README.md
In ykunisato/lcmr: Model fitting using latent cause model
lcmr
The goal of lcmr is to simulate phenomena of classical conditioning and
fit the conditioning data with the latent cause model.
lcmr is an R package of Latent Cause Model:
LCM and Latent Cause Modulated
Rescorla-Wagner model:
LCM-RW made bySam
Gershman.
Installation
You can install the development version from
GitHub with:
# install.packages("devtools")
devtools::install_github("ykunisato/lcmr")
List of functions
- fit_lcm: Fit model to conditioning data
- infer_lcm: Simulate the classical conditioning with LCM
- infer_lcm_rw: Simulate the classical conditioning with LCM-RW
How to simulate the renewal effect with LCM
The renewal effect is the phenomenon in which the change of context
after extinction can lead to a return of conditioned response (CR).
infer_lcm(X,opts) can simulate the renewal effect.
First, you have to prepare the design of conditioning. In followings, I
prepare the experimental design consisted from acquisition (CS presents
with US in context A(context = 1), 10 trials), extinction (CS presents
without US in context B(context = 0),10 trials) and test (CS without US
in context A(context = 0), 10 trials).
US <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0)
CS <- c(1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1)
Context <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1,1,1)
X <- cbind(US, CS, Context)
You can simulate the conditioned response using infer_lcm(). I simulate
the conditioned response setting the alpha = 0.4 . The alpha is the
concentrate parameter of the Chinese Restaurant Process.
library(lcmr)
sim_res <- infer_lcm(X = X, opts = list(c_alpha = 0.4,
K=10,
M=100,
a = 1,
b = 1,
stickiness = 0))
You can the plot of change of conditioned response through the trials
using the following codes.
library(tidyverse)
sim_data <- data.frame(X, Trial = seq(1,length(US)), CR = sim_res$V)
sim_data %>%
ggplot(aes(x = Trial, y = CR)) +
geom_line() +
ylim(0,1)
You can draw the plot of the posterior probability of each cause using
the following codes.
sim_post <- as.data.frame(sim_res$post)
sim_post %>%
mutate(Trial = seq(1,length(US))) %>%
rename(C01 = V1, C02 = V2, C03 = V3, C04 = V4, C05 = V5,
C06 = V6, C07 = V7, C08 = V8, C09 = V9, C10 = V10) %>%
gather(key = "Cause", value = "post",-Trial) %>%
mutate(Cause = as.factor(Cause)) %>%
ggplot(aes(x = Trial, y = post, color = Cause)) +
geom_line() +
ylim(0,1) +
labs(y="Posterior probability")
How to simulate the spontaneous recovery with LCM-RW
The spontaneous recovery is the phenomenon in which the time elapses
following extinction can lead to a return of conditioned response (CR).
infer_lcm_rw(X,opts) can simulate the spontaneous recovery.
First, you have to prepare the design of conditioning. In followings, I
prepare the experimental design consisted from acquisition (CS1 presents
with US, CS2 presents without US, 9 trials each CS), extinction (both
CSs presents without US, 6 trials each CS) and test (both CSs presents
without US after 1 day, 3 trials each CS).
US <- c(1,0,0,1,1,0,1,0,1,1,0,0,1,0,0,1,1,0, 0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0)
CS1 <- c(1,0,0,1,1,0,1,0,1,1,0,0,1,0,0,1,1,0, 1,1,0,1,0,0,1,0,1,1,0,0, 1,0,0,1,1,0)
CS2 <- c(0,1,1,0,0,1,0,1,0,0,1,1,0,1,1,0,0,1, 0,0,1,0,1,1,0,1,0,0,1,1, 0,1,1,0,0,1)
time <- c(0, seq(1:17)*4, 100+seq(1:12)*4, 86400+seq(1:6)*4)
X <- cbind(time, US, CS1, CS2)
You can simulate the conditioned response using infer_lcm(). I simulate
the conditioned response setting the alpha = 0.45 and the eta = 0.2. The
alpha is the concentrate parameter of the Chinese Restaurant Process and
eta is the learning rate of the RW model.
library(lcmr)
sim_res <- infer_lcm_rw(X = X, opts = list(
a = 1,
b = 1,
c_alpha = 0.45,
stickiness = 0,
K = 10,
g = 1,
psi = 0,
eta = 0.2,
maxIter= 3,
w0 = 0,
sr = 0.4,
sx = 1,
theta = 0.3,
lambda = 0.005,
K = 15,
nst = 0))
You can the plot of change of conditioned response through the trials
using the following codes.
library(tidyverse)
sim_data <- data.frame(X,
Trials_cs1 = cumsum(CS1),
Trials_cs2 = cumsum(CS2),
CR = sim_res$V)
sim_data %>%
filter(CS1 == 1) %>%
ggplot(aes(x = Trials_cs1, y = CR)) +
geom_line() +
ylim(0,1) +
labs(x = "Trial", y = "CR of CS1")
sim_data %>%
filter(CS2 == 1) %>%
ggplot(aes(x = Trials_cs2, y = CR)) +
geom_line() +
ylim(0,1) +
labs(x = "Trial", y = "CR of CS2")
How to fit LCM to the conditioning data.
You have to prepare the data as long format containing the following
variables (Order and name is exactly the same as following):
- ID Subject ID
- CR Conditioned Response
- US Unconditioned Stimulus
- CS Conditioned Stimului or Context. If using multiple CS, set
variables name as CS1,CS2,CS3…
I make the synthetic data for model fitting with the experiment design
of the renewal effect.
US <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0)
CS <- c(1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1)
Context <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1,1,1)
X <- cbind(US, CS, Context)
I make synthetic data for 100 participants.
number_of_perticiapnts <- 100
participants_alpha <- runif(number_of_perticiapnts, 0, 10)
data <- NULL
for (i in 1:number_of_perticiapnts) {
sim_data <- infer_lcm(X, opts = list(c_alpha = participants_alpha[i],
K=10,
M=100,
a = 1,
b = 1,
stickiness = 0))
sim_df <- data.frame(ID = rep(i,length(US)), CR = sim_data$V, X)
data <- rbind(data,sim_df)
}
You can estimate parameter alpha using fit_lcm(data, model, opts,
parameter_range, parallel, estimation_method). You have to specify the
following argument for model fitting:
-
model: 1 = latent cause model, 2 = latent cause modulated RW model
-
parameter_range: range of parameter(a_L, a_U, e_L, e_U)
-
stimation_method: 0 = optim or optimize(lcm), 1 = post mean(only
latent cause model)
results <- fit_lcm(data,
model = 1,
opts = list(K=10,
M=100,
a = 1,
b = 1,
stickiness = 0),
parameter_range = list(a_L = 0, a_U = 15),
estimation_method = 0)
#> start estimation using optim...
#> 1 negative log likelihood: -68.93107 parameter: 9.338747
#> 2 negative log likelihood: -26.02116 parameter: 0.3675782
#> 3 negative log likelihood: -80.4781 parameter: 10.51741
#> 4 negative log likelihood: -64.67058 parameter: 10.66717
#> 5 negative log likelihood: -83.33142 parameter: 7.086353
#> 6 negative log likelihood: -66.90881 parameter: 9.559258
#> 7 negative log likelihood: -77.44209 parameter: 9.442029
#> 8 negative log likelihood: -57.0935 parameter: 4.267789
#> 9 negative log likelihood: -76.41846 parameter: 8.749365
#> 10 negative log likelihood: -69.69763 parameter: 8.020849
#> start estimation using optim...
#> 1 negative log likelihood: -64.92392 parameter: 9.443177
#> 2 negative log likelihood: -57.44225 parameter: 11.32144
#> 3 negative log likelihood: -83.25872 parameter: 5.919257
#> 4 negative log likelihood: -56.49635 parameter: 10.8712
#> 5 negative log likelihood: -55.65989 parameter: 3.189967
#> 6 negative log likelihood: -48.47371 parameter: 10.51762
#> 7 negative log likelihood: -53.34074 parameter: 9.695497
#> 8 negative log likelihood: -54.042 parameter: 11.74544
#> 9 negative log likelihood: -77.35321 parameter: 7.597512
#> 10 negative log likelihood: -67.97936 parameter: 8.911302
#> start estimation using optim...
#> 1 negative log likelihood: -62.00383 parameter: 14.90562
#> 2 negative log likelihood: -77.33705 parameter: 7.813928
#> 3 negative log likelihood: -78.19267 parameter: 6.977246
#> 4 negative log likelihood: -73.88672 parameter: 13.49592
#> 5 negative log likelihood: -38.47175 parameter: 2.366243
#> 6 negative log likelihood: -47.99859 parameter: 4.19377
#> 7 negative log likelihood: -49.42245 parameter: 9.035911
#> 8 negative log likelihood: -65.73083 parameter: 11.94792
#> 9 negative log likelihood: -70.93506 parameter: 12.3099
#> 10 negative log likelihood: -79.51087 parameter: 10.11439
#> start estimation using optim...
#> 1 negative log likelihood: -32.54389 parameter: 5.178435
#> 2 negative log likelihood: -56.675 parameter: 1.81261
#> 3 negative log likelihood: -21.01611 parameter: 10.21152
#> 4 negative log likelihood: -50.91674 parameter: 2.306971
#> 5 negative log likelihood: -20.887 parameter: 12.81539
#> 6 negative log likelihood: -43.20152 parameter: 3.619507
#> 7 negative log likelihood: -56.98764 parameter: 0.7176536
#> 8 negative log likelihood: -21.46005 parameter: 9.506595
#> 9 negative log likelihood: -38.12712 parameter: 4.053021
#> 10 negative log likelihood: -18.52287 parameter: 14.34828
#> start estimation using optim...
#> 1 negative log likelihood: -62.66715 parameter: 7.478134
#> 2 negative log likelihood: -66.10861 parameter: 9.689648
#> 3 negative log likelihood: -90.04608 parameter: 8.576873
#> 4 negative log likelihood: -42.81906 parameter: 2.119464
#> 5 negative log likelihood: -39.79773 parameter: 2.811006
#> 6 negative log likelihood: -56.47538 parameter: 4.636176
#> 7 negative log likelihood: -41.02308 parameter: 2.308557
#> 8 negative log likelihood: -60.81503 parameter: 14.52489
#> 9 negative log likelihood: -63.52146 parameter: 4.920543
#> 10 negative log likelihood: -27.70265 parameter: 1.022802
#> start estimation using optim...
#> 1 negative log likelihood: -62.14771 parameter: 5.841455
#> 2 negative log likelihood: -57.79049 parameter: 10.11542
#> 3 negative log likelihood: -58.11523 parameter: 4.998664
#> 4 negative log likelihood: -94.7316 parameter: 7.932679
#> 5 negative log likelihood: -68.34737 parameter: 6.717267
#> 6 negative log likelihood: -77.29065 parameter: 8.903554
#> 7 negative log likelihood: -67.13898 parameter: 6.695447
#> 8 negative log likelihood: -83.16525 parameter: 9.330348
#> 9 negative log likelihood: -77.95292 parameter: 10.54581
#> 10 negative log likelihood: -75.86573 parameter: 8.933335
#> start estimation using optim...
#> 1 negative log likelihood: -49.51907 parameter: 1.234653
#> 2 negative log likelihood: -57.129 parameter: 2.528196
#> 3 negative log likelihood: -67.95352 parameter: 5.007662
#> 4 negative log likelihood: -46.87232 parameter: 9.250429
#> 5 negative log likelihood: -50.31762 parameter: 9.673178
#> 6 negative log likelihood: -37.28071 parameter: 12.70792
#> 7 negative log likelihood: -48.38308 parameter: 3.861842
#> 8 negative log likelihood: -58.99754 parameter: 6.539249
#> 9 negative log likelihood: -72.8623 parameter: 4.27512
#> 10 negative log likelihood: -78.85829 parameter: 5.126851
#> start estimation using optim...
#> 1 negative log likelihood: -31.86193 parameter: 1.698798
#> 2 negative log likelihood: -73.64166 parameter: 7.010969
#> 3 negative log likelihood: -47.47838 parameter: 3.598635
#> 4 negative log likelihood: -68.16131 parameter: 6.91176
#> 5 negative log likelihood: -73.63077 parameter: 15
#> 6 negative log likelihood: -40.79348 parameter: 2.34876
#> 7 negative log likelihood: -75.81475 parameter: 15
#> 8 negative log likelihood: -77.06133 parameter: 7.884721
#> 9 negative log likelihood: -62.99629 parameter: 8.728984
#> 10 negative log likelihood: -55.37552 parameter: 5.138216
#> start estimation using optim...
#> 1 negative log likelihood: -68.60547 parameter: 6.741362
#> 2 negative log likelihood: -50.27167 parameter: 14.44494
#> 3 negative log likelihood: -46.52262 parameter: 14.64926
#> 4 negative log likelihood: -82.56435 parameter: 6.156955
#> 5 negative log likelihood: -44.75029 parameter: 12.94743
#> 6 negative log likelihood: -61.13922 parameter: 7.02101
#> 7 negative log likelihood: -93.67268 parameter: 5.562689
#> 8 negative log likelihood: -72.78193 parameter: 4.908007
#> 9 negative log likelihood: -52.70558 parameter: 14.74546
#> 10 negative log likelihood: -67.47851 parameter: 8.182741
#> start estimation using optim...
#> 1 negative log likelihood: -65.59299 parameter: 1.256923
#> 2 negative log likelihood: -54.93582 parameter: 2.104381
#> 3 negative log likelihood: -20.59173 parameter: 15
#> 4 negative log likelihood: -24.46186 parameter: 8.411613
#> 5 negative log likelihood: -77.73683 parameter: 0.6783485
#> 6 negative log likelihood: -60.49068 parameter: 1.379822
#> 7 negative log likelihood: -30.66592 parameter: 5.474521
#> 8 negative log likelihood: -59.41846 parameter: 1.565369
#> 9 negative log likelihood: -27.11514 parameter: 7.028851
#> 10 negative log likelihood: -21.48897 parameter: 12.68343
#> start estimation using optim...
#> 1 negative log likelihood: -45.33594 parameter: 12.67134
#> 2 negative log likelihood: -50.2886 parameter: 7.053752
#> 3 negative log likelihood: -69.98036 parameter: 4.30463
#> 4 negative log likelihood: -88.99538 parameter: 3.81923
#> 5 negative log likelihood: -44.3736 parameter: 11.35211
#> 6 negative log likelihood: -68.61343 parameter: 4.490441
#> 7 negative log likelihood: -72.66067 parameter: 4.328148
#> 8 negative log likelihood: -42.26594 parameter: 14.29738
#> 9 negative log likelihood: -53.30546 parameter: 1.123382
#> 10 negative log likelihood: -49.8767 parameter: 8.581437
#> start estimation using optim...
#> 1 negative log likelihood: -44.24601 parameter: 13.86858
#> 2 negative log likelihood: -53.8905 parameter: 2.28762
#> 3 negative log likelihood: -48.31549 parameter: 1.548407
#> 4 negative log likelihood: -76.48998 parameter: 6.62149
#> 5 negative log likelihood: -83.94385 parameter: 6.215139
#> 6 negative log likelihood: -74.52221 parameter: 5.160426
#> 7 negative log likelihood: -48.40887 parameter: 10.98952
#> 8 negative log likelihood: -46.58893 parameter: 12.77046
#> 9 negative log likelihood: -88.18449 parameter: 4.218944
#> 10 negative log likelihood: -60.16074 parameter: 8.639111
#> start estimation using optim...
#> 1 negative log likelihood: -69.56147 parameter: 14.29508
#> 2 negative log likelihood: -64.90334 parameter: 10.99879
#> 3 negative log likelihood: -60.67211 parameter: 5.968699
#> 4 negative log likelihood: -66.72734 parameter: 7.328636
#> 5 negative log likelihood: -64.72625 parameter: 6.088899
#> 6 negative log likelihood: -55.84981 parameter: 6.603309
#> 7 negative log likelihood: -65.05975 parameter: 13.76076
#> 8 negative log likelihood: -75.07029 parameter: 13.9085
#> 9 negative log likelihood: -86.15483 parameter: 8.542471
#> 10 negative log likelihood: -43.94326 parameter: 3.276057
#> start estimation using optim...
#> 1 negative log likelihood: -75.60352 parameter: 15
#> 2 negative log likelihood: -31.23569 parameter: 0.4133886
#> 3 negative log likelihood: -75.68217 parameter: 12.39723
#> 4 negative log likelihood: -41.64245 parameter: 3.093616
#> 5 negative log likelihood: -81.78599 parameter: 11.69807
#> 6 negative log likelihood: -49.04646 parameter: 7.254776
#> 7 negative log likelihood: -86.89739 parameter: 10.97803
#> 8 negative log likelihood: -85.17596 parameter: 10.127
#> 9 negative log likelihood: -62.28164 parameter: 9.321513
#> 10 negative log likelihood: -75.85051 parameter: 11.83984
#> start estimation using optim...
#> 1 negative log likelihood: -72.38997 parameter: 2.099149
#> 2 negative log likelihood: -67.39006 parameter: 2.757206
#> 3 negative log likelihood: -63.23311 parameter: 2.797478
#> 4 negative log likelihood: -46.50171 parameter: 5.376917
#> 5 negative log likelihood: -61.07364 parameter: 3.757973
#> 6 negative log likelihood: -59.95383 parameter: 4.163329
#> 7 negative log likelihood: -60.30753 parameter: 1.531522
#> 8 negative log likelihood: -50.13731 parameter: 5.456013
#> 9 negative log likelihood: -46.94899 parameter: 5.53381
#> 10 negative log likelihood: -46.52165 parameter: 6.222871
#> start estimation using optim...
#> 1 negative log likelihood: -41.25066 parameter: 1.149321
#> 2 negative log likelihood: -42.10067 parameter: 1.23338
#> 3 negative log likelihood: -54.01341 parameter: 3.668721
#> 4 negative log likelihood: -48.26986 parameter: 9.186796
#> 5 negative log likelihood: -43.07102 parameter: 12.7331
#> 6 negative log likelihood: -58.53176 parameter: 4.458951
#> 7 negative log likelihood: -54.72104 parameter: 3.474101
#> 8 negative log likelihood: -49.42262 parameter: 10.72631
#> 9 negative log likelihood: -45.47083 parameter: 13.43693
#> 10 negative log likelihood: -77.6423 parameter: 5.0591
#> start estimation using optim...
#> 1 negative log likelihood: -87.53345 parameter: 10.2463
#> 2 negative log likelihood: -74.05624 parameter: 10.45852
#> 3 negative log likelihood: -40.36843 parameter: 2.445525
#> 4 negative log likelihood: -72.96345 parameter: 15
#> 5 negative log likelihood: -77.07866 parameter: 8.32917
#> 6 negative log likelihood: -56.42384 parameter: 4.834834
#> 7 negative log likelihood: -70.15187 parameter: 13.02544
#> 8 negative log likelihood: -84.79345 parameter: 8.653321
#> 9 negative log likelihood: -29.21501 parameter: 0.6844252
#> 10 negative log likelihood: -74.21358 parameter: 14.67927
#> start estimation using optim...
#> 1 negative log likelihood: -85.93031 parameter: 6.965475
#> 2 negative log likelihood: -89.09536 parameter: 9.333167
#> 3 negative log likelihood: -65.56472 parameter: 4.85201
#> 4 negative log likelihood: -52.79434 parameter: 12.70209
#> 5 negative log likelihood: -53.34853 parameter: 9.662431
#> 6 negative log likelihood: -60.22094 parameter: 6.583974
#> 7 negative log likelihood: -59.66208 parameter: 13.91756
#> 8 negative log likelihood: -29.60039 parameter: 0.3310106
#> 9 negative log likelihood: -84.57157 parameter: 6.058432
#> 10 negative log likelihood: -63.40726 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -34.09429 parameter: 3.307481
#> 2 negative log likelihood: -34.10379 parameter: 2.386433
#> 3 negative log likelihood: -19.57867 parameter: 13.86891
#> 4 negative log likelihood: -43.29623 parameter: 2.45228
#> 5 negative log likelihood: -21.45595 parameter: 11.55515
#> 6 negative log likelihood: -22.35129 parameter: 14.07767
#> 7 negative log likelihood: -41.29892 parameter: 3.1128
#> 8 negative log likelihood: -41.30206 parameter: 1.456905
#> 9 negative log likelihood: -40.53618 parameter: 1.215634
#> 10 negative log likelihood: -21.72874 parameter: 11.85815
#> start estimation using optim...
#> 1 negative log likelihood: -76.55429 parameter: 2.027636
#> 2 negative log likelihood: -34.03212 parameter: 10.01564
#> 3 negative log likelihood: -35.66685 parameter: 9.526202
#> 4 negative log likelihood: -45.53935 parameter: 6.434802
#> 5 negative log likelihood: -63.82621 parameter: 1.897562
#> 6 negative log likelihood: -75.56839 parameter: 1.680722
#> 7 negative log likelihood: -74.36281 parameter: 3.046716
#> 8 negative log likelihood: -67.87432 parameter: 2.667689
#> 9 negative log likelihood: -44.72969 parameter: 7.481055
#> 10 negative log likelihood: -75.88722 parameter: 2.35553
#> start estimation using optim...
#> 1 negative log likelihood: -16.53751 parameter: 12.29827
#> 2 negative log likelihood: -16.27095 parameter: 11.74293
#> 3 negative log likelihood: -24.90841 parameter: 5.956508
#> 4 negative log likelihood: -14.27769 parameter: 13.17795
#> 5 negative log likelihood: -19.99402 parameter: 11.24491
#> 6 negative log likelihood: -34.64004 parameter: 2.153256
#> 7 negative log likelihood: -17.63213 parameter: 13.00965
#> 8 negative log likelihood: -32.76135 parameter: 0.8258914
#> 9 negative log likelihood: -17.1903 parameter: 15
#> 10 negative log likelihood: -19.21381 parameter: 9.888523
#> start estimation using optim...
#> 1 negative log likelihood: -82.25249 parameter: 9.539433
#> 2 negative log likelihood: -64.73025 parameter: 9.283058
#> 3 negative log likelihood: -52.76426 parameter: 4.637397
#> 4 negative log likelihood: -66.71683 parameter: 6.098114
#> 5 negative log likelihood: -61.45548 parameter: 10.72881
#> 6 negative log likelihood: -84.3336 parameter: 8.875832
#> 7 negative log likelihood: -82.66732 parameter: 12.10117
#> 8 negative log likelihood: -86.38603 parameter: 10.92782
#> 9 negative log likelihood: -110.1366 parameter: 9.607332
#> 10 negative log likelihood: -65.94313 parameter: 7.491177
#> start estimation using optim...
#> 1 negative log likelihood: -73.70591 parameter: 2.022448
#> 2 negative log likelihood: -25.06859 parameter: 9.264398
#> 3 negative log likelihood: -51.74997 parameter: 2.826565
#> 4 negative log likelihood: -56.33536 parameter: 2.99748
#> 5 negative log likelihood: -62.6997 parameter: 1.459982
#> 6 negative log likelihood: -23.07306 parameter: 11.25321
#> 7 negative log likelihood: -73.28898 parameter: 1.651518
#> 8 negative log likelihood: -27.90453 parameter: 8.634779
#> 9 negative log likelihood: -50.77552 parameter: 0.6385759
#> 10 negative log likelihood: -82.03116 parameter: 0.6277502
#> start estimation using optim...
#> 1 negative log likelihood: -83.24167 parameter: 8.537277
#> 2 negative log likelihood: -67.82449 parameter: 8.144161
#> 3 negative log likelihood: -75.59925 parameter: 13.27375
#> 4 negative log likelihood: -68.51578 parameter: 7.402862
#> 5 negative log likelihood: -86.20981 parameter: 15
#> 6 negative log likelihood: -75.84077 parameter: 15
#> 7 negative log likelihood: -62.8798 parameter: 6.876673
#> 8 negative log likelihood: -84.53404 parameter: 15
#> 9 negative log likelihood: -82.98957 parameter: 8.52712
#> 10 negative log likelihood: -91.09953 parameter: 8.938555
#> start estimation using optim...
#> 1 negative log likelihood: -33.85104 parameter: 1.169598
#> 2 negative log likelihood: -36.77381 parameter: 1.61109
#> 3 negative log likelihood: -78.33824 parameter: 6.268581
#> 4 negative log likelihood: -64.20651 parameter: 5.556501
#> 5 negative log likelihood: -43.15798 parameter: 4.2174
#> 6 negative log likelihood: -82.62186 parameter: 7.330099
#> 7 negative log likelihood: -74.87909 parameter: 10.29183
#> 8 negative log likelihood: -66.08276 parameter: 4.98656
#> 9 negative log likelihood: -73.11966 parameter: 11.5243
#> 10 negative log likelihood: -61.6653 parameter: 14.20668
#> start estimation using optim...
#> 1 negative log likelihood: -48.95053 parameter: 13.5239
#> 2 negative log likelihood: -79.90821 parameter: 10.11142
#> 3 negative log likelihood: -54.32 parameter: 12.56012
#> 4 negative log likelihood: -72.62349 parameter: 7.297012
#> 5 negative log likelihood: -40.77968 parameter: 2.353863
#> 6 negative log likelihood: -73.40685 parameter: 6.00917
#> 7 negative log likelihood: -78.43721 parameter: 5.432832
#> 8 negative log likelihood: -47.89525 parameter: 2.91985
#> 9 negative log likelihood: -53.48126 parameter: 10.52827
#> 10 negative log likelihood: -57.84458 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -90.74454 parameter: 5.767412
#> 2 negative log likelihood: -70.32167 parameter: 9.206044
#> 3 negative log likelihood: -43.31184 parameter: 1.310498
#> 4 negative log likelihood: -37.42762 parameter: 1.367151
#> 5 negative log likelihood: -81.30936 parameter: 4.608688
#> 6 negative log likelihood: -46.36987 parameter: 2.182122
#> 7 negative log likelihood: -31.91242 parameter: 0.3446528
#> 8 negative log likelihood: -63.79256 parameter: 3.518625
#> 9 negative log likelihood: -34.66916 parameter: 1.654677
#> 10 negative log likelihood: -75.42098 parameter: 10.22701
#> start estimation using optim...
#> 1 negative log likelihood: -30.54896 parameter: 7.958593
#> 2 negative log likelihood: -28.29009 parameter: 14.28347
#> 3 negative log likelihood: -80.98744 parameter: 1.685682
#> 4 negative log likelihood: -40.60019 parameter: 5.444615
#> 5 negative log likelihood: -82.14314 parameter: 0.8103922
#> 6 negative log likelihood: -27.74404 parameter: 13.18567
#> 7 negative log likelihood: -70.18021 parameter: 2.61379
#> 8 negative log likelihood: -72.48156 parameter: 1.011445
#> 9 negative log likelihood: -27.84529 parameter: 11.95127
#> 10 negative log likelihood: -24.88216 parameter: 13.08906
#> start estimation using optim...
#> 1 negative log likelihood: -66.90396 parameter: 5.463095
#> 2 negative log likelihood: -50.44217 parameter: 6.940811
#> 3 negative log likelihood: -36.09925 parameter: 14.38933
#> 4 negative log likelihood: -39.8189 parameter: 11.34655
#> 5 negative log likelihood: -39.69457 parameter: 7.975902
#> 6 negative log likelihood: -96.65382 parameter: 3.158589
#> 7 negative log likelihood: -66.17904 parameter: 4.364559
#> 8 negative log likelihood: -66.08425 parameter: 2.282634
#> 9 negative log likelihood: -44.01731 parameter: 0.4646368
#> 10 negative log likelihood: -74.15804 parameter: 3.630944
#> start estimation using optim...
#> 1 negative log likelihood: -82.3465 parameter: 4.120349
#> 2 negative log likelihood: -95.20235 parameter: 3.562065
#> 3 negative log likelihood: -49.344 parameter: 7.311928
#> 4 negative log likelihood: -61.66706 parameter: 3.177804
#> 5 negative log likelihood: -73.23975 parameter: 3.951321
#> 6 negative log likelihood: -50.31749 parameter: 8.797769
#> 7 negative log likelihood: -49.28397 parameter: 8.30322
#> 8 negative log likelihood: -92.18546 parameter: 4.103762
#> 9 negative log likelihood: -56.59415 parameter: 6.393678
#> 10 negative log likelihood: -37.18746 parameter: 13.94622
#> start estimation using optim...
#> 1 negative log likelihood: -67.95936 parameter: 6.78567
#> 2 negative log likelihood: -28.70078 parameter: 1.748097
#> 3 negative log likelihood: -33.9806 parameter: 1.649816
#> 4 negative log likelihood: -87.72871 parameter: 11.8426
#> 5 negative log likelihood: -33.43603 parameter: 2.149289
#> 6 negative log likelihood: -88.07079 parameter: 11.7247
#> 7 negative log likelihood: -82.32831 parameter: 13.21751
#> 8 negative log likelihood: -62.01483 parameter: 5.706789
#> 9 negative log likelihood: -30.80159 parameter: 2.012303
#> 10 negative log likelihood: -82.61814 parameter: 11.41392
#> start estimation using optim...
#> 1 negative log likelihood: -60.64248 parameter: 3.433318
#> 2 negative log likelihood: -62.26185 parameter: 2.058101
#> 3 negative log likelihood: -52.26701 parameter: 1.406696
#> 4 negative log likelihood: -23.83104 parameter: 13.69293
#> 5 negative log likelihood: -25.16893 parameter: 12.86142
#> 6 negative log likelihood: -73.36519 parameter: 1.817225
#> 7 negative log likelihood: -25.38822 parameter: 13.16897
#> 8 negative log likelihood: -44.5937 parameter: 5.070478
#> 9 negative log likelihood: -64.53321 parameter: 2.815886
#> 10 negative log likelihood: -25.46476 parameter: 11.25492
#> start estimation using optim...
#> 1 negative log likelihood: -69.83222 parameter: 3.829654
#> 2 negative log likelihood: -86.72915 parameter: 3.586464
#> 3 negative log likelihood: -42.29866 parameter: 10.37479
#> 4 negative log likelihood: -74.64601 parameter: 3.783505
#> 5 negative log likelihood: -45.72632 parameter: 8.94274
#> 6 negative log likelihood: -49.17756 parameter: 5.924865
#> 7 negative log likelihood: -42.22815 parameter: 11.3358
#> 8 negative log likelihood: -82.94149 parameter: 3.218045
#> 9 negative log likelihood: -35.11917 parameter: 14.30933
#> 10 negative log likelihood: -38.66154 parameter: 11.70147
#> start estimation using optim...
#> 1 negative log likelihood: -88.75854 parameter: 9.112368
#> 2 negative log likelihood: -39.87782 parameter: 1.798267
#> 3 negative log likelihood: -48.46517 parameter: 3.155194
#> 4 negative log likelihood: -63.09472 parameter: 10.52265
#> 5 negative log likelihood: -54.94587 parameter: 11.59965
#> 6 negative log likelihood: -87.522 parameter: 8.404071
#> 7 negative log likelihood: -59.47911 parameter: 14.50615
#> 8 negative log likelihood: -62.41127 parameter: 4.510583
#> 9 negative log likelihood: -91.23758 parameter: 8.320026
#> 10 negative log likelihood: -68.32295 parameter: 9.308277
#> start estimation using optim...
#> 1 negative log likelihood: -27.57586 parameter: 6.137441
#> 2 negative log likelihood: -38.0606 parameter: 2.510832
#> 3 negative log likelihood: -44.4859 parameter: 1.803026
#> 4 negative log likelihood: -22.19358 parameter: 10.41345
#> 5 negative log likelihood: -21.97219 parameter: 9.367151
#> 6 negative log likelihood: -19.66244 parameter: 15
#> 7 negative log likelihood: -41.17847 parameter: 1.682352
#> 8 negative log likelihood: -36.81599 parameter: 2.421701
#> 9 negative log likelihood: -17.44795 parameter: 13.21448
#> 10 negative log likelihood: -31.07327 parameter: 5.023822
#> start estimation using optim...
#> 1 negative log likelihood: -35.71813 parameter: 0.7800084
#> 2 negative log likelihood: -80.39989 parameter: 8.285494
#> 3 negative log likelihood: -67.74763 parameter: 7.130382
#> 4 negative log likelihood: -77.75794 parameter: 6.495111
#> 5 negative log likelihood: -48.74721 parameter: 14.45743
#> 6 negative log likelihood: -78.89994 parameter: 7.739559
#> 7 negative log likelihood: -62.10032 parameter: 6.486105
#> 8 negative log likelihood: -57.33057 parameter: 10.61367
#> 9 negative log likelihood: -63.07836 parameter: 11.51551
#> 10 negative log likelihood: -86.69404 parameter: 6.088278
#> start estimation using optim...
#> 1 negative log likelihood: -49.23079 parameter: 6.265202
#> 2 negative log likelihood: -69.9541 parameter: 6.063429
#> 3 negative log likelihood: -46.58112 parameter: 5.223559
#> 4 negative log likelihood: -68.66055 parameter: 7.360215
#> 5 negative log likelihood: -43.55156 parameter: 12.3233
#> 6 negative log likelihood: -51.54307 parameter: 5.682261
#> 7 negative log likelihood: -36.92385 parameter: 0.4192884
#> 8 negative log likelihood: -54.96408 parameter: 5.665164
#> 9 negative log likelihood: -53.33683 parameter: 9.408152
#> 10 negative log likelihood: -41.55015 parameter: 14.64535
#> start estimation using optim...
#> 1 negative log likelihood: -85.00928 parameter: 5.511766
#> 2 negative log likelihood: -59.85152 parameter: 9.262709
#> 3 negative log likelihood: -32.40923 parameter: 0.1609748
#> 4 negative log likelihood: -71.21277 parameter: 5.16302
#> 5 negative log likelihood: -38.40445 parameter: 1.171964
#> 6 negative log likelihood: -80.13308 parameter: 5.483381
#> 7 negative log likelihood: -82.43774 parameter: 7.073029
#> 8 negative log likelihood: -60.4034 parameter: 3.185816
#> 9 negative log likelihood: -75.47323 parameter: 3.969062
#> 10 negative log likelihood: -69.55079 parameter: 6.259574
#> start estimation using optim...
#> 1 negative log likelihood: -70.1513 parameter: 6.007896
#> 2 negative log likelihood: -83.67964 parameter: 4.505687
#> 3 negative log likelihood: -43.81874 parameter: 13.26926
#> 4 negative log likelihood: -61.37985 parameter: 7.261691
#> 5 negative log likelihood: -47.61599 parameter: 11.19702
#> 6 negative log likelihood: -55.61537 parameter: 9.450091
#> 7 negative log likelihood: -66.34296 parameter: 7.814492
#> 8 negative log likelihood: -44.46693 parameter: 11.62254
#> 9 negative log likelihood: -66.71898 parameter: 6.641272
#> 10 negative log likelihood: -80.75136 parameter: 5.843982
#> start estimation using optim...
#> 1 negative log likelihood: -78.07739 parameter: 5.733908
#> 2 negative log likelihood: -59.305 parameter: 12.64969
#> 3 negative log likelihood: -67.83555 parameter: 5.38937
#> 4 negative log likelihood: -70.98456 parameter: 4.361148
#> 5 negative log likelihood: -56.93915 parameter: 13.03083
#> 6 negative log likelihood: -87.83734 parameter: 6.136771
#> 7 negative log likelihood: -85.86122 parameter: 6.074558
#> 8 negative log likelihood: -69.25626 parameter: 6.202478
#> 9 negative log likelihood: -69.85206 parameter: 5.481137
#> 10 negative log likelihood: -65.79538 parameter: 10.76259
#> start estimation using optim...
#> 1 negative log likelihood: -81.71534 parameter: 8.5301
#> 2 negative log likelihood: -53.85584 parameter: 5.058997
#> 3 negative log likelihood: -93.0578 parameter: 8.521715
#> 4 negative log likelihood: -65.11241 parameter: 14.997
#> 5 negative log likelihood: -74.01733 parameter: 13.158
#> 6 negative log likelihood: -63.71561 parameter: 15
#> 7 negative log likelihood: -25.06896 parameter: 0.4279749
#> 8 negative log likelihood: -70.08682 parameter: 10.90845
#> 9 negative log likelihood: -85.69239 parameter: 7.022433
#> 10 negative log likelihood: -68.70035 parameter: 13.96966
#> start estimation using optim...
#> 1 negative log likelihood: -35.47614 parameter: 0.8188568
#> 2 negative log likelihood: -69.26145 parameter: 8.279615
#> 3 negative log likelihood: -81.85911 parameter: 5.536929
#> 4 negative log likelihood: -53.47123 parameter: 11.36644
#> 5 negative log likelihood: -64.47399 parameter: 7.060203
#> 6 negative log likelihood: -55.31398 parameter: 5.94822
#> 7 negative log likelihood: -71.92346 parameter: 7.647822
#> 8 negative log likelihood: -51.52162 parameter: 14.86924
#> 9 negative log likelihood: -63.78892 parameter: 6.478472
#> 10 negative log likelihood: -76.13096 parameter: 6.656689
#> start estimation using optim...
#> 1 negative log likelihood: -81.5848 parameter: 8.077184
#> 2 negative log likelihood: -60.07464 parameter: 8.647308
#> 3 negative log likelihood: -61.15218 parameter: 15
#> 4 negative log likelihood: -27.53417 parameter: 0.802612
#> 5 negative log likelihood: -60.03447 parameter: 11.22596
#> 6 negative log likelihood: -66.07483 parameter: 6.800104
#> 7 negative log likelihood: -72.62981 parameter: 11.51555
#> 8 negative log likelihood: -83.31504 parameter: 5.800105
#> 9 negative log likelihood: -57.31879 parameter: 8.293923
#> 10 negative log likelihood: -71.09461 parameter: 10.73913
#> start estimation using optim...
#> 1 negative log likelihood: -49.96278 parameter: 7.517817
#> 2 negative log likelihood: -52.04595 parameter: 3.235449
#> 3 negative log likelihood: -41.10027 parameter: 1.313876
#> 4 negative log likelihood: -71.34764 parameter: 6.389983
#> 5 negative log likelihood: -89.63525 parameter: 5.56552
#> 6 negative log likelihood: -47.07305 parameter: 12.24472
#> 7 negative log likelihood: -51.90444 parameter: 6.773234
#> 8 negative log likelihood: -50.79288 parameter: 12.29835
#> 9 negative log likelihood: -70.75994 parameter: 6.981888
#> 10 negative log likelihood: -63.73869 parameter: 6.048201
#> start estimation using optim...
#> 1 negative log likelihood: -73.56138 parameter: 7.534296
#> 2 negative log likelihood: -83.71555 parameter: 6.804185
#> 3 negative log likelihood: -66.75177 parameter: 8.829685
#> 4 negative log likelihood: -30.86804 parameter: 0.5301873
#> 5 negative log likelihood: -59.57941 parameter: 6.836936
#> 6 negative log likelihood: -70.01362 parameter: 6.16402
#> 7 negative log likelihood: -44.83184 parameter: 11.62097
#> 8 negative log likelihood: -54.65167 parameter: 5.889834
#> 9 negative log likelihood: -59.61016 parameter: 3.768307
#> 10 negative log likelihood: -88.54621 parameter: 6.067795
#> start estimation using optim...
#> 1 negative log likelihood: -60.63145 parameter: 0.8025913
#> 2 negative log likelihood: -25.61703 parameter: 8.636053
#> 3 negative log likelihood: -44.05673 parameter: 3.401084
#> 4 negative log likelihood: -27.06995 parameter: 8.98917
#> 5 negative log likelihood: -40.26164 parameter: 4.469936
#> 6 negative log likelihood: -66.78068 parameter: 1.239746
#> 7 negative log likelihood: -26.63198 parameter: 9.204597
#> 8 negative log likelihood: -20.43571 parameter: 14.37538
#> 9 negative log likelihood: -27.11993 parameter: 8.788018
#> 10 negative log likelihood: -42.78254 parameter: 0.7510155
#> start estimation using optim...
#> 1 negative log likelihood: -43.34375 parameter: 10.79857
#> 2 negative log likelihood: -77.34439 parameter: 5.164785
#> 3 negative log likelihood: -52.97514 parameter: 8.223697
#> 4 negative log likelihood: -46.60238 parameter: 9.770816
#> 5 negative log likelihood: -48.236 parameter: 10.24107
#> 6 negative log likelihood: -42.68219 parameter: 10.64313
#> 7 negative log likelihood: -68.79683 parameter: 4.962512
#> 8 negative log likelihood: -66.10737 parameter: 7.413628
#> 9 negative log likelihood: -41.97573 parameter: 12.20466
#> 10 negative log likelihood: -68.4955 parameter: 4.438063
#> start estimation using optim...
#> 1 negative log likelihood: -35.19024 parameter: 13.28574
#> 2 negative log likelihood: -93.73872 parameter: 2.782206
#> 3 negative log likelihood: -43.074 parameter: 3.52805
#> 4 negative log likelihood: -82.46761 parameter: 3.136478
#> 5 negative log likelihood: -65.14128 parameter: 5.648269
#> 6 negative log likelihood: -78.2122 parameter: 2.888368
#> 7 negative log likelihood: -74.52411 parameter: 4.925291
#> 8 negative log likelihood: -83.09033 parameter: 3.245194
#> 9 negative log likelihood: -55.71187 parameter: 5.455819
#> 10 negative log likelihood: -79.90584 parameter: 4.055204
#> start estimation using optim...
#> 1 negative log likelihood: -94.49272 parameter: 9.147541
#> 2 negative log likelihood: -84.95814 parameter: 15
#> 3 negative log likelihood: -74.55103 parameter: 15
#> 4 negative log likelihood: -61.9665 parameter: 11.79524
#> 5 negative log likelihood: -77.99796 parameter: 14.21682
#> 6 negative log likelihood: -53.89908 parameter: 10.50576
#> 7 negative log likelihood: -79.72469 parameter: 10.77002
#> 8 negative log likelihood: -76.09174 parameter: 9.816975
#> 9 negative log likelihood: -89.11021 parameter: 15
#> 10 negative log likelihood: -66.28595 parameter: 7.167496
#> start estimation using optim...
#> 1 negative log likelihood: -58.12865 parameter: 5.415008
#> 2 negative log likelihood: -30.88993 parameter: 15
#> 3 negative log likelihood: -34.94784 parameter: 11.26549
#> 4 negative log likelihood: -33.89612 parameter: 10.4324
#> 5 negative log likelihood: -72.18966 parameter: 3.992682
#> 6 negative log likelihood: -73.32812 parameter: 2.367542
#> 7 negative log likelihood: -57.5561 parameter: 3.416234
#> 8 negative log likelihood: -53.20664 parameter: 5.201868
#> 9 negative log likelihood: -32.43264 parameter: 10.75404
#> 10 negative log likelihood: -37.80484 parameter: 9.051716
#> start estimation using optim...
#> 1 negative log likelihood: -36.08555 parameter: 1.844478
#> 2 negative log likelihood: -63.8507 parameter: 14.78204
#> 3 negative log likelihood: -93.16648 parameter: 6.34393
#> 4 negative log likelihood: -78.3782 parameter: 6.279647
#> 5 negative log likelihood: -79.43974 parameter: 9.914446
#> 6 negative log likelihood: -64.74089 parameter: 8.416384
#> 7 negative log likelihood: -59.37189 parameter: 13.08478
#> 8 negative log likelihood: -36.51775 parameter: 1.546999
#> 9 negative log likelihood: -90.85812 parameter: 7.199438
#> 10 negative log likelihood: -90.92438 parameter: 6.60675
#> start estimation using optim...
#> 1 negative log likelihood: -57.02511 parameter: 4.340577
#> 2 negative log likelihood: -73.82363 parameter: 14.26576
#> 3 negative log likelihood: -64.22477 parameter: 7.82121
#> 4 negative log likelihood: -69.7967 parameter: 8.652537
#> 5 negative log likelihood: -89.23614 parameter: 9.398977
#> 6 negative log likelihood: -81.14022 parameter: 12.95426
#> 7 negative log likelihood: -31.06042 parameter: 1.659973
#> 8 negative log likelihood: -65.84791 parameter: 15
#> 9 negative log likelihood: -71.20846 parameter: 15
#> 10 negative log likelihood: -45.74117 parameter: 3.382983
#> start estimation using optim...
#> 1 negative log likelihood: -64.15404 parameter: 3.578936
#> 2 negative log likelihood: -51.21501 parameter: 9.913758
#> 3 negative log likelihood: -57.07111 parameter: 8.060067
#> 4 negative log likelihood: -30.27622 parameter: 0.6508239
#> 5 negative log likelihood: -93.00935 parameter: 5.526967
#> 6 negative log likelihood: -72.09761 parameter: 5.995908
#> 7 negative log likelihood: -41.76745 parameter: 1.322811
#> 8 negative log likelihood: -69.48657 parameter: 3.496565
#> 9 negative log likelihood: -45.62946 parameter: 12.4342
#> 10 negative log likelihood: -42.847 parameter: 11.02675
#> start estimation using optim...
#> 1 negative log likelihood: -55.88996 parameter: 4.07496
#> 2 negative log likelihood: -67.66967 parameter: 10.46668
#> 3 negative log likelihood: -71.20902 parameter: 9.530763
#> 4 negative log likelihood: -64.2141 parameter: 6.363875
#> 5 negative log likelihood: -76.36247 parameter: 5.43855
#> 6 negative log likelihood: -59.43495 parameter: 13.43424
#> 7 negative log likelihood: -46.71021 parameter: 4.348673
#> 8 negative log likelihood: -51.56212 parameter: 3.689231
#> 9 negative log likelihood: -65.84961 parameter: 8.237662
#> 10 negative log likelihood: -63.03832 parameter: 6.524029
#> start estimation using optim...
#> 1 negative log likelihood: -50.10271 parameter: 14.38846
#> 2 negative log likelihood: -77.79353 parameter: 6.996787
#> 3 negative log likelihood: -64.59221 parameter: 9.273021
#> 4 negative log likelihood: -46.94971 parameter: 13.85468
#> 5 negative log likelihood: -56.3644 parameter: 15
#> 6 negative log likelihood: -85.93653 parameter: 7.941712
#> 7 negative log likelihood: -60.03191 parameter: 9.717564
#> 8 negative log likelihood: -25.76526 parameter: 0.40369
#> 9 negative log likelihood: -71.94741 parameter: 5.141918
#> 10 negative log likelihood: -44.12204 parameter: 7.404838
#> start estimation using optim...
#> 1 negative log likelihood: -90.62876 parameter: 8.077674
#> 2 negative log likelihood: -49.62579 parameter: 3.697812
#> 3 negative log likelihood: -73.8488 parameter: 4.99126
#> 4 negative log likelihood: -79.68736 parameter: 7.801352
#> 5 negative log likelihood: -91.95049 parameter: 8.346534
#> 6 negative log likelihood: -66.12805 parameter: 8.315502
#> 7 negative log likelihood: -80.16714 parameter: 7.82448
#> 8 negative log likelihood: -55.66812 parameter: 6.698771
#> 9 negative log likelihood: -46.99043 parameter: 3.674822
#> 10 negative log likelihood: -74.62983 parameter: 9.348912
#> start estimation using optim...
#> 1 negative log likelihood: -34.10835 parameter: 7.145754
#> 2 negative log likelihood: -21.93466 parameter: 14.23398
#> 3 negative log likelihood: -49.00094 parameter: 3.465755
#> 4 negative log likelihood: -39.73546 parameter: 1.553881
#> 5 negative log likelihood: -66.41656 parameter: 1.758147
#> 6 negative log likelihood: -57.25495 parameter: 1.18038
#> 7 negative log likelihood: -25.69229 parameter: 9.765804
#> 8 negative log likelihood: -30.23259 parameter: 5.318697
#> 9 negative log likelihood: -20.25462 parameter: 12.47292
#> 10 negative log likelihood: -81.16125 parameter: 0.973253
#> start estimation using optim...
#> 1 negative log likelihood: -39.72178 parameter: 13.66454
#> 2 negative log likelihood: -42.10731 parameter: 14.54376
#> 3 negative log likelihood: -46.52376 parameter: 10.15715
#> 4 negative log likelihood: -61.71778 parameter: 2.684927
#> 5 negative log likelihood: -39.1937 parameter: 13.90546
#> 6 negative log likelihood: -57.12391 parameter: 2.523272
#> 7 negative log likelihood: -71.54713 parameter: 4.216918
#> 8 negative log likelihood: -42.46973 parameter: 12.5631
#> 9 negative log likelihood: -54.57032 parameter: 1.46939
#> 10 negative log likelihood: -46.34252 parameter: 8.624326
#> start estimation using optim...
#> 1 negative log likelihood: -57.03415 parameter: 4.294668
#> 2 negative log likelihood: -57.50836 parameter: 8.687513
#> 3 negative log likelihood: -87.62975 parameter: 9.130056
#> 4 negative log likelihood: -69.67131 parameter: 7.00809
#> 5 negative log likelihood: -75.87049 parameter: 5.646678
#> 6 negative log likelihood: -88.61585 parameter: 8.072613
#> 7 negative log likelihood: -52.42328 parameter: 14.81941
#> 8 negative log likelihood: -71.18705 parameter: 12.31462
#> 9 negative log likelihood: -37.84122 parameter: 2.71003
#> 10 negative log likelihood: -37.5193 parameter: 1.757855
#> start estimation using optim...
#> 1 negative log likelihood: -24.76913 parameter: 10.92803
#> 2 negative log likelihood: -37.58646 parameter: 5.970259
#> 3 negative log likelihood: -52.77495 parameter: 2.816448
#> 4 negative log likelihood: -58.81088 parameter: 3.077195
#> 5 negative log likelihood: -30.87656 parameter: 7.225632
#> 6 negative log likelihood: -18.90153 parameter: 14.81542
#> 7 negative log likelihood: -81.43147 parameter: 1.851514
#> 8 negative log likelihood: -25.33784 parameter: 9.335249
#> 9 negative log likelihood: -26.55288 parameter: 8.815965
#> 10 negative log likelihood: -30.26666 parameter: 6.58932
#> start estimation using optim...
#> 1 negative log likelihood: -64.33227 parameter: 2.305927
#> 2 negative log likelihood: -50.33131 parameter: 0.8624255
#> 3 negative log likelihood: -46.33438 parameter: 5.974109
#> 4 negative log likelihood: -40.63852 parameter: 7.20491
#> 5 negative log likelihood: -36.80737 parameter: 14.59015
#> 6 negative log likelihood: -54.72756 parameter: 1.397906
#> 7 negative log likelihood: -48.13678 parameter: 6.552166
#> 8 negative log likelihood: -73.79054 parameter: 3.637898
#> 9 negative log likelihood: -67.74133 parameter: 3.264691
#> 10 negative log likelihood: -62.03513 parameter: 1.613296
#> start estimation using optim...
#> 1 negative log likelihood: -64.71765 parameter: 5.433715
#> 2 negative log likelihood: -49.79831 parameter: 13.7884
#> 3 negative log likelihood: -66.29834 parameter: 5.228753
#> 4 negative log likelihood: -82.61104 parameter: 4.706116
#> 5 negative log likelihood: -63.54245 parameter: 3.077266
#> 6 negative log likelihood: -54.20118 parameter: 7.249816
#> 7 negative log likelihood: -69.80951 parameter: 3.509805
#> 8 negative log likelihood: -52.07846 parameter: 3.10613
#> 9 negative log likelihood: -55.11429 parameter: 5.041747
#> 10 negative log likelihood: -46.19232 parameter: 11.71087
#> start estimation using optim...
#> 1 negative log likelihood: -67.44368 parameter: 8.032873
#> 2 negative log likelihood: -62.60529 parameter: 13.49016
#> 3 negative log likelihood: -24.95696 parameter: 0.6397825
#> 4 negative log likelihood: -59.02907 parameter: 11.11807
#> 5 negative log likelihood: -79.38515 parameter: 7.606246
#> 6 negative log likelihood: -33.99202 parameter: 1.958287
#> 7 negative log likelihood: -55.84072 parameter: 14.45416
#> 8 negative log likelihood: -71.22144 parameter: 12.08477
#> 9 negative log likelihood: -52.73372 parameter: 13.35531
#> 10 negative log likelihood: -70.3864 parameter: 9.055065
#> start estimation using optim...
#> 1 negative log likelihood: -44.84445 parameter: 1.600407
#> 2 negative log likelihood: -85.20512 parameter: 4.183528
#> 3 negative log likelihood: -37.78576 parameter: 0.5799564
#> 4 negative log likelihood: -63.93344 parameter: 3.018606
#> 5 negative log likelihood: -77.86725 parameter: 3.503767
#> 6 negative log likelihood: -30.7931 parameter: 0.2246281
#> 7 negative log likelihood: -72.70622 parameter: 6.522296
#> 8 negative log likelihood: -58.46628 parameter: 9.432239
#> 9 negative log likelihood: -62.7488 parameter: 8.450411
#> 10 negative log likelihood: -37.55 parameter: 12.83314
#> start estimation using optim...
#> 1 negative log likelihood: -60.23175 parameter: 6.673999
#> 2 negative log likelihood: -78.83614 parameter: 11.14365
#> 3 negative log likelihood: -70.66904 parameter: 15
#> 4 negative log likelihood: -61.61132 parameter: 10.04667
#> 5 negative log likelihood: -74.57897 parameter: 15
#> 6 negative log likelihood: -66.81957 parameter: 8.142744
#> 7 negative log likelihood: -47.23828 parameter: 5.016901
#> 8 negative log likelihood: -90.02694 parameter: 13.47844
#> 9 negative log likelihood: -52.46111 parameter: 7.673284
#> 10 negative log likelihood: -70.63481 parameter: 9.973206
#> start estimation using optim...
#> 1 negative log likelihood: -82.49173 parameter: 5.423651
#> 2 negative log likelihood: -77.21171 parameter: 6.717245
#> 3 negative log likelihood: -47.03054 parameter: 2.851848
#> 4 negative log likelihood: -74.03373 parameter: 7.98494
#> 5 negative log likelihood: -86.08267 parameter: 5.34441
#> 6 negative log likelihood: -46.43351 parameter: 2.546371
#> 7 negative log likelihood: -84.19985 parameter: 6.922656
#> 8 negative log likelihood: -60.00143 parameter: 3.263998
#> 9 negative log likelihood: -81.18554 parameter: 6.46113
#> 10 negative log likelihood: -66.3224 parameter: 7.284413
#> start estimation using optim...
#> 1 negative log likelihood: -69.22225 parameter: 7.008688
#> 2 negative log likelihood: -77.13881 parameter: 8.695452
#> 3 negative log likelihood: -86.16621 parameter: 5.944445
#> 4 negative log likelihood: -38.19868 parameter: 0.8630008
#> 5 negative log likelihood: -71.11444 parameter: 5.981747
#> 6 negative log likelihood: -72.58919 parameter: 6.263907
#> 7 negative log likelihood: -65.44841 parameter: 9.279529
#> 8 negative log likelihood: -75.17077 parameter: 9.253675
#> 9 negative log likelihood: -66.56479 parameter: 4.899386
#> 10 negative log likelihood: -84.44487 parameter: 5.739522
#> start estimation using optim...
#> 1 negative log likelihood: -39.38482 parameter: 5.998917
#> 2 negative log likelihood: -25.94633 parameter: 14.28141
#> 3 negative log likelihood: -23.32789 parameter: 13.94241
#> 4 negative log likelihood: -24.82887 parameter: 11.79507
#> 5 negative log likelihood: -57.13864 parameter: 1.650087
#> 6 negative log likelihood: -75.21874 parameter: 0.9715672
#> 7 negative log likelihood: -27.53859 parameter: 8.388522
#> 8 negative log likelihood: -22.794 parameter: 13.67229
#> 9 negative log likelihood: -38.7622 parameter: 5.570335
#> 10 negative log likelihood: -66.16313 parameter: 1.783371
#> start estimation using optim...
#> 1 negative log likelihood: -61.77147 parameter: 5.346981
#> 2 negative log likelihood: -87.34341 parameter: 7.917507
#> 3 negative log likelihood: -53.39506 parameter: 13.62427
#> 4 negative log likelihood: -84.01573 parameter: 6.844302
#> 5 negative log likelihood: -67.81893 parameter: 10.46011
#> 6 negative log likelihood: -29.37408 parameter: 0.6500699
#> 7 negative log likelihood: -48.44959 parameter: 4.016193
#> 8 negative log likelihood: -64.51633 parameter: 12.21377
#> 9 negative log likelihood: -53.29358 parameter: 11.16906
#> 10 negative log likelihood: -84.97841 parameter: 6.065458
#> start estimation using optim...
#> 1 negative log likelihood: -78.52032 parameter: 2.481949
#> 2 negative log likelihood: -38.47178 parameter: 9.956931
#> 3 negative log likelihood: -48.39755 parameter: 7.925059
#> 4 negative log likelihood: -42.60598 parameter: 1.004426
#> 5 negative log likelihood: -97.29765 parameter: 3.082448
#> 6 negative log likelihood: -72.68878 parameter: 3.90689
#> 7 negative log likelihood: -59.95673 parameter: 3.796059
#> 8 negative log likelihood: -44.72203 parameter: 3.731083
#> 9 negative log likelihood: -40.79391 parameter: 10.61134
#> 10 negative log likelihood: -88.4979 parameter: 2.729298
#> start estimation using optim...
#> 1 negative log likelihood: -36.91863 parameter: 11.10509
#> 2 negative log likelihood: -35.21457 parameter: 10.20363
#> 3 negative log likelihood: -65.66348 parameter: 3.7838
#> 4 negative log likelihood: -39.83891 parameter: 7.735724
#> 5 negative log likelihood: -55.25155 parameter: 3.229395
#> 6 negative log likelihood: -56.87868 parameter: 4.447437
#> 7 negative log likelihood: -42.06015 parameter: 8.662118
#> 8 negative log likelihood: -56.53222 parameter: 1.796352
#> 9 negative log likelihood: -38.77571 parameter: 9.939153
#> 10 negative log likelihood: -64.18535 parameter: 2.765896
#> start estimation using optim...
#> 1 negative log likelihood: -53.71205 parameter: 4.346291
#> 2 negative log likelihood: -25.5213 parameter: 0.4165143
#> 3 negative log likelihood: -52.58676 parameter: 4.578773
#> 4 negative log likelihood: -97.31634 parameter: 8.630862
#> 5 negative log likelihood: -69.46762 parameter: 13.50063
#> 6 negative log likelihood: -71.74288 parameter: 13.84832
#> 7 negative log likelihood: -73.17166 parameter: 12.44227
#> 8 negative log likelihood: -70.21653 parameter: 14.70259
#> 9 negative log likelihood: -43.09305 parameter: 2.992235
#> 10 negative log likelihood: -83.88146 parameter: 10.62823
#> start estimation using optim...
#> 1 negative log likelihood: -64.47086 parameter: 0.2659586
#> 2 negative log likelihood: -47.69684 parameter: 2.480987
#> 3 negative log likelihood: -49.93466 parameter: 2.62035
#> 4 negative log likelihood: -23.45942 parameter: 10.82441
#> 5 negative log likelihood: -56.29586 parameter: 2.652226
#> 6 negative log likelihood: -50.26165 parameter: 2.334396
#> 7 negative log likelihood: -48.54273 parameter: 2.639527
#> 8 negative log likelihood: -32.25921 parameter: 6.652256
#> 9 negative log likelihood: -58.28906 parameter: 2.247655
#> 10 negative log likelihood: -21.34748 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -57.01719 parameter: 3.009708
#> 2 negative log likelihood: -30.09148 parameter: 8.904923
#> 3 negative log likelihood: -39.05101 parameter: 4.713663
#> 4 negative log likelihood: -23.2419 parameter: 14.72432
#> 5 negative log likelihood: -36.98243 parameter: 6.150717
#> 6 negative log likelihood: -50.69788 parameter: 2.72366
#> 7 negative log likelihood: -64.97338 parameter: 2.168778
#> 8 negative log likelihood: -24.81401 parameter: 13.2342
#> 9 negative log likelihood: -44.35131 parameter: 3.239052
#> 10 negative log likelihood: -23.10873 parameter: 13.90798
#> start estimation using optim...
#> 1 negative log likelihood: -52.12222 parameter: 6.533657
#> 2 negative log likelihood: -40.50899 parameter: 15
#> 3 negative log likelihood: -48.4586 parameter: 7.753655
#> 4 negative log likelihood: -55.49128 parameter: 4.428029
#> 5 negative log likelihood: -43.69537 parameter: 12.71493
#> 6 negative log likelihood: -56.79839 parameter: 3.294894
#> 7 negative log likelihood: -51.36402 parameter: 7.186867
#> 8 negative log likelihood: -43.49387 parameter: 1.584355
#> 9 negative log likelihood: -60.13823 parameter: 4.001622
#> 10 negative log likelihood: -39.9135 parameter: 11.86426
#> start estimation using optim...
#> 1 negative log likelihood: -59.82795 parameter: 12.29747
#> 2 negative log likelihood: -82.53452 parameter: 6.876065
#> 3 negative log likelihood: -69.65321 parameter: 9.295218
#> 4 negative log likelihood: -81.63814 parameter: 6.894904
#> 5 negative log likelihood: -64.06135 parameter: 14.96636
#> 6 negative log likelihood: -89.52122 parameter: 8.080609
#> 7 negative log likelihood: -67.72039 parameter: 4.956629
#> 8 negative log likelihood: -52.86244 parameter: 12.60145
#> 9 negative log likelihood: -71.23622 parameter: 6.654401
#> 10 negative log likelihood: -59.00084 parameter: 9.214527
#> start estimation using optim...
#> 1 negative log likelihood: -21.29844 parameter: 10.7648
#> 2 negative log likelihood: -50.82538 parameter: 0.245616
#> 3 negative log likelihood: -25.42329 parameter: 8.577951
#> 4 negative log likelihood: -23.44822 parameter: 9.860196
#> 5 negative log likelihood: -48.21011 parameter: 1.27735
#> 6 negative log likelihood: -21.06065 parameter: 10.72964
#> 7 negative log likelihood: -27.34163 parameter: 6.608464
#> 8 negative log likelihood: -21.73131 parameter: 11.62761
#> 9 negative log likelihood: -30.75897 parameter: 6.027605
#> 10 negative log likelihood: -76.35762 parameter: 0.8214421
#> start estimation using optim...
#> 1 negative log likelihood: -62.13016 parameter: 15
#> 2 negative log likelihood: -63.35504 parameter: 7.728115
#> 3 negative log likelihood: -25.8205 parameter: 0.1144307
#> 4 negative log likelihood: -62.78869 parameter: 6.688262
#> 5 negative log likelihood: -79.92456 parameter: 8.715017
#> 6 negative log likelihood: -70.76292 parameter: 7.105032
#> 7 negative log likelihood: -75.37313 parameter: 5.651011
#> 8 negative log likelihood: -69.86694 parameter: 5.073563
#> 9 negative log likelihood: -73.71402 parameter: 7.75283
#> 10 negative log likelihood: -66.3814 parameter: 7.053595
#> start estimation using optim...
#> 1 negative log likelihood: -30.63042 parameter: 11.6289
#> 2 negative log likelihood: -28.77083 parameter: 14.34826
#> 3 negative log likelihood: -35.36241 parameter: 9.52598
#> 4 negative log likelihood: -36.60824 parameter: 7.833519
#> 5 negative log likelihood: -27.89036 parameter: 14.31532
#> 6 negative log likelihood: -39.9809 parameter: 8.013474
#> 7 negative log likelihood: -90.46272 parameter: 2.252343
#> 8 negative log likelihood: -28.52374 parameter: 15
#> 9 negative log likelihood: -31.68431 parameter: 9.347108
#> 10 negative log likelihood: -66.61731 parameter: 1.004346
#> start estimation using optim...
#> 1 negative log likelihood: -80.56309 parameter: 2.807144
#> 2 negative log likelihood: -78.71889 parameter: 2.456716
#> 3 negative log likelihood: -49.99627 parameter: 5.814356
#> 4 negative log likelihood: -31.48497 parameter: 13.44827
#> 5 negative log likelihood: -33.67344 parameter: 11.98264
#> 6 negative log likelihood: -36.18739 parameter: 12.91561
#> 7 negative log likelihood: -42.73292 parameter: 6.837991
#> 8 negative log likelihood: -35.14096 parameter: 13.30942
#> 9 negative log likelihood: -34.98782 parameter: 13.32378
#> 10 negative log likelihood: -61.73349 parameter: 1.777951
#> start estimation using optim...
#> 1 negative log likelihood: -77.71746 parameter: 9.063132
#> 2 negative log likelihood: -68.31274 parameter: 10.87924
#> 3 negative log likelihood: -48.9244 parameter: 4.49039
#> 4 negative log likelihood: -84.37071 parameter: 8.519927
#> 5 negative log likelihood: -70.54089 parameter: 12.93665
#> 6 negative log likelihood: -95.53483 parameter: 8.919281
#> 7 negative log likelihood: -44.19299 parameter: 2.239829
#> 8 negative log likelihood: -62.48257 parameter: 10.29736
#> 9 negative log likelihood: -42.13919 parameter: 2.95145
#> 10 negative log likelihood: -69.61454 parameter: 11.48073
#> start estimation using optim...
#> 1 negative log likelihood: -89.54054 parameter: 2.320884
#> 2 negative log likelihood: -52.0286 parameter: 0.2752352
#> 3 negative log likelihood: -32.03437 parameter: 10.17442
#> 4 negative log likelihood: -64.97933 parameter: 2.443657
#> 5 negative log likelihood: -74.86674 parameter: 2.015312
#> 6 negative log likelihood: -60.54026 parameter: 2.925204
#> 7 negative log likelihood: -66.49045 parameter: 3.033311
#> 8 negative log likelihood: -33.67684 parameter: 11.5142
#> 9 negative log likelihood: -33.64244 parameter: 13.36049
#> 10 negative log likelihood: -43.08251 parameter: 8.230612
#> start estimation using optim...
#> 1 negative log likelihood: -59.45086 parameter: 1.791414
#> 2 negative log likelihood: -34.26545 parameter: 7.451297
#> 3 negative log likelihood: -53.00045 parameter: 3.681973
#> 4 negative log likelihood: -53.05109 parameter: 1.788663
#> 5 negative log likelihood: -53.57201 parameter: 2.736528
#> 6 negative log likelihood: -67.98959 parameter: 1.944259
#> 7 negative log likelihood: -26.99593 parameter: 13.83321
#> 8 negative log likelihood: -67.47607 parameter: 2.201573
#> 9 negative log likelihood: -25.93246 parameter: 11.49358
#> 10 negative log likelihood: -40.814 parameter: 5.196217
#> start estimation using optim...
#> 1 negative log likelihood: -15.88344 parameter: 14.66358
#> 2 negative log likelihood: -37.41547 parameter: 2.639703
#> 3 negative log likelihood: -51.79257 parameter: 1.535406
#> 4 negative log likelihood: -74.2947 parameter: 0.4151221
#> 5 negative log likelihood: -15.4014 parameter: 14.88858
#> 6 negative log likelihood: -61.65332 parameter: 0.4273607
#> 7 negative log likelihood: -17.74396 parameter: 10.95433
#> 8 negative log likelihood: -52.44809 parameter: 1.650205
#> 9 negative log likelihood: -16.68026 parameter: 14.04102
#> 10 negative log likelihood: -43.14693 parameter: 2.652424
#> start estimation using optim...
#> 1 negative log likelihood: -81.56174 parameter: 7.879122
#> 2 negative log likelihood: -86.21402 parameter: 7.613049
#> 3 negative log likelihood: -68.39954 parameter: 13.66177
#> 4 negative log likelihood: -101.3071 parameter: 8.629758
#> 5 negative log likelihood: -86.56596 parameter: 7.344129
#> 6 negative log likelihood: -52.28515 parameter: 10.44374
#> 7 negative log likelihood: -85.41548 parameter: 9.603713
#> 8 negative log likelihood: -72.23445 parameter: 6.753873
#> 9 negative log likelihood: -73.02982 parameter: 6.225139
#> 10 negative log likelihood: -45.26858 parameter: 3.626544
#> start estimation using optim...
#> 1 negative log likelihood: -28.34717 parameter: 1.017375
#> 2 negative log likelihood: -34.50967 parameter: 11.93734
#> 3 negative log likelihood: -66.60214 parameter: 4.143199
#> 4 negative log likelihood: -68.52142 parameter: 5.909832
#> 5 negative log likelihood: -63.73961 parameter: 3.315441
#> 6 negative log likelihood: -55.49614 parameter: 6.072455
#> 7 negative log likelihood: -53.40357 parameter: 5.405891
#> 8 negative log likelihood: -35.46975 parameter: 11.34234
#> 9 negative log likelihood: -49.81761 parameter: 1.793529
#> 10 negative log likelihood: -56.32335 parameter: 2.045711
#> start estimation using optim...
#> 1 negative log likelihood: -36.41888 parameter: 7.169769
#> 2 negative log likelihood: -86.14928 parameter: 1.597299
#> 3 negative log likelihood: -71.07805 parameter: 2.10008
#> 4 negative log likelihood: -46.3349 parameter: 2.398746
#> 5 negative log likelihood: -62.60597 parameter: 2.417216
#> 6 negative log likelihood: -41.83473 parameter: 5.398146
#> 7 negative log likelihood: -58.8308 parameter: 2.549324
#> 8 negative log likelihood: -54.40054 parameter: 4.595962
#> 9 negative log likelihood: -31.73756 parameter: 10.14318
#> 10 negative log likelihood: -23.87074 parameter: 14.38647
#> start estimation using optim...
#> 1 negative log likelihood: -43.38037 parameter: 3.585437
#> 2 negative log likelihood: -87.11609 parameter: 7.087684
#> 3 negative log likelihood: -91.19868 parameter: 8.158841
#> 4 negative log likelihood: -74.15359 parameter: 6.672031
#> 5 negative log likelihood: -76.89991 parameter: 6.057405
#> 6 negative log likelihood: -102.5736 parameter: 8.395765
#> 7 negative log likelihood: -83.88873 parameter: 6.465923
#> 8 negative log likelihood: -82.88863 parameter: 7.816633
#> 9 negative log likelihood: -92.53796 parameter: 9.736215
#> 10 negative log likelihood: -105.5456 parameter: 7.70469
#> start estimation using optim...
#> 1 negative log likelihood: -61.35119 parameter: 4.97687
#> 2 negative log likelihood: -60.7058 parameter: 3.304192
#> 3 negative log likelihood: -57.26525 parameter: 5.445231
#> 4 negative log likelihood: -77.35231 parameter: 3.36617
#> 5 negative log likelihood: -66.31353 parameter: 3.839654
#> 6 negative log likelihood: -74.47096 parameter: 4.409622
#> 7 negative log likelihood: -65.05687 parameter: 4.746534
#> 8 negative log likelihood: -48.09354 parameter: 8.05994
#> 9 negative log likelihood: -63.67962 parameter: 5.695262
#> 10 negative log likelihood: -46.08773 parameter: 8.636648
#> start estimation using optim...
#> 1 negative log likelihood: -45.1696 parameter: 9.733579
#> 2 negative log likelihood: -42.76874 parameter: 14.34319
#> 3 negative log likelihood: -37.19164 parameter: 0.2216856
#> 4 negative log likelihood: -32.54938 parameter: 0.2933489
#> 5 negative log likelihood: -83.11613 parameter: 4.179994
#> 6 negative log likelihood: -52.81978 parameter: 1.580026
#> 7 negative log likelihood: -49.5541 parameter: 9.624107
#> 8 negative log likelihood: -40.78155 parameter: 13.09128
#> 9 negative log likelihood: -30.51982 parameter: 0.3140837
#> 10 negative log likelihood: -55.89179 parameter: 2.791234
#> start estimation using optim...
#> 1 negative log likelihood: -25.68051 parameter: 0.03310395
#> 2 negative log likelihood: -44.42821 parameter: 2.368436
#> 3 negative log likelihood: -50.15541 parameter: 15
#> 4 negative log likelihood: -91.25667 parameter: 5.277104
#> 5 negative log likelihood: -55.01554 parameter: 14.19819
#> 6 negative log likelihood: -44.03335 parameter: 1.813041
#> 7 negative log likelihood: -79.35969 parameter: 4.773266
#> 8 negative log likelihood: -82.88687 parameter: 6.473904
#> 9 negative log likelihood: -103.1155 parameter: 6.081627
#> 10 negative log likelihood: -79.61277 parameter: 7.720722
#> start estimation using optim...
#> 1 negative log likelihood: -61.23553 parameter: 4.101819
#> 2 negative log likelihood: -42.6622 parameter: 7.325901
#> 3 negative log likelihood: -34.11208 parameter: 14.8139
#> 4 negative log likelihood: -73.65602 parameter: 3.351217
#> 5 negative log likelihood: -54.48829 parameter: 1.024545
#> 6 negative log likelihood: -54.4163 parameter: 3.973848
#> 7 negative log likelihood: -59.64293 parameter: 4.439985
#> 8 negative log likelihood: -52.29652 parameter: 5.940664
#> 9 negative log likelihood: -63.52218 parameter: 3.498558
#> 10 negative log likelihood: -36.81601 parameter: 10.55432
#> start estimation using optim...
#> 1 negative log likelihood: -75.63461 parameter: 3.880409
#> 2 negative log likelihood: -59.44773 parameter: 4.536184
#> 3 negative log likelihood: -47.73816 parameter: 11.26275
#> 4 negative log likelihood: -78.82147 parameter: 5.045812
#> 5 negative log likelihood: -44.59114 parameter: 13.08078
#> 6 negative log likelihood: -49.47838 parameter: 11.95821
#> 7 negative log likelihood: -84.0158 parameter: 3.736038
#> 8 negative log likelihood: -67.84121 parameter: 6.213392
#> 9 negative log likelihood: -78.217 parameter: 4.01522
#> 10 negative log likelihood: -59.64956 parameter: 8.12052
#> start estimation using optim...
#> 1 negative log likelihood: -65.85366 parameter: 10.54604
#> 2 negative log likelihood: -49.27575 parameter: 10.46301
#> 3 negative log likelihood: -65.44398 parameter: 5.402709
#> 4 negative log likelihood: -53.59697 parameter: 12.39436
#> 5 negative log likelihood: -57.33765 parameter: 2.552668
#> 6 negative log likelihood: -61.57662 parameter: 10.16161
#> 7 negative log likelihood: -83.04065 parameter: 4.788835
#> 8 negative log likelihood: -66.3179 parameter: 7.533912
#> 9 negative log likelihood: -70.59374 parameter: 5.199642
#> 10 negative log likelihood: -104.6957 parameter: 5.414883
#> start estimation using optim...
#> 1 negative log likelihood: -23.75059 parameter: 15
#> 2 negative log likelihood: -23.43914 parameter: 12.86905
#> 3 negative log likelihood: -23.24774 parameter: 13.64497
#> 4 negative log likelihood: -56.9013 parameter: 1.229324
#> 5 negative log likelihood: -26.38202 parameter: 10.2908
#> 6 negative log likelihood: -29.23713 parameter: 6.614228
#> 7 negative log likelihood: -54.81224 parameter: 3.010447
#> 8 negative log likelihood: -32.55941 parameter: 5.739426
#> 9 negative log likelihood: -39.88642 parameter: 3.728913
#> 10 negative log likelihood: -54.1342 parameter: 1.934333
#> start estimation using optim...
#> 1 negative log likelihood: -73.43009 parameter: 15
#> 2 negative log likelihood: -81.66174 parameter: 7.700503
#> 3 negative log likelihood: -71.46943 parameter: 11.76964
#> 4 negative log likelihood: -72.82213 parameter: 12.91229
#> 5 negative log likelihood: -76.20798 parameter: 8.827436
#> 6 negative log likelihood: -33.18744 parameter: 2.027405
#> 7 negative log likelihood: -66.49371 parameter: 5.839873
#> 8 negative log likelihood: -78.80965 parameter: 5.750555
#> 9 negative log likelihood: -53.62187 parameter: 3.651106
#> 10 negative log likelihood: -37.9099 parameter: 1.690494
#> start estimation using optim...
#> 1 negative log likelihood: -32.04688 parameter: 1.307361
#> 2 negative log likelihood: -19.94778 parameter: 15
#> 3 negative log likelihood: -26.6372 parameter: 2.338118
#> 4 negative log likelihood: -24.18024 parameter: 4.832242
#> 5 negative log likelihood: -17.75375 parameter: 14.76674
#> 6 negative log likelihood: -24.08885 parameter: 4.169689
#> 7 negative log likelihood: -30.71159 parameter: 1.167649
#> 8 negative log likelihood: -28.44755 parameter: 1.491737
#> 9 negative log likelihood: -21.13997 parameter: 15
#> 10 negative log likelihood: -34.18898 parameter: 1.46595
#> start estimation using optim...
#> 1 negative log likelihood: -83.48249 parameter: 3.348061
#> 2 negative log likelihood: -57.13221 parameter: 5.768043
#> 3 negative log likelihood: -76.16815 parameter: 3.072904
#> 4 negative log likelihood: -86.13708 parameter: 3.750408
#> 5 negative log likelihood: -73.60106 parameter: 3.537519
#> 6 negative log likelihood: -42.04767 parameter: 10.09521
#> 7 negative log likelihood: -83.70183 parameter: 3.427186
#> 8 negative log likelihood: -49.96914 parameter: 0.7686392
#> 9 negative log likelihood: -34.53889 parameter: 13.53042
#> 10 negative log likelihood: -39.96583 parameter: 11.25335
#> start estimation using optim...
#> 1 negative log likelihood: -78.54462 parameter: 12.29841
#> 2 negative log likelihood: -49.59653 parameter: 4.588141
#> 3 negative log likelihood: -97.26625 parameter: 9.061627
#> 4 negative log likelihood: -78.035 parameter: 12.2691
#> 5 negative log likelihood: -53.40447 parameter: 5.612518
#> 6 negative log likelihood: -28.90079 parameter: 0.7219027
#> 7 negative log likelihood: -57.91749 parameter: 6.00326
#> 8 negative log likelihood: -43.51794 parameter: 3.410035
#> 9 negative log likelihood: -83.14167 parameter: 7.372223
#> 10 negative log likelihood: -72.26327 parameter: 13.7905
#> start estimation using optim...
#> 1 negative log likelihood: -77.61959 parameter: 5.735607
#> 2 negative log likelihood: -53.60147 parameter: 14.28342
#> 3 negative log likelihood: -44.93065 parameter: 1.864417
#> 4 negative log likelihood: -53.32727 parameter: 13.01498
#> 5 negative log likelihood: -72.66786 parameter: 5.461107
#> 6 negative log likelihood: -58.79321 parameter: 14.98508
#> 7 negative log likelihood: -56.11402 parameter: 2.713145
#> 8 negative log likelihood: -83.05565 parameter: 6.300184
#> 9 negative log likelihood: -61.66933 parameter: 13.3725
#> 10 negative log likelihood: -83.56333 parameter: 5.252607
I check the parameter recovery. It looks well recovery of parameter
alpha.
parameter_recovery <- data.frame(true_alpha = participants_alpha, estimated_alpha = results$parameters$alpha)
parameter_recovery %>%
ggplot(aes(x = true_alpha, y= estimated_alpha)) +
geom_point()
How to fit LCM-RW to the conditioning data.
The fit_lcm() allow to estimate alpha and eta of LCM-RW (set model = 2).
However, fit_lcm() can not to estimate parameter adequatly at this
time(fit_lcm can not recover the parameter adequately).
Bugs and question
Please report on this repository’s
issues
ykunisato/lcmr documentation built on Nov. 28, 2024, 2:40 p.m.
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lcmr
The goal of lcmr is to simulate phenomena of classical conditioning and fit the conditioning data with the latent cause model.
lcmr is an R package of Latent Cause Model: LCM and Latent Cause Modulated Rescorla-Wagner model: LCM-RW made bySam Gershman.
Installation
You can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("ykunisato/lcmr")
List of functions
- fit_lcm: Fit model to conditioning data
- infer_lcm: Simulate the classical conditioning with LCM
- infer_lcm_rw: Simulate the classical conditioning with LCM-RW
How to simulate the renewal effect with LCM
The renewal effect is the phenomenon in which the change of context after extinction can lead to a return of conditioned response (CR). infer_lcm(X,opts) can simulate the renewal effect.
First, you have to prepare the design of conditioning. In followings, I prepare the experimental design consisted from acquisition (CS presents with US in context A(context = 1), 10 trials), extinction (CS presents without US in context B(context = 0),10 trials) and test (CS without US in context A(context = 0), 10 trials).
US <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0)
CS <- c(1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1)
Context <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1,1,1)
X <- cbind(US, CS, Context)
You can simulate the conditioned response using infer_lcm(). I simulate the conditioned response setting the alpha = 0.4 . The alpha is the concentrate parameter of the Chinese Restaurant Process.
library(lcmr)
sim_res <- infer_lcm(X = X, opts = list(c_alpha = 0.4,
K=10,
M=100,
a = 1,
b = 1,
stickiness = 0))
You can the plot of change of conditioned response through the trials using the following codes.
library(tidyverse)
sim_data <- data.frame(X, Trial = seq(1,length(US)), CR = sim_res$V)
sim_data %>%
ggplot(aes(x = Trial, y = CR)) +
geom_line() +
ylim(0,1)
You can draw the plot of the posterior probability of each cause using the following codes.
sim_post <- as.data.frame(sim_res$post)
sim_post %>%
mutate(Trial = seq(1,length(US))) %>%
rename(C01 = V1, C02 = V2, C03 = V3, C04 = V4, C05 = V5,
C06 = V6, C07 = V7, C08 = V8, C09 = V9, C10 = V10) %>%
gather(key = "Cause", value = "post",-Trial) %>%
mutate(Cause = as.factor(Cause)) %>%
ggplot(aes(x = Trial, y = post, color = Cause)) +
geom_line() +
ylim(0,1) +
labs(y="Posterior probability")
How to simulate the spontaneous recovery with LCM-RW
The spontaneous recovery is the phenomenon in which the time elapses following extinction can lead to a return of conditioned response (CR). infer_lcm_rw(X,opts) can simulate the spontaneous recovery.
First, you have to prepare the design of conditioning. In followings, I prepare the experimental design consisted from acquisition (CS1 presents with US, CS2 presents without US, 9 trials each CS), extinction (both CSs presents without US, 6 trials each CS) and test (both CSs presents without US after 1 day, 3 trials each CS).
US <- c(1,0,0,1,1,0,1,0,1,1,0,0,1,0,0,1,1,0, 0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0)
CS1 <- c(1,0,0,1,1,0,1,0,1,1,0,0,1,0,0,1,1,0, 1,1,0,1,0,0,1,0,1,1,0,0, 1,0,0,1,1,0)
CS2 <- c(0,1,1,0,0,1,0,1,0,0,1,1,0,1,1,0,0,1, 0,0,1,0,1,1,0,1,0,0,1,1, 0,1,1,0,0,1)
time <- c(0, seq(1:17)*4, 100+seq(1:12)*4, 86400+seq(1:6)*4)
X <- cbind(time, US, CS1, CS2)
You can simulate the conditioned response using infer_lcm(). I simulate the conditioned response setting the alpha = 0.45 and the eta = 0.2. The alpha is the concentrate parameter of the Chinese Restaurant Process and eta is the learning rate of the RW model.
library(lcmr)
sim_res <- infer_lcm_rw(X = X, opts = list(
a = 1,
b = 1,
c_alpha = 0.45,
stickiness = 0,
K = 10,
g = 1,
psi = 0,
eta = 0.2,
maxIter= 3,
w0 = 0,
sr = 0.4,
sx = 1,
theta = 0.3,
lambda = 0.005,
K = 15,
nst = 0))
You can the plot of change of conditioned response through the trials using the following codes.
library(tidyverse)
sim_data <- data.frame(X,
Trials_cs1 = cumsum(CS1),
Trials_cs2 = cumsum(CS2),
CR = sim_res$V)
sim_data %>%
filter(CS1 == 1) %>%
ggplot(aes(x = Trials_cs1, y = CR)) +
geom_line() +
ylim(0,1) +
labs(x = "Trial", y = "CR of CS1")
sim_data %>%
filter(CS2 == 1) %>%
ggplot(aes(x = Trials_cs2, y = CR)) +
geom_line() +
ylim(0,1) +
labs(x = "Trial", y = "CR of CS2")
How to fit LCM to the conditioning data.
You have to prepare the data as long format containing the following variables (Order and name is exactly the same as following):
- ID Subject ID
- CR Conditioned Response
- US Unconditioned Stimulus
- CS Conditioned Stimului or Context. If using multiple CS, set variables name as CS1,CS2,CS3…
I make the synthetic data for model fitting with the experiment design of the renewal effect.
US <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0)
CS <- c(1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1)
Context <- c(1,1,1,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1,1,1)
X <- cbind(US, CS, Context)
I make synthetic data for 100 participants.
number_of_perticiapnts <- 100
participants_alpha <- runif(number_of_perticiapnts, 0, 10)
data <- NULL
for (i in 1:number_of_perticiapnts) {
sim_data <- infer_lcm(X, opts = list(c_alpha = participants_alpha[i],
K=10,
M=100,
a = 1,
b = 1,
stickiness = 0))
sim_df <- data.frame(ID = rep(i,length(US)), CR = sim_data$V, X)
data <- rbind(data,sim_df)
}
You can estimate parameter alpha using fit_lcm(data, model, opts, parameter_range, parallel, estimation_method). You have to specify the following argument for model fitting:
-
model: 1 = latent cause model, 2 = latent cause modulated RW model
-
parameter_range: range of parameter(a_L, a_U, e_L, e_U)
-
stimation_method: 0 = optim or optimize(lcm), 1 = post mean(only latent cause model)
results <- fit_lcm(data,
model = 1,
opts = list(K=10,
M=100,
a = 1,
b = 1,
stickiness = 0),
parameter_range = list(a_L = 0, a_U = 15),
estimation_method = 0)
#> start estimation using optim...
#> 1 negative log likelihood: -68.93107 parameter: 9.338747
#> 2 negative log likelihood: -26.02116 parameter: 0.3675782
#> 3 negative log likelihood: -80.4781 parameter: 10.51741
#> 4 negative log likelihood: -64.67058 parameter: 10.66717
#> 5 negative log likelihood: -83.33142 parameter: 7.086353
#> 6 negative log likelihood: -66.90881 parameter: 9.559258
#> 7 negative log likelihood: -77.44209 parameter: 9.442029
#> 8 negative log likelihood: -57.0935 parameter: 4.267789
#> 9 negative log likelihood: -76.41846 parameter: 8.749365
#> 10 negative log likelihood: -69.69763 parameter: 8.020849
#> start estimation using optim...
#> 1 negative log likelihood: -64.92392 parameter: 9.443177
#> 2 negative log likelihood: -57.44225 parameter: 11.32144
#> 3 negative log likelihood: -83.25872 parameter: 5.919257
#> 4 negative log likelihood: -56.49635 parameter: 10.8712
#> 5 negative log likelihood: -55.65989 parameter: 3.189967
#> 6 negative log likelihood: -48.47371 parameter: 10.51762
#> 7 negative log likelihood: -53.34074 parameter: 9.695497
#> 8 negative log likelihood: -54.042 parameter: 11.74544
#> 9 negative log likelihood: -77.35321 parameter: 7.597512
#> 10 negative log likelihood: -67.97936 parameter: 8.911302
#> start estimation using optim...
#> 1 negative log likelihood: -62.00383 parameter: 14.90562
#> 2 negative log likelihood: -77.33705 parameter: 7.813928
#> 3 negative log likelihood: -78.19267 parameter: 6.977246
#> 4 negative log likelihood: -73.88672 parameter: 13.49592
#> 5 negative log likelihood: -38.47175 parameter: 2.366243
#> 6 negative log likelihood: -47.99859 parameter: 4.19377
#> 7 negative log likelihood: -49.42245 parameter: 9.035911
#> 8 negative log likelihood: -65.73083 parameter: 11.94792
#> 9 negative log likelihood: -70.93506 parameter: 12.3099
#> 10 negative log likelihood: -79.51087 parameter: 10.11439
#> start estimation using optim...
#> 1 negative log likelihood: -32.54389 parameter: 5.178435
#> 2 negative log likelihood: -56.675 parameter: 1.81261
#> 3 negative log likelihood: -21.01611 parameter: 10.21152
#> 4 negative log likelihood: -50.91674 parameter: 2.306971
#> 5 negative log likelihood: -20.887 parameter: 12.81539
#> 6 negative log likelihood: -43.20152 parameter: 3.619507
#> 7 negative log likelihood: -56.98764 parameter: 0.7176536
#> 8 negative log likelihood: -21.46005 parameter: 9.506595
#> 9 negative log likelihood: -38.12712 parameter: 4.053021
#> 10 negative log likelihood: -18.52287 parameter: 14.34828
#> start estimation using optim...
#> 1 negative log likelihood: -62.66715 parameter: 7.478134
#> 2 negative log likelihood: -66.10861 parameter: 9.689648
#> 3 negative log likelihood: -90.04608 parameter: 8.576873
#> 4 negative log likelihood: -42.81906 parameter: 2.119464
#> 5 negative log likelihood: -39.79773 parameter: 2.811006
#> 6 negative log likelihood: -56.47538 parameter: 4.636176
#> 7 negative log likelihood: -41.02308 parameter: 2.308557
#> 8 negative log likelihood: -60.81503 parameter: 14.52489
#> 9 negative log likelihood: -63.52146 parameter: 4.920543
#> 10 negative log likelihood: -27.70265 parameter: 1.022802
#> start estimation using optim...
#> 1 negative log likelihood: -62.14771 parameter: 5.841455
#> 2 negative log likelihood: -57.79049 parameter: 10.11542
#> 3 negative log likelihood: -58.11523 parameter: 4.998664
#> 4 negative log likelihood: -94.7316 parameter: 7.932679
#> 5 negative log likelihood: -68.34737 parameter: 6.717267
#> 6 negative log likelihood: -77.29065 parameter: 8.903554
#> 7 negative log likelihood: -67.13898 parameter: 6.695447
#> 8 negative log likelihood: -83.16525 parameter: 9.330348
#> 9 negative log likelihood: -77.95292 parameter: 10.54581
#> 10 negative log likelihood: -75.86573 parameter: 8.933335
#> start estimation using optim...
#> 1 negative log likelihood: -49.51907 parameter: 1.234653
#> 2 negative log likelihood: -57.129 parameter: 2.528196
#> 3 negative log likelihood: -67.95352 parameter: 5.007662
#> 4 negative log likelihood: -46.87232 parameter: 9.250429
#> 5 negative log likelihood: -50.31762 parameter: 9.673178
#> 6 negative log likelihood: -37.28071 parameter: 12.70792
#> 7 negative log likelihood: -48.38308 parameter: 3.861842
#> 8 negative log likelihood: -58.99754 parameter: 6.539249
#> 9 negative log likelihood: -72.8623 parameter: 4.27512
#> 10 negative log likelihood: -78.85829 parameter: 5.126851
#> start estimation using optim...
#> 1 negative log likelihood: -31.86193 parameter: 1.698798
#> 2 negative log likelihood: -73.64166 parameter: 7.010969
#> 3 negative log likelihood: -47.47838 parameter: 3.598635
#> 4 negative log likelihood: -68.16131 parameter: 6.91176
#> 5 negative log likelihood: -73.63077 parameter: 15
#> 6 negative log likelihood: -40.79348 parameter: 2.34876
#> 7 negative log likelihood: -75.81475 parameter: 15
#> 8 negative log likelihood: -77.06133 parameter: 7.884721
#> 9 negative log likelihood: -62.99629 parameter: 8.728984
#> 10 negative log likelihood: -55.37552 parameter: 5.138216
#> start estimation using optim...
#> 1 negative log likelihood: -68.60547 parameter: 6.741362
#> 2 negative log likelihood: -50.27167 parameter: 14.44494
#> 3 negative log likelihood: -46.52262 parameter: 14.64926
#> 4 negative log likelihood: -82.56435 parameter: 6.156955
#> 5 negative log likelihood: -44.75029 parameter: 12.94743
#> 6 negative log likelihood: -61.13922 parameter: 7.02101
#> 7 negative log likelihood: -93.67268 parameter: 5.562689
#> 8 negative log likelihood: -72.78193 parameter: 4.908007
#> 9 negative log likelihood: -52.70558 parameter: 14.74546
#> 10 negative log likelihood: -67.47851 parameter: 8.182741
#> start estimation using optim...
#> 1 negative log likelihood: -65.59299 parameter: 1.256923
#> 2 negative log likelihood: -54.93582 parameter: 2.104381
#> 3 negative log likelihood: -20.59173 parameter: 15
#> 4 negative log likelihood: -24.46186 parameter: 8.411613
#> 5 negative log likelihood: -77.73683 parameter: 0.6783485
#> 6 negative log likelihood: -60.49068 parameter: 1.379822
#> 7 negative log likelihood: -30.66592 parameter: 5.474521
#> 8 negative log likelihood: -59.41846 parameter: 1.565369
#> 9 negative log likelihood: -27.11514 parameter: 7.028851
#> 10 negative log likelihood: -21.48897 parameter: 12.68343
#> start estimation using optim...
#> 1 negative log likelihood: -45.33594 parameter: 12.67134
#> 2 negative log likelihood: -50.2886 parameter: 7.053752
#> 3 negative log likelihood: -69.98036 parameter: 4.30463
#> 4 negative log likelihood: -88.99538 parameter: 3.81923
#> 5 negative log likelihood: -44.3736 parameter: 11.35211
#> 6 negative log likelihood: -68.61343 parameter: 4.490441
#> 7 negative log likelihood: -72.66067 parameter: 4.328148
#> 8 negative log likelihood: -42.26594 parameter: 14.29738
#> 9 negative log likelihood: -53.30546 parameter: 1.123382
#> 10 negative log likelihood: -49.8767 parameter: 8.581437
#> start estimation using optim...
#> 1 negative log likelihood: -44.24601 parameter: 13.86858
#> 2 negative log likelihood: -53.8905 parameter: 2.28762
#> 3 negative log likelihood: -48.31549 parameter: 1.548407
#> 4 negative log likelihood: -76.48998 parameter: 6.62149
#> 5 negative log likelihood: -83.94385 parameter: 6.215139
#> 6 negative log likelihood: -74.52221 parameter: 5.160426
#> 7 negative log likelihood: -48.40887 parameter: 10.98952
#> 8 negative log likelihood: -46.58893 parameter: 12.77046
#> 9 negative log likelihood: -88.18449 parameter: 4.218944
#> 10 negative log likelihood: -60.16074 parameter: 8.639111
#> start estimation using optim...
#> 1 negative log likelihood: -69.56147 parameter: 14.29508
#> 2 negative log likelihood: -64.90334 parameter: 10.99879
#> 3 negative log likelihood: -60.67211 parameter: 5.968699
#> 4 negative log likelihood: -66.72734 parameter: 7.328636
#> 5 negative log likelihood: -64.72625 parameter: 6.088899
#> 6 negative log likelihood: -55.84981 parameter: 6.603309
#> 7 negative log likelihood: -65.05975 parameter: 13.76076
#> 8 negative log likelihood: -75.07029 parameter: 13.9085
#> 9 negative log likelihood: -86.15483 parameter: 8.542471
#> 10 negative log likelihood: -43.94326 parameter: 3.276057
#> start estimation using optim...
#> 1 negative log likelihood: -75.60352 parameter: 15
#> 2 negative log likelihood: -31.23569 parameter: 0.4133886
#> 3 negative log likelihood: -75.68217 parameter: 12.39723
#> 4 negative log likelihood: -41.64245 parameter: 3.093616
#> 5 negative log likelihood: -81.78599 parameter: 11.69807
#> 6 negative log likelihood: -49.04646 parameter: 7.254776
#> 7 negative log likelihood: -86.89739 parameter: 10.97803
#> 8 negative log likelihood: -85.17596 parameter: 10.127
#> 9 negative log likelihood: -62.28164 parameter: 9.321513
#> 10 negative log likelihood: -75.85051 parameter: 11.83984
#> start estimation using optim...
#> 1 negative log likelihood: -72.38997 parameter: 2.099149
#> 2 negative log likelihood: -67.39006 parameter: 2.757206
#> 3 negative log likelihood: -63.23311 parameter: 2.797478
#> 4 negative log likelihood: -46.50171 parameter: 5.376917
#> 5 negative log likelihood: -61.07364 parameter: 3.757973
#> 6 negative log likelihood: -59.95383 parameter: 4.163329
#> 7 negative log likelihood: -60.30753 parameter: 1.531522
#> 8 negative log likelihood: -50.13731 parameter: 5.456013
#> 9 negative log likelihood: -46.94899 parameter: 5.53381
#> 10 negative log likelihood: -46.52165 parameter: 6.222871
#> start estimation using optim...
#> 1 negative log likelihood: -41.25066 parameter: 1.149321
#> 2 negative log likelihood: -42.10067 parameter: 1.23338
#> 3 negative log likelihood: -54.01341 parameter: 3.668721
#> 4 negative log likelihood: -48.26986 parameter: 9.186796
#> 5 negative log likelihood: -43.07102 parameter: 12.7331
#> 6 negative log likelihood: -58.53176 parameter: 4.458951
#> 7 negative log likelihood: -54.72104 parameter: 3.474101
#> 8 negative log likelihood: -49.42262 parameter: 10.72631
#> 9 negative log likelihood: -45.47083 parameter: 13.43693
#> 10 negative log likelihood: -77.6423 parameter: 5.0591
#> start estimation using optim...
#> 1 negative log likelihood: -87.53345 parameter: 10.2463
#> 2 negative log likelihood: -74.05624 parameter: 10.45852
#> 3 negative log likelihood: -40.36843 parameter: 2.445525
#> 4 negative log likelihood: -72.96345 parameter: 15
#> 5 negative log likelihood: -77.07866 parameter: 8.32917
#> 6 negative log likelihood: -56.42384 parameter: 4.834834
#> 7 negative log likelihood: -70.15187 parameter: 13.02544
#> 8 negative log likelihood: -84.79345 parameter: 8.653321
#> 9 negative log likelihood: -29.21501 parameter: 0.6844252
#> 10 negative log likelihood: -74.21358 parameter: 14.67927
#> start estimation using optim...
#> 1 negative log likelihood: -85.93031 parameter: 6.965475
#> 2 negative log likelihood: -89.09536 parameter: 9.333167
#> 3 negative log likelihood: -65.56472 parameter: 4.85201
#> 4 negative log likelihood: -52.79434 parameter: 12.70209
#> 5 negative log likelihood: -53.34853 parameter: 9.662431
#> 6 negative log likelihood: -60.22094 parameter: 6.583974
#> 7 negative log likelihood: -59.66208 parameter: 13.91756
#> 8 negative log likelihood: -29.60039 parameter: 0.3310106
#> 9 negative log likelihood: -84.57157 parameter: 6.058432
#> 10 negative log likelihood: -63.40726 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -34.09429 parameter: 3.307481
#> 2 negative log likelihood: -34.10379 parameter: 2.386433
#> 3 negative log likelihood: -19.57867 parameter: 13.86891
#> 4 negative log likelihood: -43.29623 parameter: 2.45228
#> 5 negative log likelihood: -21.45595 parameter: 11.55515
#> 6 negative log likelihood: -22.35129 parameter: 14.07767
#> 7 negative log likelihood: -41.29892 parameter: 3.1128
#> 8 negative log likelihood: -41.30206 parameter: 1.456905
#> 9 negative log likelihood: -40.53618 parameter: 1.215634
#> 10 negative log likelihood: -21.72874 parameter: 11.85815
#> start estimation using optim...
#> 1 negative log likelihood: -76.55429 parameter: 2.027636
#> 2 negative log likelihood: -34.03212 parameter: 10.01564
#> 3 negative log likelihood: -35.66685 parameter: 9.526202
#> 4 negative log likelihood: -45.53935 parameter: 6.434802
#> 5 negative log likelihood: -63.82621 parameter: 1.897562
#> 6 negative log likelihood: -75.56839 parameter: 1.680722
#> 7 negative log likelihood: -74.36281 parameter: 3.046716
#> 8 negative log likelihood: -67.87432 parameter: 2.667689
#> 9 negative log likelihood: -44.72969 parameter: 7.481055
#> 10 negative log likelihood: -75.88722 parameter: 2.35553
#> start estimation using optim...
#> 1 negative log likelihood: -16.53751 parameter: 12.29827
#> 2 negative log likelihood: -16.27095 parameter: 11.74293
#> 3 negative log likelihood: -24.90841 parameter: 5.956508
#> 4 negative log likelihood: -14.27769 parameter: 13.17795
#> 5 negative log likelihood: -19.99402 parameter: 11.24491
#> 6 negative log likelihood: -34.64004 parameter: 2.153256
#> 7 negative log likelihood: -17.63213 parameter: 13.00965
#> 8 negative log likelihood: -32.76135 parameter: 0.8258914
#> 9 negative log likelihood: -17.1903 parameter: 15
#> 10 negative log likelihood: -19.21381 parameter: 9.888523
#> start estimation using optim...
#> 1 negative log likelihood: -82.25249 parameter: 9.539433
#> 2 negative log likelihood: -64.73025 parameter: 9.283058
#> 3 negative log likelihood: -52.76426 parameter: 4.637397
#> 4 negative log likelihood: -66.71683 parameter: 6.098114
#> 5 negative log likelihood: -61.45548 parameter: 10.72881
#> 6 negative log likelihood: -84.3336 parameter: 8.875832
#> 7 negative log likelihood: -82.66732 parameter: 12.10117
#> 8 negative log likelihood: -86.38603 parameter: 10.92782
#> 9 negative log likelihood: -110.1366 parameter: 9.607332
#> 10 negative log likelihood: -65.94313 parameter: 7.491177
#> start estimation using optim...
#> 1 negative log likelihood: -73.70591 parameter: 2.022448
#> 2 negative log likelihood: -25.06859 parameter: 9.264398
#> 3 negative log likelihood: -51.74997 parameter: 2.826565
#> 4 negative log likelihood: -56.33536 parameter: 2.99748
#> 5 negative log likelihood: -62.6997 parameter: 1.459982
#> 6 negative log likelihood: -23.07306 parameter: 11.25321
#> 7 negative log likelihood: -73.28898 parameter: 1.651518
#> 8 negative log likelihood: -27.90453 parameter: 8.634779
#> 9 negative log likelihood: -50.77552 parameter: 0.6385759
#> 10 negative log likelihood: -82.03116 parameter: 0.6277502
#> start estimation using optim...
#> 1 negative log likelihood: -83.24167 parameter: 8.537277
#> 2 negative log likelihood: -67.82449 parameter: 8.144161
#> 3 negative log likelihood: -75.59925 parameter: 13.27375
#> 4 negative log likelihood: -68.51578 parameter: 7.402862
#> 5 negative log likelihood: -86.20981 parameter: 15
#> 6 negative log likelihood: -75.84077 parameter: 15
#> 7 negative log likelihood: -62.8798 parameter: 6.876673
#> 8 negative log likelihood: -84.53404 parameter: 15
#> 9 negative log likelihood: -82.98957 parameter: 8.52712
#> 10 negative log likelihood: -91.09953 parameter: 8.938555
#> start estimation using optim...
#> 1 negative log likelihood: -33.85104 parameter: 1.169598
#> 2 negative log likelihood: -36.77381 parameter: 1.61109
#> 3 negative log likelihood: -78.33824 parameter: 6.268581
#> 4 negative log likelihood: -64.20651 parameter: 5.556501
#> 5 negative log likelihood: -43.15798 parameter: 4.2174
#> 6 negative log likelihood: -82.62186 parameter: 7.330099
#> 7 negative log likelihood: -74.87909 parameter: 10.29183
#> 8 negative log likelihood: -66.08276 parameter: 4.98656
#> 9 negative log likelihood: -73.11966 parameter: 11.5243
#> 10 negative log likelihood: -61.6653 parameter: 14.20668
#> start estimation using optim...
#> 1 negative log likelihood: -48.95053 parameter: 13.5239
#> 2 negative log likelihood: -79.90821 parameter: 10.11142
#> 3 negative log likelihood: -54.32 parameter: 12.56012
#> 4 negative log likelihood: -72.62349 parameter: 7.297012
#> 5 negative log likelihood: -40.77968 parameter: 2.353863
#> 6 negative log likelihood: -73.40685 parameter: 6.00917
#> 7 negative log likelihood: -78.43721 parameter: 5.432832
#> 8 negative log likelihood: -47.89525 parameter: 2.91985
#> 9 negative log likelihood: -53.48126 parameter: 10.52827
#> 10 negative log likelihood: -57.84458 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -90.74454 parameter: 5.767412
#> 2 negative log likelihood: -70.32167 parameter: 9.206044
#> 3 negative log likelihood: -43.31184 parameter: 1.310498
#> 4 negative log likelihood: -37.42762 parameter: 1.367151
#> 5 negative log likelihood: -81.30936 parameter: 4.608688
#> 6 negative log likelihood: -46.36987 parameter: 2.182122
#> 7 negative log likelihood: -31.91242 parameter: 0.3446528
#> 8 negative log likelihood: -63.79256 parameter: 3.518625
#> 9 negative log likelihood: -34.66916 parameter: 1.654677
#> 10 negative log likelihood: -75.42098 parameter: 10.22701
#> start estimation using optim...
#> 1 negative log likelihood: -30.54896 parameter: 7.958593
#> 2 negative log likelihood: -28.29009 parameter: 14.28347
#> 3 negative log likelihood: -80.98744 parameter: 1.685682
#> 4 negative log likelihood: -40.60019 parameter: 5.444615
#> 5 negative log likelihood: -82.14314 parameter: 0.8103922
#> 6 negative log likelihood: -27.74404 parameter: 13.18567
#> 7 negative log likelihood: -70.18021 parameter: 2.61379
#> 8 negative log likelihood: -72.48156 parameter: 1.011445
#> 9 negative log likelihood: -27.84529 parameter: 11.95127
#> 10 negative log likelihood: -24.88216 parameter: 13.08906
#> start estimation using optim...
#> 1 negative log likelihood: -66.90396 parameter: 5.463095
#> 2 negative log likelihood: -50.44217 parameter: 6.940811
#> 3 negative log likelihood: -36.09925 parameter: 14.38933
#> 4 negative log likelihood: -39.8189 parameter: 11.34655
#> 5 negative log likelihood: -39.69457 parameter: 7.975902
#> 6 negative log likelihood: -96.65382 parameter: 3.158589
#> 7 negative log likelihood: -66.17904 parameter: 4.364559
#> 8 negative log likelihood: -66.08425 parameter: 2.282634
#> 9 negative log likelihood: -44.01731 parameter: 0.4646368
#> 10 negative log likelihood: -74.15804 parameter: 3.630944
#> start estimation using optim...
#> 1 negative log likelihood: -82.3465 parameter: 4.120349
#> 2 negative log likelihood: -95.20235 parameter: 3.562065
#> 3 negative log likelihood: -49.344 parameter: 7.311928
#> 4 negative log likelihood: -61.66706 parameter: 3.177804
#> 5 negative log likelihood: -73.23975 parameter: 3.951321
#> 6 negative log likelihood: -50.31749 parameter: 8.797769
#> 7 negative log likelihood: -49.28397 parameter: 8.30322
#> 8 negative log likelihood: -92.18546 parameter: 4.103762
#> 9 negative log likelihood: -56.59415 parameter: 6.393678
#> 10 negative log likelihood: -37.18746 parameter: 13.94622
#> start estimation using optim...
#> 1 negative log likelihood: -67.95936 parameter: 6.78567
#> 2 negative log likelihood: -28.70078 parameter: 1.748097
#> 3 negative log likelihood: -33.9806 parameter: 1.649816
#> 4 negative log likelihood: -87.72871 parameter: 11.8426
#> 5 negative log likelihood: -33.43603 parameter: 2.149289
#> 6 negative log likelihood: -88.07079 parameter: 11.7247
#> 7 negative log likelihood: -82.32831 parameter: 13.21751
#> 8 negative log likelihood: -62.01483 parameter: 5.706789
#> 9 negative log likelihood: -30.80159 parameter: 2.012303
#> 10 negative log likelihood: -82.61814 parameter: 11.41392
#> start estimation using optim...
#> 1 negative log likelihood: -60.64248 parameter: 3.433318
#> 2 negative log likelihood: -62.26185 parameter: 2.058101
#> 3 negative log likelihood: -52.26701 parameter: 1.406696
#> 4 negative log likelihood: -23.83104 parameter: 13.69293
#> 5 negative log likelihood: -25.16893 parameter: 12.86142
#> 6 negative log likelihood: -73.36519 parameter: 1.817225
#> 7 negative log likelihood: -25.38822 parameter: 13.16897
#> 8 negative log likelihood: -44.5937 parameter: 5.070478
#> 9 negative log likelihood: -64.53321 parameter: 2.815886
#> 10 negative log likelihood: -25.46476 parameter: 11.25492
#> start estimation using optim...
#> 1 negative log likelihood: -69.83222 parameter: 3.829654
#> 2 negative log likelihood: -86.72915 parameter: 3.586464
#> 3 negative log likelihood: -42.29866 parameter: 10.37479
#> 4 negative log likelihood: -74.64601 parameter: 3.783505
#> 5 negative log likelihood: -45.72632 parameter: 8.94274
#> 6 negative log likelihood: -49.17756 parameter: 5.924865
#> 7 negative log likelihood: -42.22815 parameter: 11.3358
#> 8 negative log likelihood: -82.94149 parameter: 3.218045
#> 9 negative log likelihood: -35.11917 parameter: 14.30933
#> 10 negative log likelihood: -38.66154 parameter: 11.70147
#> start estimation using optim...
#> 1 negative log likelihood: -88.75854 parameter: 9.112368
#> 2 negative log likelihood: -39.87782 parameter: 1.798267
#> 3 negative log likelihood: -48.46517 parameter: 3.155194
#> 4 negative log likelihood: -63.09472 parameter: 10.52265
#> 5 negative log likelihood: -54.94587 parameter: 11.59965
#> 6 negative log likelihood: -87.522 parameter: 8.404071
#> 7 negative log likelihood: -59.47911 parameter: 14.50615
#> 8 negative log likelihood: -62.41127 parameter: 4.510583
#> 9 negative log likelihood: -91.23758 parameter: 8.320026
#> 10 negative log likelihood: -68.32295 parameter: 9.308277
#> start estimation using optim...
#> 1 negative log likelihood: -27.57586 parameter: 6.137441
#> 2 negative log likelihood: -38.0606 parameter: 2.510832
#> 3 negative log likelihood: -44.4859 parameter: 1.803026
#> 4 negative log likelihood: -22.19358 parameter: 10.41345
#> 5 negative log likelihood: -21.97219 parameter: 9.367151
#> 6 negative log likelihood: -19.66244 parameter: 15
#> 7 negative log likelihood: -41.17847 parameter: 1.682352
#> 8 negative log likelihood: -36.81599 parameter: 2.421701
#> 9 negative log likelihood: -17.44795 parameter: 13.21448
#> 10 negative log likelihood: -31.07327 parameter: 5.023822
#> start estimation using optim...
#> 1 negative log likelihood: -35.71813 parameter: 0.7800084
#> 2 negative log likelihood: -80.39989 parameter: 8.285494
#> 3 negative log likelihood: -67.74763 parameter: 7.130382
#> 4 negative log likelihood: -77.75794 parameter: 6.495111
#> 5 negative log likelihood: -48.74721 parameter: 14.45743
#> 6 negative log likelihood: -78.89994 parameter: 7.739559
#> 7 negative log likelihood: -62.10032 parameter: 6.486105
#> 8 negative log likelihood: -57.33057 parameter: 10.61367
#> 9 negative log likelihood: -63.07836 parameter: 11.51551
#> 10 negative log likelihood: -86.69404 parameter: 6.088278
#> start estimation using optim...
#> 1 negative log likelihood: -49.23079 parameter: 6.265202
#> 2 negative log likelihood: -69.9541 parameter: 6.063429
#> 3 negative log likelihood: -46.58112 parameter: 5.223559
#> 4 negative log likelihood: -68.66055 parameter: 7.360215
#> 5 negative log likelihood: -43.55156 parameter: 12.3233
#> 6 negative log likelihood: -51.54307 parameter: 5.682261
#> 7 negative log likelihood: -36.92385 parameter: 0.4192884
#> 8 negative log likelihood: -54.96408 parameter: 5.665164
#> 9 negative log likelihood: -53.33683 parameter: 9.408152
#> 10 negative log likelihood: -41.55015 parameter: 14.64535
#> start estimation using optim...
#> 1 negative log likelihood: -85.00928 parameter: 5.511766
#> 2 negative log likelihood: -59.85152 parameter: 9.262709
#> 3 negative log likelihood: -32.40923 parameter: 0.1609748
#> 4 negative log likelihood: -71.21277 parameter: 5.16302
#> 5 negative log likelihood: -38.40445 parameter: 1.171964
#> 6 negative log likelihood: -80.13308 parameter: 5.483381
#> 7 negative log likelihood: -82.43774 parameter: 7.073029
#> 8 negative log likelihood: -60.4034 parameter: 3.185816
#> 9 negative log likelihood: -75.47323 parameter: 3.969062
#> 10 negative log likelihood: -69.55079 parameter: 6.259574
#> start estimation using optim...
#> 1 negative log likelihood: -70.1513 parameter: 6.007896
#> 2 negative log likelihood: -83.67964 parameter: 4.505687
#> 3 negative log likelihood: -43.81874 parameter: 13.26926
#> 4 negative log likelihood: -61.37985 parameter: 7.261691
#> 5 negative log likelihood: -47.61599 parameter: 11.19702
#> 6 negative log likelihood: -55.61537 parameter: 9.450091
#> 7 negative log likelihood: -66.34296 parameter: 7.814492
#> 8 negative log likelihood: -44.46693 parameter: 11.62254
#> 9 negative log likelihood: -66.71898 parameter: 6.641272
#> 10 negative log likelihood: -80.75136 parameter: 5.843982
#> start estimation using optim...
#> 1 negative log likelihood: -78.07739 parameter: 5.733908
#> 2 negative log likelihood: -59.305 parameter: 12.64969
#> 3 negative log likelihood: -67.83555 parameter: 5.38937
#> 4 negative log likelihood: -70.98456 parameter: 4.361148
#> 5 negative log likelihood: -56.93915 parameter: 13.03083
#> 6 negative log likelihood: -87.83734 parameter: 6.136771
#> 7 negative log likelihood: -85.86122 parameter: 6.074558
#> 8 negative log likelihood: -69.25626 parameter: 6.202478
#> 9 negative log likelihood: -69.85206 parameter: 5.481137
#> 10 negative log likelihood: -65.79538 parameter: 10.76259
#> start estimation using optim...
#> 1 negative log likelihood: -81.71534 parameter: 8.5301
#> 2 negative log likelihood: -53.85584 parameter: 5.058997
#> 3 negative log likelihood: -93.0578 parameter: 8.521715
#> 4 negative log likelihood: -65.11241 parameter: 14.997
#> 5 negative log likelihood: -74.01733 parameter: 13.158
#> 6 negative log likelihood: -63.71561 parameter: 15
#> 7 negative log likelihood: -25.06896 parameter: 0.4279749
#> 8 negative log likelihood: -70.08682 parameter: 10.90845
#> 9 negative log likelihood: -85.69239 parameter: 7.022433
#> 10 negative log likelihood: -68.70035 parameter: 13.96966
#> start estimation using optim...
#> 1 negative log likelihood: -35.47614 parameter: 0.8188568
#> 2 negative log likelihood: -69.26145 parameter: 8.279615
#> 3 negative log likelihood: -81.85911 parameter: 5.536929
#> 4 negative log likelihood: -53.47123 parameter: 11.36644
#> 5 negative log likelihood: -64.47399 parameter: 7.060203
#> 6 negative log likelihood: -55.31398 parameter: 5.94822
#> 7 negative log likelihood: -71.92346 parameter: 7.647822
#> 8 negative log likelihood: -51.52162 parameter: 14.86924
#> 9 negative log likelihood: -63.78892 parameter: 6.478472
#> 10 negative log likelihood: -76.13096 parameter: 6.656689
#> start estimation using optim...
#> 1 negative log likelihood: -81.5848 parameter: 8.077184
#> 2 negative log likelihood: -60.07464 parameter: 8.647308
#> 3 negative log likelihood: -61.15218 parameter: 15
#> 4 negative log likelihood: -27.53417 parameter: 0.802612
#> 5 negative log likelihood: -60.03447 parameter: 11.22596
#> 6 negative log likelihood: -66.07483 parameter: 6.800104
#> 7 negative log likelihood: -72.62981 parameter: 11.51555
#> 8 negative log likelihood: -83.31504 parameter: 5.800105
#> 9 negative log likelihood: -57.31879 parameter: 8.293923
#> 10 negative log likelihood: -71.09461 parameter: 10.73913
#> start estimation using optim...
#> 1 negative log likelihood: -49.96278 parameter: 7.517817
#> 2 negative log likelihood: -52.04595 parameter: 3.235449
#> 3 negative log likelihood: -41.10027 parameter: 1.313876
#> 4 negative log likelihood: -71.34764 parameter: 6.389983
#> 5 negative log likelihood: -89.63525 parameter: 5.56552
#> 6 negative log likelihood: -47.07305 parameter: 12.24472
#> 7 negative log likelihood: -51.90444 parameter: 6.773234
#> 8 negative log likelihood: -50.79288 parameter: 12.29835
#> 9 negative log likelihood: -70.75994 parameter: 6.981888
#> 10 negative log likelihood: -63.73869 parameter: 6.048201
#> start estimation using optim...
#> 1 negative log likelihood: -73.56138 parameter: 7.534296
#> 2 negative log likelihood: -83.71555 parameter: 6.804185
#> 3 negative log likelihood: -66.75177 parameter: 8.829685
#> 4 negative log likelihood: -30.86804 parameter: 0.5301873
#> 5 negative log likelihood: -59.57941 parameter: 6.836936
#> 6 negative log likelihood: -70.01362 parameter: 6.16402
#> 7 negative log likelihood: -44.83184 parameter: 11.62097
#> 8 negative log likelihood: -54.65167 parameter: 5.889834
#> 9 negative log likelihood: -59.61016 parameter: 3.768307
#> 10 negative log likelihood: -88.54621 parameter: 6.067795
#> start estimation using optim...
#> 1 negative log likelihood: -60.63145 parameter: 0.8025913
#> 2 negative log likelihood: -25.61703 parameter: 8.636053
#> 3 negative log likelihood: -44.05673 parameter: 3.401084
#> 4 negative log likelihood: -27.06995 parameter: 8.98917
#> 5 negative log likelihood: -40.26164 parameter: 4.469936
#> 6 negative log likelihood: -66.78068 parameter: 1.239746
#> 7 negative log likelihood: -26.63198 parameter: 9.204597
#> 8 negative log likelihood: -20.43571 parameter: 14.37538
#> 9 negative log likelihood: -27.11993 parameter: 8.788018
#> 10 negative log likelihood: -42.78254 parameter: 0.7510155
#> start estimation using optim...
#> 1 negative log likelihood: -43.34375 parameter: 10.79857
#> 2 negative log likelihood: -77.34439 parameter: 5.164785
#> 3 negative log likelihood: -52.97514 parameter: 8.223697
#> 4 negative log likelihood: -46.60238 parameter: 9.770816
#> 5 negative log likelihood: -48.236 parameter: 10.24107
#> 6 negative log likelihood: -42.68219 parameter: 10.64313
#> 7 negative log likelihood: -68.79683 parameter: 4.962512
#> 8 negative log likelihood: -66.10737 parameter: 7.413628
#> 9 negative log likelihood: -41.97573 parameter: 12.20466
#> 10 negative log likelihood: -68.4955 parameter: 4.438063
#> start estimation using optim...
#> 1 negative log likelihood: -35.19024 parameter: 13.28574
#> 2 negative log likelihood: -93.73872 parameter: 2.782206
#> 3 negative log likelihood: -43.074 parameter: 3.52805
#> 4 negative log likelihood: -82.46761 parameter: 3.136478
#> 5 negative log likelihood: -65.14128 parameter: 5.648269
#> 6 negative log likelihood: -78.2122 parameter: 2.888368
#> 7 negative log likelihood: -74.52411 parameter: 4.925291
#> 8 negative log likelihood: -83.09033 parameter: 3.245194
#> 9 negative log likelihood: -55.71187 parameter: 5.455819
#> 10 negative log likelihood: -79.90584 parameter: 4.055204
#> start estimation using optim...
#> 1 negative log likelihood: -94.49272 parameter: 9.147541
#> 2 negative log likelihood: -84.95814 parameter: 15
#> 3 negative log likelihood: -74.55103 parameter: 15
#> 4 negative log likelihood: -61.9665 parameter: 11.79524
#> 5 negative log likelihood: -77.99796 parameter: 14.21682
#> 6 negative log likelihood: -53.89908 parameter: 10.50576
#> 7 negative log likelihood: -79.72469 parameter: 10.77002
#> 8 negative log likelihood: -76.09174 parameter: 9.816975
#> 9 negative log likelihood: -89.11021 parameter: 15
#> 10 negative log likelihood: -66.28595 parameter: 7.167496
#> start estimation using optim...
#> 1 negative log likelihood: -58.12865 parameter: 5.415008
#> 2 negative log likelihood: -30.88993 parameter: 15
#> 3 negative log likelihood: -34.94784 parameter: 11.26549
#> 4 negative log likelihood: -33.89612 parameter: 10.4324
#> 5 negative log likelihood: -72.18966 parameter: 3.992682
#> 6 negative log likelihood: -73.32812 parameter: 2.367542
#> 7 negative log likelihood: -57.5561 parameter: 3.416234
#> 8 negative log likelihood: -53.20664 parameter: 5.201868
#> 9 negative log likelihood: -32.43264 parameter: 10.75404
#> 10 negative log likelihood: -37.80484 parameter: 9.051716
#> start estimation using optim...
#> 1 negative log likelihood: -36.08555 parameter: 1.844478
#> 2 negative log likelihood: -63.8507 parameter: 14.78204
#> 3 negative log likelihood: -93.16648 parameter: 6.34393
#> 4 negative log likelihood: -78.3782 parameter: 6.279647
#> 5 negative log likelihood: -79.43974 parameter: 9.914446
#> 6 negative log likelihood: -64.74089 parameter: 8.416384
#> 7 negative log likelihood: -59.37189 parameter: 13.08478
#> 8 negative log likelihood: -36.51775 parameter: 1.546999
#> 9 negative log likelihood: -90.85812 parameter: 7.199438
#> 10 negative log likelihood: -90.92438 parameter: 6.60675
#> start estimation using optim...
#> 1 negative log likelihood: -57.02511 parameter: 4.340577
#> 2 negative log likelihood: -73.82363 parameter: 14.26576
#> 3 negative log likelihood: -64.22477 parameter: 7.82121
#> 4 negative log likelihood: -69.7967 parameter: 8.652537
#> 5 negative log likelihood: -89.23614 parameter: 9.398977
#> 6 negative log likelihood: -81.14022 parameter: 12.95426
#> 7 negative log likelihood: -31.06042 parameter: 1.659973
#> 8 negative log likelihood: -65.84791 parameter: 15
#> 9 negative log likelihood: -71.20846 parameter: 15
#> 10 negative log likelihood: -45.74117 parameter: 3.382983
#> start estimation using optim...
#> 1 negative log likelihood: -64.15404 parameter: 3.578936
#> 2 negative log likelihood: -51.21501 parameter: 9.913758
#> 3 negative log likelihood: -57.07111 parameter: 8.060067
#> 4 negative log likelihood: -30.27622 parameter: 0.6508239
#> 5 negative log likelihood: -93.00935 parameter: 5.526967
#> 6 negative log likelihood: -72.09761 parameter: 5.995908
#> 7 negative log likelihood: -41.76745 parameter: 1.322811
#> 8 negative log likelihood: -69.48657 parameter: 3.496565
#> 9 negative log likelihood: -45.62946 parameter: 12.4342
#> 10 negative log likelihood: -42.847 parameter: 11.02675
#> start estimation using optim...
#> 1 negative log likelihood: -55.88996 parameter: 4.07496
#> 2 negative log likelihood: -67.66967 parameter: 10.46668
#> 3 negative log likelihood: -71.20902 parameter: 9.530763
#> 4 negative log likelihood: -64.2141 parameter: 6.363875
#> 5 negative log likelihood: -76.36247 parameter: 5.43855
#> 6 negative log likelihood: -59.43495 parameter: 13.43424
#> 7 negative log likelihood: -46.71021 parameter: 4.348673
#> 8 negative log likelihood: -51.56212 parameter: 3.689231
#> 9 negative log likelihood: -65.84961 parameter: 8.237662
#> 10 negative log likelihood: -63.03832 parameter: 6.524029
#> start estimation using optim...
#> 1 negative log likelihood: -50.10271 parameter: 14.38846
#> 2 negative log likelihood: -77.79353 parameter: 6.996787
#> 3 negative log likelihood: -64.59221 parameter: 9.273021
#> 4 negative log likelihood: -46.94971 parameter: 13.85468
#> 5 negative log likelihood: -56.3644 parameter: 15
#> 6 negative log likelihood: -85.93653 parameter: 7.941712
#> 7 negative log likelihood: -60.03191 parameter: 9.717564
#> 8 negative log likelihood: -25.76526 parameter: 0.40369
#> 9 negative log likelihood: -71.94741 parameter: 5.141918
#> 10 negative log likelihood: -44.12204 parameter: 7.404838
#> start estimation using optim...
#> 1 negative log likelihood: -90.62876 parameter: 8.077674
#> 2 negative log likelihood: -49.62579 parameter: 3.697812
#> 3 negative log likelihood: -73.8488 parameter: 4.99126
#> 4 negative log likelihood: -79.68736 parameter: 7.801352
#> 5 negative log likelihood: -91.95049 parameter: 8.346534
#> 6 negative log likelihood: -66.12805 parameter: 8.315502
#> 7 negative log likelihood: -80.16714 parameter: 7.82448
#> 8 negative log likelihood: -55.66812 parameter: 6.698771
#> 9 negative log likelihood: -46.99043 parameter: 3.674822
#> 10 negative log likelihood: -74.62983 parameter: 9.348912
#> start estimation using optim...
#> 1 negative log likelihood: -34.10835 parameter: 7.145754
#> 2 negative log likelihood: -21.93466 parameter: 14.23398
#> 3 negative log likelihood: -49.00094 parameter: 3.465755
#> 4 negative log likelihood: -39.73546 parameter: 1.553881
#> 5 negative log likelihood: -66.41656 parameter: 1.758147
#> 6 negative log likelihood: -57.25495 parameter: 1.18038
#> 7 negative log likelihood: -25.69229 parameter: 9.765804
#> 8 negative log likelihood: -30.23259 parameter: 5.318697
#> 9 negative log likelihood: -20.25462 parameter: 12.47292
#> 10 negative log likelihood: -81.16125 parameter: 0.973253
#> start estimation using optim...
#> 1 negative log likelihood: -39.72178 parameter: 13.66454
#> 2 negative log likelihood: -42.10731 parameter: 14.54376
#> 3 negative log likelihood: -46.52376 parameter: 10.15715
#> 4 negative log likelihood: -61.71778 parameter: 2.684927
#> 5 negative log likelihood: -39.1937 parameter: 13.90546
#> 6 negative log likelihood: -57.12391 parameter: 2.523272
#> 7 negative log likelihood: -71.54713 parameter: 4.216918
#> 8 negative log likelihood: -42.46973 parameter: 12.5631
#> 9 negative log likelihood: -54.57032 parameter: 1.46939
#> 10 negative log likelihood: -46.34252 parameter: 8.624326
#> start estimation using optim...
#> 1 negative log likelihood: -57.03415 parameter: 4.294668
#> 2 negative log likelihood: -57.50836 parameter: 8.687513
#> 3 negative log likelihood: -87.62975 parameter: 9.130056
#> 4 negative log likelihood: -69.67131 parameter: 7.00809
#> 5 negative log likelihood: -75.87049 parameter: 5.646678
#> 6 negative log likelihood: -88.61585 parameter: 8.072613
#> 7 negative log likelihood: -52.42328 parameter: 14.81941
#> 8 negative log likelihood: -71.18705 parameter: 12.31462
#> 9 negative log likelihood: -37.84122 parameter: 2.71003
#> 10 negative log likelihood: -37.5193 parameter: 1.757855
#> start estimation using optim...
#> 1 negative log likelihood: -24.76913 parameter: 10.92803
#> 2 negative log likelihood: -37.58646 parameter: 5.970259
#> 3 negative log likelihood: -52.77495 parameter: 2.816448
#> 4 negative log likelihood: -58.81088 parameter: 3.077195
#> 5 negative log likelihood: -30.87656 parameter: 7.225632
#> 6 negative log likelihood: -18.90153 parameter: 14.81542
#> 7 negative log likelihood: -81.43147 parameter: 1.851514
#> 8 negative log likelihood: -25.33784 parameter: 9.335249
#> 9 negative log likelihood: -26.55288 parameter: 8.815965
#> 10 negative log likelihood: -30.26666 parameter: 6.58932
#> start estimation using optim...
#> 1 negative log likelihood: -64.33227 parameter: 2.305927
#> 2 negative log likelihood: -50.33131 parameter: 0.8624255
#> 3 negative log likelihood: -46.33438 parameter: 5.974109
#> 4 negative log likelihood: -40.63852 parameter: 7.20491
#> 5 negative log likelihood: -36.80737 parameter: 14.59015
#> 6 negative log likelihood: -54.72756 parameter: 1.397906
#> 7 negative log likelihood: -48.13678 parameter: 6.552166
#> 8 negative log likelihood: -73.79054 parameter: 3.637898
#> 9 negative log likelihood: -67.74133 parameter: 3.264691
#> 10 negative log likelihood: -62.03513 parameter: 1.613296
#> start estimation using optim...
#> 1 negative log likelihood: -64.71765 parameter: 5.433715
#> 2 negative log likelihood: -49.79831 parameter: 13.7884
#> 3 negative log likelihood: -66.29834 parameter: 5.228753
#> 4 negative log likelihood: -82.61104 parameter: 4.706116
#> 5 negative log likelihood: -63.54245 parameter: 3.077266
#> 6 negative log likelihood: -54.20118 parameter: 7.249816
#> 7 negative log likelihood: -69.80951 parameter: 3.509805
#> 8 negative log likelihood: -52.07846 parameter: 3.10613
#> 9 negative log likelihood: -55.11429 parameter: 5.041747
#> 10 negative log likelihood: -46.19232 parameter: 11.71087
#> start estimation using optim...
#> 1 negative log likelihood: -67.44368 parameter: 8.032873
#> 2 negative log likelihood: -62.60529 parameter: 13.49016
#> 3 negative log likelihood: -24.95696 parameter: 0.6397825
#> 4 negative log likelihood: -59.02907 parameter: 11.11807
#> 5 negative log likelihood: -79.38515 parameter: 7.606246
#> 6 negative log likelihood: -33.99202 parameter: 1.958287
#> 7 negative log likelihood: -55.84072 parameter: 14.45416
#> 8 negative log likelihood: -71.22144 parameter: 12.08477
#> 9 negative log likelihood: -52.73372 parameter: 13.35531
#> 10 negative log likelihood: -70.3864 parameter: 9.055065
#> start estimation using optim...
#> 1 negative log likelihood: -44.84445 parameter: 1.600407
#> 2 negative log likelihood: -85.20512 parameter: 4.183528
#> 3 negative log likelihood: -37.78576 parameter: 0.5799564
#> 4 negative log likelihood: -63.93344 parameter: 3.018606
#> 5 negative log likelihood: -77.86725 parameter: 3.503767
#> 6 negative log likelihood: -30.7931 parameter: 0.2246281
#> 7 negative log likelihood: -72.70622 parameter: 6.522296
#> 8 negative log likelihood: -58.46628 parameter: 9.432239
#> 9 negative log likelihood: -62.7488 parameter: 8.450411
#> 10 negative log likelihood: -37.55 parameter: 12.83314
#> start estimation using optim...
#> 1 negative log likelihood: -60.23175 parameter: 6.673999
#> 2 negative log likelihood: -78.83614 parameter: 11.14365
#> 3 negative log likelihood: -70.66904 parameter: 15
#> 4 negative log likelihood: -61.61132 parameter: 10.04667
#> 5 negative log likelihood: -74.57897 parameter: 15
#> 6 negative log likelihood: -66.81957 parameter: 8.142744
#> 7 negative log likelihood: -47.23828 parameter: 5.016901
#> 8 negative log likelihood: -90.02694 parameter: 13.47844
#> 9 negative log likelihood: -52.46111 parameter: 7.673284
#> 10 negative log likelihood: -70.63481 parameter: 9.973206
#> start estimation using optim...
#> 1 negative log likelihood: -82.49173 parameter: 5.423651
#> 2 negative log likelihood: -77.21171 parameter: 6.717245
#> 3 negative log likelihood: -47.03054 parameter: 2.851848
#> 4 negative log likelihood: -74.03373 parameter: 7.98494
#> 5 negative log likelihood: -86.08267 parameter: 5.34441
#> 6 negative log likelihood: -46.43351 parameter: 2.546371
#> 7 negative log likelihood: -84.19985 parameter: 6.922656
#> 8 negative log likelihood: -60.00143 parameter: 3.263998
#> 9 negative log likelihood: -81.18554 parameter: 6.46113
#> 10 negative log likelihood: -66.3224 parameter: 7.284413
#> start estimation using optim...
#> 1 negative log likelihood: -69.22225 parameter: 7.008688
#> 2 negative log likelihood: -77.13881 parameter: 8.695452
#> 3 negative log likelihood: -86.16621 parameter: 5.944445
#> 4 negative log likelihood: -38.19868 parameter: 0.8630008
#> 5 negative log likelihood: -71.11444 parameter: 5.981747
#> 6 negative log likelihood: -72.58919 parameter: 6.263907
#> 7 negative log likelihood: -65.44841 parameter: 9.279529
#> 8 negative log likelihood: -75.17077 parameter: 9.253675
#> 9 negative log likelihood: -66.56479 parameter: 4.899386
#> 10 negative log likelihood: -84.44487 parameter: 5.739522
#> start estimation using optim...
#> 1 negative log likelihood: -39.38482 parameter: 5.998917
#> 2 negative log likelihood: -25.94633 parameter: 14.28141
#> 3 negative log likelihood: -23.32789 parameter: 13.94241
#> 4 negative log likelihood: -24.82887 parameter: 11.79507
#> 5 negative log likelihood: -57.13864 parameter: 1.650087
#> 6 negative log likelihood: -75.21874 parameter: 0.9715672
#> 7 negative log likelihood: -27.53859 parameter: 8.388522
#> 8 negative log likelihood: -22.794 parameter: 13.67229
#> 9 negative log likelihood: -38.7622 parameter: 5.570335
#> 10 negative log likelihood: -66.16313 parameter: 1.783371
#> start estimation using optim...
#> 1 negative log likelihood: -61.77147 parameter: 5.346981
#> 2 negative log likelihood: -87.34341 parameter: 7.917507
#> 3 negative log likelihood: -53.39506 parameter: 13.62427
#> 4 negative log likelihood: -84.01573 parameter: 6.844302
#> 5 negative log likelihood: -67.81893 parameter: 10.46011
#> 6 negative log likelihood: -29.37408 parameter: 0.6500699
#> 7 negative log likelihood: -48.44959 parameter: 4.016193
#> 8 negative log likelihood: -64.51633 parameter: 12.21377
#> 9 negative log likelihood: -53.29358 parameter: 11.16906
#> 10 negative log likelihood: -84.97841 parameter: 6.065458
#> start estimation using optim...
#> 1 negative log likelihood: -78.52032 parameter: 2.481949
#> 2 negative log likelihood: -38.47178 parameter: 9.956931
#> 3 negative log likelihood: -48.39755 parameter: 7.925059
#> 4 negative log likelihood: -42.60598 parameter: 1.004426
#> 5 negative log likelihood: -97.29765 parameter: 3.082448
#> 6 negative log likelihood: -72.68878 parameter: 3.90689
#> 7 negative log likelihood: -59.95673 parameter: 3.796059
#> 8 negative log likelihood: -44.72203 parameter: 3.731083
#> 9 negative log likelihood: -40.79391 parameter: 10.61134
#> 10 negative log likelihood: -88.4979 parameter: 2.729298
#> start estimation using optim...
#> 1 negative log likelihood: -36.91863 parameter: 11.10509
#> 2 negative log likelihood: -35.21457 parameter: 10.20363
#> 3 negative log likelihood: -65.66348 parameter: 3.7838
#> 4 negative log likelihood: -39.83891 parameter: 7.735724
#> 5 negative log likelihood: -55.25155 parameter: 3.229395
#> 6 negative log likelihood: -56.87868 parameter: 4.447437
#> 7 negative log likelihood: -42.06015 parameter: 8.662118
#> 8 negative log likelihood: -56.53222 parameter: 1.796352
#> 9 negative log likelihood: -38.77571 parameter: 9.939153
#> 10 negative log likelihood: -64.18535 parameter: 2.765896
#> start estimation using optim...
#> 1 negative log likelihood: -53.71205 parameter: 4.346291
#> 2 negative log likelihood: -25.5213 parameter: 0.4165143
#> 3 negative log likelihood: -52.58676 parameter: 4.578773
#> 4 negative log likelihood: -97.31634 parameter: 8.630862
#> 5 negative log likelihood: -69.46762 parameter: 13.50063
#> 6 negative log likelihood: -71.74288 parameter: 13.84832
#> 7 negative log likelihood: -73.17166 parameter: 12.44227
#> 8 negative log likelihood: -70.21653 parameter: 14.70259
#> 9 negative log likelihood: -43.09305 parameter: 2.992235
#> 10 negative log likelihood: -83.88146 parameter: 10.62823
#> start estimation using optim...
#> 1 negative log likelihood: -64.47086 parameter: 0.2659586
#> 2 negative log likelihood: -47.69684 parameter: 2.480987
#> 3 negative log likelihood: -49.93466 parameter: 2.62035
#> 4 negative log likelihood: -23.45942 parameter: 10.82441
#> 5 negative log likelihood: -56.29586 parameter: 2.652226
#> 6 negative log likelihood: -50.26165 parameter: 2.334396
#> 7 negative log likelihood: -48.54273 parameter: 2.639527
#> 8 negative log likelihood: -32.25921 parameter: 6.652256
#> 9 negative log likelihood: -58.28906 parameter: 2.247655
#> 10 negative log likelihood: -21.34748 parameter: 15
#> start estimation using optim...
#> 1 negative log likelihood: -57.01719 parameter: 3.009708
#> 2 negative log likelihood: -30.09148 parameter: 8.904923
#> 3 negative log likelihood: -39.05101 parameter: 4.713663
#> 4 negative log likelihood: -23.2419 parameter: 14.72432
#> 5 negative log likelihood: -36.98243 parameter: 6.150717
#> 6 negative log likelihood: -50.69788 parameter: 2.72366
#> 7 negative log likelihood: -64.97338 parameter: 2.168778
#> 8 negative log likelihood: -24.81401 parameter: 13.2342
#> 9 negative log likelihood: -44.35131 parameter: 3.239052
#> 10 negative log likelihood: -23.10873 parameter: 13.90798
#> start estimation using optim...
#> 1 negative log likelihood: -52.12222 parameter: 6.533657
#> 2 negative log likelihood: -40.50899 parameter: 15
#> 3 negative log likelihood: -48.4586 parameter: 7.753655
#> 4 negative log likelihood: -55.49128 parameter: 4.428029
#> 5 negative log likelihood: -43.69537 parameter: 12.71493
#> 6 negative log likelihood: -56.79839 parameter: 3.294894
#> 7 negative log likelihood: -51.36402 parameter: 7.186867
#> 8 negative log likelihood: -43.49387 parameter: 1.584355
#> 9 negative log likelihood: -60.13823 parameter: 4.001622
#> 10 negative log likelihood: -39.9135 parameter: 11.86426
#> start estimation using optim...
#> 1 negative log likelihood: -59.82795 parameter: 12.29747
#> 2 negative log likelihood: -82.53452 parameter: 6.876065
#> 3 negative log likelihood: -69.65321 parameter: 9.295218
#> 4 negative log likelihood: -81.63814 parameter: 6.894904
#> 5 negative log likelihood: -64.06135 parameter: 14.96636
#> 6 negative log likelihood: -89.52122 parameter: 8.080609
#> 7 negative log likelihood: -67.72039 parameter: 4.956629
#> 8 negative log likelihood: -52.86244 parameter: 12.60145
#> 9 negative log likelihood: -71.23622 parameter: 6.654401
#> 10 negative log likelihood: -59.00084 parameter: 9.214527
#> start estimation using optim...
#> 1 negative log likelihood: -21.29844 parameter: 10.7648
#> 2 negative log likelihood: -50.82538 parameter: 0.245616
#> 3 negative log likelihood: -25.42329 parameter: 8.577951
#> 4 negative log likelihood: -23.44822 parameter: 9.860196
#> 5 negative log likelihood: -48.21011 parameter: 1.27735
#> 6 negative log likelihood: -21.06065 parameter: 10.72964
#> 7 negative log likelihood: -27.34163 parameter: 6.608464
#> 8 negative log likelihood: -21.73131 parameter: 11.62761
#> 9 negative log likelihood: -30.75897 parameter: 6.027605
#> 10 negative log likelihood: -76.35762 parameter: 0.8214421
#> start estimation using optim...
#> 1 negative log likelihood: -62.13016 parameter: 15
#> 2 negative log likelihood: -63.35504 parameter: 7.728115
#> 3 negative log likelihood: -25.8205 parameter: 0.1144307
#> 4 negative log likelihood: -62.78869 parameter: 6.688262
#> 5 negative log likelihood: -79.92456 parameter: 8.715017
#> 6 negative log likelihood: -70.76292 parameter: 7.105032
#> 7 negative log likelihood: -75.37313 parameter: 5.651011
#> 8 negative log likelihood: -69.86694 parameter: 5.073563
#> 9 negative log likelihood: -73.71402 parameter: 7.75283
#> 10 negative log likelihood: -66.3814 parameter: 7.053595
#> start estimation using optim...
#> 1 negative log likelihood: -30.63042 parameter: 11.6289
#> 2 negative log likelihood: -28.77083 parameter: 14.34826
#> 3 negative log likelihood: -35.36241 parameter: 9.52598
#> 4 negative log likelihood: -36.60824 parameter: 7.833519
#> 5 negative log likelihood: -27.89036 parameter: 14.31532
#> 6 negative log likelihood: -39.9809 parameter: 8.013474
#> 7 negative log likelihood: -90.46272 parameter: 2.252343
#> 8 negative log likelihood: -28.52374 parameter: 15
#> 9 negative log likelihood: -31.68431 parameter: 9.347108
#> 10 negative log likelihood: -66.61731 parameter: 1.004346
#> start estimation using optim...
#> 1 negative log likelihood: -80.56309 parameter: 2.807144
#> 2 negative log likelihood: -78.71889 parameter: 2.456716
#> 3 negative log likelihood: -49.99627 parameter: 5.814356
#> 4 negative log likelihood: -31.48497 parameter: 13.44827
#> 5 negative log likelihood: -33.67344 parameter: 11.98264
#> 6 negative log likelihood: -36.18739 parameter: 12.91561
#> 7 negative log likelihood: -42.73292 parameter: 6.837991
#> 8 negative log likelihood: -35.14096 parameter: 13.30942
#> 9 negative log likelihood: -34.98782 parameter: 13.32378
#> 10 negative log likelihood: -61.73349 parameter: 1.777951
#> start estimation using optim...
#> 1 negative log likelihood: -77.71746 parameter: 9.063132
#> 2 negative log likelihood: -68.31274 parameter: 10.87924
#> 3 negative log likelihood: -48.9244 parameter: 4.49039
#> 4 negative log likelihood: -84.37071 parameter: 8.519927
#> 5 negative log likelihood: -70.54089 parameter: 12.93665
#> 6 negative log likelihood: -95.53483 parameter: 8.919281
#> 7 negative log likelihood: -44.19299 parameter: 2.239829
#> 8 negative log likelihood: -62.48257 parameter: 10.29736
#> 9 negative log likelihood: -42.13919 parameter: 2.95145
#> 10 negative log likelihood: -69.61454 parameter: 11.48073
#> start estimation using optim...
#> 1 negative log likelihood: -89.54054 parameter: 2.320884
#> 2 negative log likelihood: -52.0286 parameter: 0.2752352
#> 3 negative log likelihood: -32.03437 parameter: 10.17442
#> 4 negative log likelihood: -64.97933 parameter: 2.443657
#> 5 negative log likelihood: -74.86674 parameter: 2.015312
#> 6 negative log likelihood: -60.54026 parameter: 2.925204
#> 7 negative log likelihood: -66.49045 parameter: 3.033311
#> 8 negative log likelihood: -33.67684 parameter: 11.5142
#> 9 negative log likelihood: -33.64244 parameter: 13.36049
#> 10 negative log likelihood: -43.08251 parameter: 8.230612
#> start estimation using optim...
#> 1 negative log likelihood: -59.45086 parameter: 1.791414
#> 2 negative log likelihood: -34.26545 parameter: 7.451297
#> 3 negative log likelihood: -53.00045 parameter: 3.681973
#> 4 negative log likelihood: -53.05109 parameter: 1.788663
#> 5 negative log likelihood: -53.57201 parameter: 2.736528
#> 6 negative log likelihood: -67.98959 parameter: 1.944259
#> 7 negative log likelihood: -26.99593 parameter: 13.83321
#> 8 negative log likelihood: -67.47607 parameter: 2.201573
#> 9 negative log likelihood: -25.93246 parameter: 11.49358
#> 10 negative log likelihood: -40.814 parameter: 5.196217
#> start estimation using optim...
#> 1 negative log likelihood: -15.88344 parameter: 14.66358
#> 2 negative log likelihood: -37.41547 parameter: 2.639703
#> 3 negative log likelihood: -51.79257 parameter: 1.535406
#> 4 negative log likelihood: -74.2947 parameter: 0.4151221
#> 5 negative log likelihood: -15.4014 parameter: 14.88858
#> 6 negative log likelihood: -61.65332 parameter: 0.4273607
#> 7 negative log likelihood: -17.74396 parameter: 10.95433
#> 8 negative log likelihood: -52.44809 parameter: 1.650205
#> 9 negative log likelihood: -16.68026 parameter: 14.04102
#> 10 negative log likelihood: -43.14693 parameter: 2.652424
#> start estimation using optim...
#> 1 negative log likelihood: -81.56174 parameter: 7.879122
#> 2 negative log likelihood: -86.21402 parameter: 7.613049
#> 3 negative log likelihood: -68.39954 parameter: 13.66177
#> 4 negative log likelihood: -101.3071 parameter: 8.629758
#> 5 negative log likelihood: -86.56596 parameter: 7.344129
#> 6 negative log likelihood: -52.28515 parameter: 10.44374
#> 7 negative log likelihood: -85.41548 parameter: 9.603713
#> 8 negative log likelihood: -72.23445 parameter: 6.753873
#> 9 negative log likelihood: -73.02982 parameter: 6.225139
#> 10 negative log likelihood: -45.26858 parameter: 3.626544
#> start estimation using optim...
#> 1 negative log likelihood: -28.34717 parameter: 1.017375
#> 2 negative log likelihood: -34.50967 parameter: 11.93734
#> 3 negative log likelihood: -66.60214 parameter: 4.143199
#> 4 negative log likelihood: -68.52142 parameter: 5.909832
#> 5 negative log likelihood: -63.73961 parameter: 3.315441
#> 6 negative log likelihood: -55.49614 parameter: 6.072455
#> 7 negative log likelihood: -53.40357 parameter: 5.405891
#> 8 negative log likelihood: -35.46975 parameter: 11.34234
#> 9 negative log likelihood: -49.81761 parameter: 1.793529
#> 10 negative log likelihood: -56.32335 parameter: 2.045711
#> start estimation using optim...
#> 1 negative log likelihood: -36.41888 parameter: 7.169769
#> 2 negative log likelihood: -86.14928 parameter: 1.597299
#> 3 negative log likelihood: -71.07805 parameter: 2.10008
#> 4 negative log likelihood: -46.3349 parameter: 2.398746
#> 5 negative log likelihood: -62.60597 parameter: 2.417216
#> 6 negative log likelihood: -41.83473 parameter: 5.398146
#> 7 negative log likelihood: -58.8308 parameter: 2.549324
#> 8 negative log likelihood: -54.40054 parameter: 4.595962
#> 9 negative log likelihood: -31.73756 parameter: 10.14318
#> 10 negative log likelihood: -23.87074 parameter: 14.38647
#> start estimation using optim...
#> 1 negative log likelihood: -43.38037 parameter: 3.585437
#> 2 negative log likelihood: -87.11609 parameter: 7.087684
#> 3 negative log likelihood: -91.19868 parameter: 8.158841
#> 4 negative log likelihood: -74.15359 parameter: 6.672031
#> 5 negative log likelihood: -76.89991 parameter: 6.057405
#> 6 negative log likelihood: -102.5736 parameter: 8.395765
#> 7 negative log likelihood: -83.88873 parameter: 6.465923
#> 8 negative log likelihood: -82.88863 parameter: 7.816633
#> 9 negative log likelihood: -92.53796 parameter: 9.736215
#> 10 negative log likelihood: -105.5456 parameter: 7.70469
#> start estimation using optim...
#> 1 negative log likelihood: -61.35119 parameter: 4.97687
#> 2 negative log likelihood: -60.7058 parameter: 3.304192
#> 3 negative log likelihood: -57.26525 parameter: 5.445231
#> 4 negative log likelihood: -77.35231 parameter: 3.36617
#> 5 negative log likelihood: -66.31353 parameter: 3.839654
#> 6 negative log likelihood: -74.47096 parameter: 4.409622
#> 7 negative log likelihood: -65.05687 parameter: 4.746534
#> 8 negative log likelihood: -48.09354 parameter: 8.05994
#> 9 negative log likelihood: -63.67962 parameter: 5.695262
#> 10 negative log likelihood: -46.08773 parameter: 8.636648
#> start estimation using optim...
#> 1 negative log likelihood: -45.1696 parameter: 9.733579
#> 2 negative log likelihood: -42.76874 parameter: 14.34319
#> 3 negative log likelihood: -37.19164 parameter: 0.2216856
#> 4 negative log likelihood: -32.54938 parameter: 0.2933489
#> 5 negative log likelihood: -83.11613 parameter: 4.179994
#> 6 negative log likelihood: -52.81978 parameter: 1.580026
#> 7 negative log likelihood: -49.5541 parameter: 9.624107
#> 8 negative log likelihood: -40.78155 parameter: 13.09128
#> 9 negative log likelihood: -30.51982 parameter: 0.3140837
#> 10 negative log likelihood: -55.89179 parameter: 2.791234
#> start estimation using optim...
#> 1 negative log likelihood: -25.68051 parameter: 0.03310395
#> 2 negative log likelihood: -44.42821 parameter: 2.368436
#> 3 negative log likelihood: -50.15541 parameter: 15
#> 4 negative log likelihood: -91.25667 parameter: 5.277104
#> 5 negative log likelihood: -55.01554 parameter: 14.19819
#> 6 negative log likelihood: -44.03335 parameter: 1.813041
#> 7 negative log likelihood: -79.35969 parameter: 4.773266
#> 8 negative log likelihood: -82.88687 parameter: 6.473904
#> 9 negative log likelihood: -103.1155 parameter: 6.081627
#> 10 negative log likelihood: -79.61277 parameter: 7.720722
#> start estimation using optim...
#> 1 negative log likelihood: -61.23553 parameter: 4.101819
#> 2 negative log likelihood: -42.6622 parameter: 7.325901
#> 3 negative log likelihood: -34.11208 parameter: 14.8139
#> 4 negative log likelihood: -73.65602 parameter: 3.351217
#> 5 negative log likelihood: -54.48829 parameter: 1.024545
#> 6 negative log likelihood: -54.4163 parameter: 3.973848
#> 7 negative log likelihood: -59.64293 parameter: 4.439985
#> 8 negative log likelihood: -52.29652 parameter: 5.940664
#> 9 negative log likelihood: -63.52218 parameter: 3.498558
#> 10 negative log likelihood: -36.81601 parameter: 10.55432
#> start estimation using optim...
#> 1 negative log likelihood: -75.63461 parameter: 3.880409
#> 2 negative log likelihood: -59.44773 parameter: 4.536184
#> 3 negative log likelihood: -47.73816 parameter: 11.26275
#> 4 negative log likelihood: -78.82147 parameter: 5.045812
#> 5 negative log likelihood: -44.59114 parameter: 13.08078
#> 6 negative log likelihood: -49.47838 parameter: 11.95821
#> 7 negative log likelihood: -84.0158 parameter: 3.736038
#> 8 negative log likelihood: -67.84121 parameter: 6.213392
#> 9 negative log likelihood: -78.217 parameter: 4.01522
#> 10 negative log likelihood: -59.64956 parameter: 8.12052
#> start estimation using optim...
#> 1 negative log likelihood: -65.85366 parameter: 10.54604
#> 2 negative log likelihood: -49.27575 parameter: 10.46301
#> 3 negative log likelihood: -65.44398 parameter: 5.402709
#> 4 negative log likelihood: -53.59697 parameter: 12.39436
#> 5 negative log likelihood: -57.33765 parameter: 2.552668
#> 6 negative log likelihood: -61.57662 parameter: 10.16161
#> 7 negative log likelihood: -83.04065 parameter: 4.788835
#> 8 negative log likelihood: -66.3179 parameter: 7.533912
#> 9 negative log likelihood: -70.59374 parameter: 5.199642
#> 10 negative log likelihood: -104.6957 parameter: 5.414883
#> start estimation using optim...
#> 1 negative log likelihood: -23.75059 parameter: 15
#> 2 negative log likelihood: -23.43914 parameter: 12.86905
#> 3 negative log likelihood: -23.24774 parameter: 13.64497
#> 4 negative log likelihood: -56.9013 parameter: 1.229324
#> 5 negative log likelihood: -26.38202 parameter: 10.2908
#> 6 negative log likelihood: -29.23713 parameter: 6.614228
#> 7 negative log likelihood: -54.81224 parameter: 3.010447
#> 8 negative log likelihood: -32.55941 parameter: 5.739426
#> 9 negative log likelihood: -39.88642 parameter: 3.728913
#> 10 negative log likelihood: -54.1342 parameter: 1.934333
#> start estimation using optim...
#> 1 negative log likelihood: -73.43009 parameter: 15
#> 2 negative log likelihood: -81.66174 parameter: 7.700503
#> 3 negative log likelihood: -71.46943 parameter: 11.76964
#> 4 negative log likelihood: -72.82213 parameter: 12.91229
#> 5 negative log likelihood: -76.20798 parameter: 8.827436
#> 6 negative log likelihood: -33.18744 parameter: 2.027405
#> 7 negative log likelihood: -66.49371 parameter: 5.839873
#> 8 negative log likelihood: -78.80965 parameter: 5.750555
#> 9 negative log likelihood: -53.62187 parameter: 3.651106
#> 10 negative log likelihood: -37.9099 parameter: 1.690494
#> start estimation using optim...
#> 1 negative log likelihood: -32.04688 parameter: 1.307361
#> 2 negative log likelihood: -19.94778 parameter: 15
#> 3 negative log likelihood: -26.6372 parameter: 2.338118
#> 4 negative log likelihood: -24.18024 parameter: 4.832242
#> 5 negative log likelihood: -17.75375 parameter: 14.76674
#> 6 negative log likelihood: -24.08885 parameter: 4.169689
#> 7 negative log likelihood: -30.71159 parameter: 1.167649
#> 8 negative log likelihood: -28.44755 parameter: 1.491737
#> 9 negative log likelihood: -21.13997 parameter: 15
#> 10 negative log likelihood: -34.18898 parameter: 1.46595
#> start estimation using optim...
#> 1 negative log likelihood: -83.48249 parameter: 3.348061
#> 2 negative log likelihood: -57.13221 parameter: 5.768043
#> 3 negative log likelihood: -76.16815 parameter: 3.072904
#> 4 negative log likelihood: -86.13708 parameter: 3.750408
#> 5 negative log likelihood: -73.60106 parameter: 3.537519
#> 6 negative log likelihood: -42.04767 parameter: 10.09521
#> 7 negative log likelihood: -83.70183 parameter: 3.427186
#> 8 negative log likelihood: -49.96914 parameter: 0.7686392
#> 9 negative log likelihood: -34.53889 parameter: 13.53042
#> 10 negative log likelihood: -39.96583 parameter: 11.25335
#> start estimation using optim...
#> 1 negative log likelihood: -78.54462 parameter: 12.29841
#> 2 negative log likelihood: -49.59653 parameter: 4.588141
#> 3 negative log likelihood: -97.26625 parameter: 9.061627
#> 4 negative log likelihood: -78.035 parameter: 12.2691
#> 5 negative log likelihood: -53.40447 parameter: 5.612518
#> 6 negative log likelihood: -28.90079 parameter: 0.7219027
#> 7 negative log likelihood: -57.91749 parameter: 6.00326
#> 8 negative log likelihood: -43.51794 parameter: 3.410035
#> 9 negative log likelihood: -83.14167 parameter: 7.372223
#> 10 negative log likelihood: -72.26327 parameter: 13.7905
#> start estimation using optim...
#> 1 negative log likelihood: -77.61959 parameter: 5.735607
#> 2 negative log likelihood: -53.60147 parameter: 14.28342
#> 3 negative log likelihood: -44.93065 parameter: 1.864417
#> 4 negative log likelihood: -53.32727 parameter: 13.01498
#> 5 negative log likelihood: -72.66786 parameter: 5.461107
#> 6 negative log likelihood: -58.79321 parameter: 14.98508
#> 7 negative log likelihood: -56.11402 parameter: 2.713145
#> 8 negative log likelihood: -83.05565 parameter: 6.300184
#> 9 negative log likelihood: -61.66933 parameter: 13.3725
#> 10 negative log likelihood: -83.56333 parameter: 5.252607
I check the parameter recovery. It looks well recovery of parameter alpha.
parameter_recovery <- data.frame(true_alpha = participants_alpha, estimated_alpha = results$parameters$alpha)
parameter_recovery %>%
ggplot(aes(x = true_alpha, y= estimated_alpha)) +
geom_point()
How to fit LCM-RW to the conditioning data.
The fit_lcm() allow to estimate alpha and eta of LCM-RW (set model = 2). However, fit_lcm() can not to estimate parameter adequatly at this time(fit_lcm can not recover the parameter adequately).
Bugs and question
Please report on this repository’s issues
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