.01835 0.93410 0.28070
## Iter: 2 fn: 1386.4757     Pars:  0.04755 0.01835 0.93410 0.28070
## solnp--> Completed in 2 iterations
## [1] 10
## 
## Iter: 1 fn: 128.4439  Pars:  0.057142802903 0.000000007229 0.942857189576 0.299999831435
## Iter: 2 fn: 128.4439  Pars:  0.057142806076 0.000000001737 0.942857192187 0.299999844731
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 160.6000  Pars:  0.05188 0.02471 0.92341 0.19047
## Iter: 2 fn: 160.6000  Pars:  0.05188 0.02471 0.92341 0.19048
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 100.0937  Pars:  0.04050 0.02250 0.93700 0.55555
## Iter: 2 fn: 100.0937  Pars:  0.04050 0.02250 0.93700 0.55555
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 121.2452  Pars:  0.04800 0.02400 0.92800 0.49998
## Iter: 2 fn: 121.2452  Pars:  0.04800 0.02400 0.92800 0.50000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 118.5063  Pars:  0.06424384 0.00004192 0.93571425 0.53318186
## Iter: 2 fn: 118.5062  Pars:  0.0642847581 0.0000008747 0.9357143672 0.5333297539
## Iter: 3 fn: 118.5062  Pars:  0.0642849366 0.0000006959 0.9357143675 0.5333304101
## solnp--> Completed in 3 iterations
## 
## Iter: 1 fn: 114.0325  Pars:  0.03462 0.01385 0.95154 0.13334
## Iter: 2 fn: 114.0325  Pars:  0.03462 0.01385 0.95154 0.13333
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 156.3493  Pars:  0.06453 0.01173 0.92373 0.31818
## Iter: 2 fn: 156.3493  Pars:  0.06453 0.01173 0.92373 0.31818
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 142.8815  Pars:  0.04444 0.02000 0.93556 0.10000
## Iter: 2 fn: 142.8815  Pars:  0.04444 0.02000 0.93556 0.10000
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 220.6438  Pars:  0.08736 0.03382 0.87882 0.29033
## Iter: 2 fn: 220.6438  Pars:  0.08736 0.03382 0.87882 0.29032
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 167.0704  Pars:  0.05009 0.02922 0.92069 0.04168
## Iter: 2 fn: 167.0704  Pars:  0.05009 0.02922 0.92070 0.04167
## solnp--> Completed in 2 iterations
## 
## Iter: 1 fn: 1461.9631     Pars:  0.05249 0.01704 0.93047 0.27225
## Iter: 2 fn: 1461.9631     Pars:  0.05249 0.01704 0.93047 0.27225
## solnp--> Completed in 2 iterations
sapply(lca_dk_stnd_err, function(x) round(head(x, 1),3))
## $stnderrs.lca.params
##     [,1]  [,2]  [,3]  [,4]  [,5] [,6]  [,7] [,8]  [,9] [,10]
## lgg 0.01 0.009 0.009 0.043 0.009 0.01 0.017 0.01 0.021 0.006
## 
## $avg.effects
##      [,1] [,2] [,3]  [,4]  [,5]  [,6]  [,7]  [,8] [,9] [,10] [,11]
## lca 0.005 0.02 0.02 0.025 0.019 0.012 0.026 0.029 0.03 0.033  0.02
## 
## $stnderrs.effects
##      [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11]
## lca 0.008 0.009 0.007 0.026 0.013 0.008 0.012 0.016 0.014 0.008 0.002

Fit

fit <- fit_nodk(alldat[,t1], alldat[,t2], res$param.lca[4,], res$param.lca[1:3,])

print(fit[,1:4])
##                item1        item2     item3    item4
## chi-square 2.5791029 5.136378e+01 3.8689664 0.636025
## p-value    0.4611649 4.092471e-11 0.2759655 0.888138
fit <- fit_dk(alldat_dk[,t1], alldat_dk[,t2], res_dk$param.lca[8,], res_dk$param.lca[1:7,], force9=TRUE)

print(fit[,1:4])
##            item1 item2 item3 item4
## chi-square   Inf   Inf   Inf   Inf
## p-value        0     0     0     0

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