I've specified a Latent Class model for BWS Case 1 (no covariates). The model converges but is missing the Rho-sq parameters and the BIC. I'm using Apollo 0.2.9
See below for data structure, code and output:
Best wishes,
Jay
Data structure:
Code: Select all
glimpse(database)
Rows: 7,408
Columns: 77
$ uuid <chr> "01nemk…
$ panel <dbl> 13, 13,…
$ setno <dbl> 1, 2, 3…
$ choice_best <dbl> 4, 2, 3…
$ choice_worst <dbl> 3, 1, 1…
$ T1_1 <dbl> 0, 0, 0…
$ T1_2 <dbl> 0, 0, 0…
$ T1_3 <dbl> 1, 0, 0…
$ T1_4 <dbl> 0, 0, 0…
$ T2_1 <dbl> 0, 0, 0…
$ T2_2 <dbl> 0, 0, 0…
$ T2_3 <dbl> 0, 0, 0…
$ T2_4 <dbl> 0, 1, 0…
$ T3_1 <dbl> 0, 0, 0…
$ T3_2 <dbl> 0, 0, 0…
$ T3_3 <dbl> 0, 1, 0…
$ T3_4 <dbl> 0, 0, 0…
$ T4_1 <dbl> 1, 0, 0…
$ T4_2 <dbl> 0, 0, 0…
$ T4_3 <dbl> 0, 0, 0…
$ T4_4 <dbl> 0, 0, 0…
$ T5_1 <dbl> 0, 0, 0…
$ T5_2 <dbl> 0, 0, 0…
$ T5_3 <dbl> 0, 0, 0…
$ T5_4 <dbl> 0, 0, 0…
$ T6_1 <dbl> 0, 0, 0…
$ T6_2 <dbl> 0, 0, 0…
$ T6_3 <dbl> 0, 0, 0…
$ T6_4 <dbl> 0, 0, 1…
$ T7_1 <dbl> 0, 0, 0…
$ T7_2 <dbl> 0, 0, 1…
$ T7_3 <dbl> 0, 0, 0…
$ T7_4 <dbl> 0, 0, 0…
$ T8_1 <dbl> 0, 0, 0…
$ T8_2 <dbl> 0, 0, 0…
$ T8_3 <dbl> 0, 0, 0…
$ T8_4 <dbl> 0, 0, 0…
$ T9_1 <dbl> 0, 0, 0…
$ T9_2 <dbl> 0, 0, 0…
$ T9_3 <dbl> 0, 0, 1…
$ T9_4 <dbl> 0, 0, 0…
$ T10_1 <dbl> 0, 0, 0…
$ T10_2 <dbl> 0, 0, 0…
$ T10_3 <dbl> 0, 0, 0…
$ T10_4 <dbl> 0, 0, 0…
$ T11_1 <dbl> 0, 0, 0…
$ T11_2 <dbl> 0, 0, 0…
$ T11_3 <dbl> 0, 0, 0…
$ T11_4 <dbl> 0, 0, 0…
$ T12_1 <dbl> 0, 0, 1…
$ T12_2 <dbl> 0, 0, 0…
$ T12_3 <dbl> 0, 0, 0…
$ T12_4 <dbl> 0, 0, 0…
$ T13_1 <dbl> 0, 0, 0…
$ T13_2 <dbl> 0, 1, 0…
$ T13_3 <dbl> 0, 0, 0…
$ T13_4 <dbl> 0, 0, 0…
$ T14_1 <dbl> 0, 0, 0…
$ T14_2 <dbl> 0, 0, 0…
$ T14_3 <dbl> 0, 0, 0…
$ T14_4 <dbl> 1, 0, 0…
$ T15_1 <dbl> 0, 0, 0…
$ T15_2 <dbl> 1, 0, 0…
$ T15_3 <dbl> 0, 0, 0…
$ T15_4 <dbl> 0, 0, 0…
$ T16_1 <dbl> 0, 1, 0…
$ T16_2 <dbl> 0, 0, 0…
$ T16_3 <dbl> 0, 0, 0…
$ T16_4 <dbl> 0, 0, 0…
$ avail1B <dbl> 1, 1, 1…
$ avail1W <dbl> 1, 1, 1…
$ avail2B <dbl> 1, 1, 1…
$ avail2W <dbl> 1, 0, 1…
$ avail3B <dbl> 0, 1, 1…
$ avail3W <dbl> 1, 1, 0…
$ avail4B <dbl> 1, 1, 1…
$ avail4W <dbl> 1, 1, 1…
Code: Select all
# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
### Clear memory
rm(list = ls())
### Load Apollo and tidyverse library
library(apollo)
library(tidyverse)
library(readxl)
select <- dplyr::select
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "TEST_NEW_BW_2LCMNL_no_covariates",
modelDescr = "LCMNL model on TEST BW choice data, no covariates in class allocation model",
indivID = "uuid",
nCores = 3,
outputDirectory = "output",
seed = 1234
)
# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #
database
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(set_names(rep(0, 42),
c(paste0("asc_alt", 1:4, "_", "B"),
paste0("asc_alt", 1:4, "_", "W"),
paste0("beta_T", rep(1:16, each = 2), "_", letters[1:2]),
paste0("delta_", letters[1:2]))),
mu_worst = 1)
### Vector with names (in quotes) of parameters to be kept fixed at their starting value in apollo_beta, use apollo_beta_fixed = c() if none
apollo_fixed = c("asc_alt1_B", "asc_alt1_W", "beta_T2_a", "beta_T2_b", "delta_a")
# ################################################################# #
#### DEFINE LATENT CLASS COMPONENTS ####
# ################################################################# #
apollo_lcPars=function(apollo_beta, apollo_inputs){
lcpars = list()
lcpars[["beta_T1"]] = list(beta_T1_a, beta_T1_b)
lcpars[["beta_T2"]] = list(beta_T2_a, beta_T2_b)
lcpars[["beta_T3"]] = list(beta_T3_a, beta_T3_b)
lcpars[["beta_T4"]] = list(beta_T4_a, beta_T4_b)
lcpars[["beta_T5"]] = list(beta_T5_a, beta_T5_b)
lcpars[["beta_T6"]] = list(beta_T6_a, beta_T6_b)
lcpars[["beta_T7"]] = list(beta_T7_a, beta_T7_b)
lcpars[["beta_T8"]] = list(beta_T8_a, beta_T8_b)
lcpars[["beta_T9"]] = list(beta_T9_a, beta_T9_b)
lcpars[["beta_T10"]] = list(beta_T10_a, beta_T10_b)
lcpars[["beta_T11"]] = list(beta_T11_a, beta_T11_b)
lcpars[["beta_T12"]] = list(beta_T12_a, beta_T12_b)
lcpars[["beta_T13"]] = list(beta_T13_a, beta_T13_b)
lcpars[["beta_T14"]] = list(beta_T14_a, beta_T14_b)
lcpars[["beta_T15"]] = list(beta_T15_a, beta_T15_b)
lcpars[["beta_T16"]] = list(beta_T16_a, beta_T16_b)
V=list()
V[["class_a"]] = delta_a
V[["class_b"]] = delta_b
mnl_settings = list(
alternatives = c(class_a = 1, class_b = 2),
avail = 1,
choiceVar = NA,
V = V
)
lcpars[["pi_values"]] = apollo_mnl(mnl_settings, functionality = "raw")
lcpars[["pi_values"]] = apollo_firstRow(lcpars[["pi_values"]], apollo_inputs)
return(lcpars)
}
# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #
apollo_inputs = apollo_validateInputs()
# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality = "estimate"){
### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
### Create list of probabilities P
P = list()
### define class
for(s in 1:2){
### Create tmp list of probabilities P_bw
P_bw = list()
### List of utilities for the "best" choice
V_best=list()
V_best[["alt1B"]] = asc_alt1_B + beta_T1[[s]]*T1_1 + beta_T2[[s]]*T2_1 + beta_T3[[s]]*T3_1 + beta_T4[[s]]*T4_1 +
beta_T5[[s]]*T5_1 + beta_T6[[s]]*T6_1 + beta_T7[[s]]*T7_1 +
beta_T8[[s]]*T8_1 + beta_T9[[s]]*T9_1 + beta_T10[[s]]*T10_1 +
beta_T11[[s]]*T11_1 + beta_T12[[s]]*T12_1 + beta_T13[[s]]*T13_1 +
beta_T14[[s]]*T14_1 + beta_T15[[s]]*T15_1 + beta_T16[[s]]*T16_1
V_best[["alt2B"]] = asc_alt2_B + beta_T1[[s]]*T1_2 + beta_T2[[s]]*T2_2 + beta_T3[[s]]*T3_2 + beta_T4[[s]]*T4_2 +
beta_T5[[s]]*T5_2 + beta_T6[[s]]*T6_2 + beta_T7[[s]]*T7_2 +
beta_T8[[s]]*T8_2 + beta_T9[[s]]*T9_2 + beta_T10[[s]]*T10_2 +
beta_T11[[s]]*T11_2 + beta_T12[[s]]*T12_2 + beta_T13[[s]]*T13_2 +
beta_T14[[s]]*T14_2 + beta_T15[[s]]*T15_2 + beta_T16[[s]]*T16_2
V_best[["alt3B"]] = asc_alt3_B + beta_T1[[s]]*T1_3 + beta_T2[[s]]*T2_3 + beta_T3[[s]]*T3_3 + beta_T4[[s]]*T4_3 +
beta_T5[[s]]*T5_3 + beta_T6[[s]]*T6_3 + beta_T7[[s]]*T7_3 +
beta_T8[[s]]*T8_3 + beta_T9[[s]]*T9_3 + beta_T10[[s]]*T10_3 +
beta_T11[[s]]*T11_3 + beta_T12[[s]]*T12_3 + beta_T13[[s]]*T13_3 +
beta_T14[[s]]*T14_3 + beta_T15[[s]]*T15_3 + beta_T16[[s]]*T16_3
V_best[["alt4B"]] = asc_alt4_B + beta_T1[[s]]*T1_4 + beta_T2[[s]]*T2_4 + beta_T3[[s]]*T3_4 + beta_T4[[s]]*T4_4 +
beta_T5[[s]]*T5_4 + beta_T6[[s]]*T6_4 + beta_T7[[s]]*T7_4 +
beta_T8[[s]]*T8_4 + beta_T9[[s]]*T9_4 + beta_T10[[s]]*T10_4 +
beta_T11[[s]]*T11_4 + beta_T12[[s]]*T12_4 + beta_T13[[s]]*T13_4 +
beta_T14[[s]]*T14_4 + beta_T15[[s]]*T15_4 + beta_T16[[s]]*T16_4
### Compute probabilities for "best" choice using MNL model
mnl_settings_best = list(
alternatives = c(alt1B=1, alt2B=2, alt3B=3, alt4B=4),
avail = list(alt1B=avail1B, alt2B=avail2B, alt3B=avail3B, alt4B=avail4B),
choiceVar = choice_best,
utilities = V_best,
componentName = paste0("Best_Class_", s)
)
P_bw[["choice_best"]] = apollo_mnl(mnl_settings_best, functionality)
### List of utilities for the "worse" choice
V_worst = list()
V_worst[["alt1W"]] = -mu_worst * (asc_alt1_W + beta_T1[[s]]*T1_1 + beta_T2[[s]]*T2_1 + beta_T3[[s]]*T3_1 + beta_T4[[s]]*T4_1 +
beta_T5[[s]]*T5_1 + beta_T6[[s]]*T6_1 + beta_T7[[s]]*T7_1 +
beta_T8[[s]]*T8_1 + beta_T9[[s]]*T9_1 + beta_T10[[s]]*T10_1 +
beta_T11[[s]]*T11_1 + beta_T12[[s]]*T12_1 + beta_T13[[s]]*T13_1 )+
beta_T14[[s]]*T14_1 + beta_T15[[s]]*T15_1 + beta_T16[[s]]*T16_1
V_worst[["alt2W"]] = -mu_worst * (asc_alt2_W + beta_T1[[s]]*T1_2 + beta_T2[[s]]*T2_2 + beta_T3[[s]]*T3_2 + beta_T4[[s]]*T4_2 +
beta_T5[[s]]*T5_2 + beta_T6[[s]]*T6_2 + beta_T7[[s]]*T7_2 +
beta_T8[[s]]*T8_2 + beta_T9[[s]]*T9_2 + beta_T10[[s]]*T10_2 +
beta_T11[[s]]*T11_2 + beta_T12[[s]]*T12_2 + beta_T13[[s]]*T13_2 +
beta_T14[[s]]*T14_2 + beta_T15[[s]]*T15_2 + beta_T16[[s]]*T16_2)
V_worst[["alt3W"]] = -mu_worst * (asc_alt3_W + beta_T1[[s]]*T1_3 + beta_T2[[s]]*T2_3 + beta_T3[[s]]*T3_3 + beta_T4[[s]]*T4_3 +
beta_T5[[s]]*T5_3 + beta_T6[[s]]*T6_3 + beta_T7[[s]]*T7_3 +
beta_T8[[s]]*T8_3 + beta_T9[[s]]*T9_3 + beta_T10[[s]]*T10_3 +
beta_T11[[s]]*T11_3 + beta_T12[[s]]*T12_3 + beta_T13[[s]]*T13_3 +
beta_T14[[s]]*T14_3 + beta_T15[[s]]*T15_3 + beta_T16[[s]]*T16_3)
V_worst[["alt4W"]] = -mu_worst * (asc_alt4_W + beta_T1[[s]]*T1_4 + beta_T2[[s]]*T2_4 + beta_T3[[s]]*T3_4 + beta_T4[[s]]*T4_4 +
beta_T5[[s]]*T5_4 + beta_T6[[s]]*T6_4 + beta_T7[[s]]*T7_4 +
beta_T8[[s]]*T8_4 + beta_T9[[s]]*T9_4 + beta_T10[[s]]*T10_4 +
beta_T11[[s]]*T11_4 + beta_T12[[s]]*T12_4 + beta_T13[[s]]*T13_4 +
beta_T14[[s]]*T14_4 + beta_T15[[s]]*T15_4 + beta_T16[[s]]*T16_4)
### Compute probabilities for "worst" choice using MNL model
mnl_settings_worst = list(
alternatives = c(alt1W=1, alt2W=2, alt3W=3, alt4W=4),
avail = list(alt1W=avail1W, alt2W=avail2W, alt3W=avail3W, alt4W=avail4W),
choiceVar = choice_worst,
utilities = V_worst,
componentName = paste0("Worst_Class_", s)
)
P_bw[["choice_worst"]] = apollo_mnl(mnl_settings_worst, functionality)
### Combined model
P[[paste0("Class_", s)]] = apollo_combineModels(P_bw, apollo_inputs, functionality)$model
### Take product across observation for same individual
P[[paste0("Class_", s)]] = apollo_panelProd(P[[paste0("Class_", s)]], apollo_inputs, functionality)
}
### Compute latent class model probabilities
lc_settings = list(inClassProb = P, classProb = pi_values)
P[["model"]] = apollo_lc(lc_settings, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #
### Optional starting values search
# apollo_beta=apollo_searchStart(apollo_beta, apollo_fixed,apollo_probabilities, apollo_inputs)
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model, modelOutput_settings = list(printPVal=1))
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO FILE, using model name) ----
# ----------------------------------------------------------------- #
apollo_saveOutput(model, saveOutput_settings = list(printPVal=1))
Code: Select all
Preparing user-defined functions.
Testing likelihood function...
Overview of choices for MNL model component Best_Class_1:
alt1B alt2B alt3B alt4B
Times available 6762.00 6842.00 6875.00 6891.00
Times chosen 2099.00 1870.00 1712.00 1727.00
Percentage chosen overall 28.33 25.24 23.11 23.31
Percentage chosen when available 31.04 27.33 24.90 25.06
Overview of choices for MNL model component Worst_Class_1:
alt1W alt2W alt3W alt4W
Times available 5859.00 6053.00 6213.00 6293.00
Times chosen 1868.00 1715.00 1881.00 1944.00
Percentage chosen overall 25.22 23.15 25.39 26.24
Percentage chosen when available 31.88 28.33 30.28 30.89
Overview of choices for MNL model component Best_Class_2:
alt1B alt2B alt3B alt4B
Times available 6762.00 6842.00 6875.00 6891.00
Times chosen 2099.00 1870.00 1712.00 1727.00
Percentage chosen overall 28.33 25.24 23.11 23.31
Percentage chosen when available 31.04 27.33 24.90 25.06
Overview of choices for MNL model component Worst_Class_2:
alt1W alt2W alt3W alt4W
Times available 5859.00 6053.00 6213.00 6293.00
Times chosen 1868.00 1715.00 1881.00 1944.00
Percentage chosen overall 25.22 23.15 25.39 26.24
Percentage chosen when available 31.88 28.33 30.28 30.89
Summary of class allocation for model component :
Mean prob.
Class_1 0.5000
Class_2 0.5000
Pre-processing likelihood function...
Creating cluster...
Preparing workers for multithreading...
INFORMATION: Apollo was not able to compute analytical gradients for your model.
This could be because you are using model components for which
analytical gradients are not yet implemented, or because you coded
your own model functions. If however you only used apollo_mnl,
apollo_fmnl, apollo_normalDensity, apollo_ol or apollo_op then there
could be another issue. You might want to ask for help in the Apollo
forum (http://www.apollochoicemodelling.com/forum) on how to solve
this issue. If you do, please post your code and data (if not
confidential).
Current process will resume in 5 seconds unless interrupted by the
user.....
Analytical gradients could not be calculated for all components, numerical gradients will be used.
Testing influence of parameters......................................
Starting main estimation
Initial function value: -18388.63
Initial gradient value:
asc_alt2_B asc_alt3_B asc_alt4_B asc_alt2_W asc_alt3_W asc_alt4_W beta_T1_a beta_T1_b beta_T3_a beta_T3_b beta_T4_a beta_T4_b
18.166666 -150.833333 -141.166667 119.833334 7.166665 -29.166666 -64.916665 -64.916665 86.666667 86.666667 43.249998 43.249998
beta_T5_a beta_T5_b beta_T6_a beta_T6_b beta_T7_a beta_T7_b beta_T8_a beta_T8_b beta_T9_a beta_T9_b beta_T10_a beta_T10_b
20.541669 20.541669 -43.916669 -43.916669 3.583333 3.583333 1.083332 1.083332 -53.666667 -53.666667 -249.875000 -249.875000
beta_T11_a beta_T11_b beta_T12_a beta_T12_b beta_T13_a beta_T13_b beta_T14_a beta_T14_b beta_T15_a beta_T15_b beta_T16_a beta_T16_b
165.833335 165.833335 -60.666665 -60.666665 75.833334 75.833334 252.541668 252.541668 -116.541665 -116.541665 163.541667 163.541667
delta_b mu_worst
0.000000 0.000000
initial value 18388.626081
iter 2 value 17859.727383
iter 3 value 17769.948065
iter 4 value 17703.175543
iter 5 value 17687.815877
iter 6 value 17669.104311
iter 7 value 17659.153141
iter 8 value 17643.408518
iter 9 value 17635.183456
iter 10 value 17633.485223
iter 11 value 17632.984056
iter 12 value 17632.875485
iter 13 value 17630.526578
iter 14 value 17622.949525
iter 15 value 17620.320690
iter 16 value 17616.513862
iter 17 value 17615.470293
iter 18 value 17614.170020
iter 19 value 17414.614631
iter 20 value 17311.599819
iter 21 value 17286.429247
iter 22 value 17273.890577
iter 23 value 17262.846313
iter 24 value 17246.459498
iter 25 value 17241.861015
iter 26 value 17241.201433
iter 27 value 17240.293042
iter 28 value 17239.090533
iter 29 value 17238.796939
iter 30 value 17238.426550
iter 31 value 17237.286312
iter 32 value 17229.261875
iter 33 value 17220.134966
iter 34 value 17218.459536
iter 35 value 17217.036898
iter 36 value 17214.968085
iter 37 value 17214.739770
iter 38 value 17214.637630
iter 39 value 17214.468842
iter 40 value 17213.959256
iter 41 value 17213.745646
iter 42 value 17213.431499
iter 43 value 17212.475123
iter 44 value 17210.658732
iter 45 value 17210.616148
iter 46 value 17210.597836
iter 47 value 17210.576266
iter 48 value 17210.255316
iter 49 value 17209.697710
iter 50 value 17209.685611
iter 51 value 17209.684428
iter 52 value 17209.670543
iter 53 value 17209.656133
iter 54 value 17209.648083
iter 55 value 17209.646848
iter 56 value 17209.636539
iter 57 value 17209.601246
iter 58 value 17209.587566
iter 58 value 17209.587349
iter 59 value 17209.573010
iter 60 value 17209.569862
iter 61 value 17209.568405
iter 62 value 17209.567206
iter 63 value 17209.566941
iter 64 value 17209.566321
iter 64 value 17209.566223
iter 65 value 17209.565063
iter 66 value 17209.563995
iter 66 value 17209.563924
iter 66 value 17209.563732
final value 17209.563732
converged
Additional convergence test using scaled estimation. Parameters will be scaled by their current estimates and additional iterations will
be performed.
initial value 17209.563732
iter 2 value 17209.563378
iter 2 value 17209.563134
iter 2 value 17209.563134
final value 17209.563134
converged
Estimated parameters with approximate standard errors from BHHH matrix:
Estimate BHHH se BHH t-ratio
asc_alt1_B 0.00000 NA NA
asc_alt2_B -0.14673 0.03335 -4.4000
asc_alt3_B -0.23823 0.03336 -7.1418
asc_alt4_B -0.23358 0.03268 -7.1477
asc_alt1_W 0.00000 NA NA
asc_alt2_W -0.03823 0.03114 -1.2277
asc_alt3_W -0.09717 0.03022 -3.2154
asc_alt4_W -0.12210 0.03050 -4.0029
beta_T1_a 0.67694 0.06535 10.3585
beta_T1_b -0.48531 0.06396 -7.5872
beta_T2_a 0.00000 NA NA
beta_T2_b 0.00000 NA NA
beta_T3_a 0.14142 0.06132 2.3065
beta_T3_b 1.03926 0.07392 14.0589
beta_T4_a 0.91417 0.07102 12.8723
beta_T4_b -0.10537 0.06679 -1.5776
beta_T5_a 0.14113 0.06685 2.1112
beta_T5_b 0.58500 0.07335 7.9750
beta_T6_a 0.01218 0.05670 0.2147
beta_T6_b 0.33160 0.06575 5.0432
beta_T7_a 0.78727 0.07129 11.0435
beta_T7_b -0.19973 0.06471 -3.0866
beta_T8_a 0.21817 0.06478 3.3676
beta_T8_b 0.39217 0.07250 5.4090
beta_T9_a -0.40291 0.06496 -6.2020
beta_T9_b 0.82334 0.07387 11.1458
beta_T10_a -0.54886 0.06919 -7.9329
beta_T10_b -0.23299 0.06404 -3.6381
beta_T11_a 1.56578 0.07989 19.5988
beta_T11_b 0.06541 0.06715 0.9741
beta_T12_a -0.13454 0.05856 -2.2976
beta_T12_b 0.38004 0.06179 6.1508
beta_T13_a 0.73050 0.06132 11.9122
beta_T13_b 0.27721 0.06861 4.0406
beta_T14_a 1.27846 0.06241 20.4861
beta_T14_b 0.84128 0.05984 14.0594
beta_T15_a 0.23505 0.06473 3.6314
beta_T15_b -0.42243 0.06551 -6.4485
beta_T16_a 0.88968 0.06103 14.5772
beta_T16_b 0.65635 0.06676 9.8318
delta_a 0.00000 NA NA
delta_b -0.14146 0.09678 -1.4617
mu_worst 1.18995 0.05529 21.5233
Final LL: -17209.5631
Calculating log-likelihood at equal shares (LL(0)) for applicable models...
Calculating log-likelihood at observed shares from estimation data (LL(c)) for applicable models...
Calculating LL of each model component...
Computing covariance matrix using numerical methods (numDeriv).
0%....25%....50%....75%....100%
Negative definite Hessian with maximum eigenvalue: -17.427067
> apollo_modelOutput(model, modelOutput_settings = list(printPVal=1))
Model run by jburns10 using Apollo 0.2.9 on R 4.2.2 for Windows.
www.ApolloChoiceModelling.com
Model name : TEST_NEW_BW_2LCMNL_no_covariates
Model description : LCMNL model on TEST BW choice data, no covariates in class allocation model
Model run at : 2024-03-26 10:19:42
Estimation method : bfgs
Model diagnosis : successful convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definitive
maximum eigenvalue : -17.427067
Number of individuals : 926
Number of rows in database : 7408
Number of modelled outcomes : 0
Number of cores used : 3
Model without mixing
LL(start) : -18388.63
LL (whole model) at equal shares, LL(0) : -18388.63
LL (whole model) at observed shares, LL(C) : -18348.42
LL(final, whole model) : -17209.56
Rho-squared vs equal shares : Not applicable
Adj.Rho-squared vs equal shares : Not applicable
Rho-squared vs observed shares : Not applicable
Adj.Rho-squared vs observed shares : Not applicable
AIC : 34495.13
BIC : NA
LL(0,Class_1) : -18388.63
LL(final,Class_1) : -18450.09
LL(0,Class_2) : -18388.63
LL(final,Class_2) : -18566.13
Estimated parameters : 38
Time taken (hh:mm:ss) : 00:05:20.69
pre-estimation : 00:00:32.37
estimation : 00:02:30.76
initial estimation : 00:02:22.59
estimation after rescaling : 00:00:8.17
post-estimation : 00:02:17.56
Iterations : 73
initial estimation : 69
estimation after rescaling : 4
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) p(1-sided) Rob.s.e. Rob.t.rat.(0) p(1-sided)
asc_alt1_B 0.00000 NA NA NA NA NA NA
asc_alt2_B -0.14673 0.03409 -4.3036 8.402e-06 0.03600 -4.0760 2.291e-05
asc_alt3_B -0.23823 0.03479 -6.8479 3.748e-12 0.03719 -6.4053 7.504e-11
asc_alt4_B -0.23358 0.03475 -6.7218 8.975e-12 0.03752 -6.2258 2.395e-10
asc_alt1_W 0.00000 NA NA NA NA NA NA
asc_alt2_W -0.03823 0.03305 -1.1567 0.123698 0.03659 -1.0448 0.148067
asc_alt3_W -0.09717 0.03250 -2.9904 0.001393 0.03587 -2.7087 0.003377
asc_alt4_W -0.12210 0.03242 -3.7662 8.288e-05 0.03576 -3.4147 3.1922e-04
beta_T1_a 0.67694 0.09395 7.2055 2.891e-13 0.17629 3.8400 6.151e-05
beta_T1_b -0.48531 0.08402 -5.7758 3.829e-09 0.12692 -3.8236 6.576e-05
beta_T2_a 0.00000 NA NA NA NA NA NA
beta_T2_b 0.00000 NA NA NA NA NA NA
beta_T3_a 0.14142 0.06832 2.0700 0.019228 0.08216 1.7213 0.042599
beta_T3_b 1.03926 0.10422 9.9722 0.000000 0.19870 5.2303 8.461e-08
beta_T4_a 0.91417 0.08991 10.1677 0.000000 0.15460 5.9132 1.677e-09
beta_T4_b -0.10537 0.07539 -1.3977 0.081107 0.10304 -1.0227 0.153228
beta_T5_a 0.14113 0.06729 2.0973 0.017985 0.07779 1.8143 0.034819
beta_T5_b 0.58500 0.07810 7.4901 3.442e-14 0.09874 5.9247 1.564e-09
beta_T6_a 0.01218 0.06741 0.1806 0.428328 0.08556 0.1423 0.443416
beta_T6_b 0.33160 0.07814 4.2436 1.100e-05 0.10898 3.0427 0.001172
beta_T7_a 0.78727 0.08076 9.7480 0.000000 0.12254 6.4244 6.618e-11
beta_T7_b -0.19973 0.07650 -2.6108 0.004516 0.11521 -1.7337 0.041489
beta_T8_a 0.21817 0.06739 3.2374 6.0316e-04 0.07570 2.8822 0.001975
beta_T8_b 0.39217 0.07705 5.0900 1.791e-07 0.09487 4.1338 1.784e-05
beta_T9_a -0.40291 0.07839 -5.1396 1.377e-07 0.11819 -3.4090 3.2598e-04
beta_T9_b 0.82334 0.10013 8.2228 1.110e-16 0.19083 4.3146 7.993e-06
beta_T10_a -0.54886 0.07514 -7.3042 1.394e-13 0.09265 -5.9241 1.570e-09
beta_T10_b -0.23299 0.07231 -3.2222 6.3613e-04 0.08504 -2.7398 0.003074
beta_T11_a 1.56578 0.09997 15.6630 0.000000 0.17744 8.8242 0.000000
beta_T11_b 0.06541 0.08347 0.7836 0.216629 0.13783 0.4746 0.317548
beta_T12_a -0.13454 0.07045 -1.9096 0.028091 0.09360 -1.4373 0.075313
beta_T12_b 0.38004 0.08909 4.2658 9.959e-06 0.16209 2.3447 0.009521
beta_T13_a 0.73050 0.08129 8.9866 0.000000 0.13176 5.5441 1.478e-08
beta_T13_b 0.27721 0.07567 3.6634 1.2446e-04 0.09536 2.9070 0.001825
beta_T14_a 1.27846 0.08385 15.2463 0.000000 0.13992 9.1368 0.000000
beta_T14_b 0.84128 0.08111 10.3722 0.000000 0.12207 6.8917 2.756e-12
beta_T15_a 0.23505 0.06746 3.4841 2.4690e-04 0.08659 2.7147 0.003317
beta_T15_b -0.42243 0.07759 -5.4445 2.598e-08 0.11209 -3.7687 8.206e-05
beta_T16_a 0.88968 0.07032 12.6520 0.000000 0.09195 9.6760 0.000000
beta_T16_b 0.65635 0.07297 8.9947 0.000000 0.08426 7.7891 3.331e-15
delta_a 0.00000 NA NA NA NA NA NA
delta_b -0.14146 0.15163 -0.9330 0.175421 0.32963 -0.4292 0.333904
mu_worst 1.18995 0.06322 18.8217 0.000000 0.08032 14.8149 0.000000