ICLV model using ordered measurement model for indicators
Posted: 16 Apr 2023, 01:22
Hi Stephane,
I am replicating the "ICLV ordered logit attitudinal model" used in your paper "Using ordered attitudinal indicators in a latent variable choice model: a study of the impact of security on rail travel behaviour" for my data which has binary choice. Can you please check if my code is correct. I have attached the code and result below.
Thanks,
Yash
Result:
I am replicating the "ICLV ordered logit attitudinal model" used in your paper "Using ordered attitudinal indicators in a latent variable choice model: a study of the impact of security on rail travel behaviour" for my data which has binary choice. Can you please check if my code is correct. I have attached the code and result below.
Thanks,
Yash
Code: Select all
# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
### Clear memory
rm(list = ls())
### Load Apollo library
library(apollo)
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "Ordered HCM 12",
modelDescr = "Hybrid choice model, using ordered measurement model for indicators",
indivID = "Person_ID",
mixing = TRUE,
nCores = 24,
outputDirectory = "New"
)
# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #
#setwd("D")
getwd()
database = read.csv("file.csv",header=TRUE)
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(# Alternative specific parameters
asc_CV = 0,
asc_EV = 0,
b_pp = 0,
b_oc = 0,
b_ct = 0,
b_r = 0,
b_cf = 0,
b_e = 0,
# Socio-demographic characteristic parameters
gamma_Male_monBen = 0,
gamma_female_monBen = 0,
gamma_dailyDistanceAvg_monBen = 0,
gamma_ageAvg_monBen = 0,
gamma_knowledgeLow_monBen = 0,
gamma_knowledgeMiddle_monBen = 0,
gamma_knowledgeHigh_monBen = 0,
gamma_Male_envEnth = 0,
gamma_female_envEnth = 0,
gamma_dailyDistanceAvg_envEnth = 0,
gamma_ageAvg_envEnth = 0,
gamma_knowledgeLow_envEnth = 0,
gamma_knowledgeMiddle_envEnth = 0,
gamma_knowledgeHigh_envEnth = 0,
gamma_Male_socIma = 0,
gamma_female_socIma = 0,
gamma_dailyDistanceAvg_socIma = 0,
gamma_ageAvg_socIma = 0,
gamma_knowledgeLow_socIma = 0,
gamma_knowledgeMiddle_socIma = 0,
gamma_knowledgeHigh_socIma = 0,
gamma_Male_techEnth = 0,
gamma_female_techEnth = 0,
gamma_dailyDistanceAvg_techEnth = 0,
gamma_ageAvg_techEnth = 0,
gamma_knowledgeLow_techEnth = 0,
gamma_knowledgeMiddle_techEnth = 0,
gamma_knowledgeHigh_techEnth = 0,
# Latent variable_1
lambda_monBen = 0,
sigma_eta_monBen =-1,
zeta_monBen_1 = 1,
zeta_monBen_2 = 1,
zeta_monBen_3 = 1,
constant_monBen_1 = 5,
constant_monBen_2 = 5,
constant_monBen_3 = 5,
tau_monBen_1_1 = 0,
tau_monBen_1_2 = 1,
tau_monBen_1_3 = 3,
tau_monBen_1_4 = 6,
tau_monBen_2_1 = 0,
tau_monBen_2_2 = 1,
tau_monBen_2_3 = 3,
tau_monBen_2_4 = 6,
tau_monBen_3_1 = 0,
tau_monBen_3_2 = 1,
tau_monBen_3_3 = 3,
tau_monBen_3_4 = 6,
# latent varaible_2
lambda_envEnth = 0,
sigma_eta_envEnth =-1,
zeta_envEnth_1 = 1,
zeta_envEnth_2 = 1,
zeta_envEnth_3 = 1,
constant_envEnth_1 = 5,
constant_envEnth_2 = 5,
constant_envEnth_3 = 5,
tau_envEnth_1_1 = 0,
tau_envEnth_1_2 = 1,
tau_envEnth_1_3 = 3,
tau_envEnth_1_4 = 6,
tau_envEnth_2_1 = 0,
tau_envEnth_2_2 = 1,
tau_envEnth_2_3 = 3,
tau_envEnth_2_4 = 6,
tau_envEnth_3_1 = 0,
tau_envEnth_3_2 = 1,
tau_envEnth_3_3 = 3,
tau_envEnth_3_4 = 6,
# latent variable_3
lambda_socIma = 0,
sigma_eta_socIma =-1,
zeta_socIma_1 = 1,
zeta_socIma_2 = 1,
zeta_socIma_3 = 1,
zeta_socIma_4 = 1,
constant_socIma_1 = 5,
constant_socIma_2 = 5,
constant_socIma_3 = 5,
constant_socIma_4 = 5,
tau_socIma_1_1 = 0,
tau_socIma_1_2 = 1,
tau_socIma_1_3 = 3,
tau_socIma_1_4 = 6,
tau_socIma_2_1 = 0,
tau_socIma_2_2 = 1,
tau_socIma_2_3 = 3,
tau_socIma_2_4 = 6,
tau_socIma_3_1 = 0,
tau_socIma_3_2 = 1,
tau_socIma_3_3 = 3,
tau_socIma_3_4 = 6,
tau_socIma_4_1 = 0,
tau_socIma_4_2 = 1,
tau_socIma_4_3 = 3,
tau_socIma_4_4 = 6,
# latent variable_4
lambda_techEnth = 1,
sigma_eta_techEnth =-3,
zeta_techEnth_1 = 1,
zeta_techEnth_2 = 1,
zeta_techEnth_3r = 1,
#zeta_techEnth_4 = 1,
constant_techEnth_1 = 0,
constant_techEnth_2 = 0,
constant_techEnth_3r = 0,
#constant_techEnth_4 = 0,
tau_techEnth_1_1 = 0,
tau_techEnth_1_2 = 1,
tau_techEnth_1_3 = 2,
tau_techEnth_1_4 = 3,
tau_techEnth_2_1 = 0,
tau_techEnth_2_2 = 1,
tau_techEnth_2_3 = 2,
tau_techEnth_2_4 = 3,
tau_techEnth_3r_1 = 0,
tau_techEnth_3r_2 = 1,
tau_techEnth_3r_3 = 2,
tau_techEnth_3r_4 = 3)
### 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_CV","gamma_female_monBen","gamma_female_envEnth","gamma_female_socIma","gamma_female_techEnth","gamma_knowledgeHigh_monBen","gamma_knowledgeHigh_envEnth","gamma_knowledgeHigh_socIma","gamma_knowledgeHigh_techEnth","tau_monBen_1_1","tau_monBen_2_1","tau_monBen_3_1","zeta_monBen_1","tau_envEnth_1_1","tau_envEnth_2_1","tau_envEnth_3_1","zeta_envEnth_1", "tau_socIma_1_1","tau_socIma_2_1","tau_socIma_3_1","tau_socIma_4_1","zeta_socIma_1", "tau_techEnth_1_1","tau_techEnth_2_1","tau_techEnth_3r_1","zeta_techEnth_1")
# ################################################################# #
#### DEFINE RANDOM COMPONENTS ####
# ################################################################# #
### Set parameters for generating draws
apollo_draws = list(
interDrawsType="halton",
interNDraws=500,
interUnifDraws=c(),
interNormDraws=c("eta_monBen","eta_envEnth", "eta_socIma", "eta_techEnth"),
intraDrawsType="",
intraNDraws=0,
intraUnifDraws=c(),
intraNormDraws=c()
)
### Create random parameters
apollo_randCoeff=function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["LV_monBen"]] = gamma_Male_monBen*genderCoded + gamma_dailyDistanceAvg_monBen*dailyDistanceAvg + gamma_ageAvg_monBen*ageAvg + gamma_knowledgeLow_monBen*knowledgeLow + gamma_knowledgeMiddle_monBen*knowledgeMiddle + gamma_knowledgeHigh_monBen*knowledgeHigh + sigma_eta_monBen*eta_monBen
randcoeff[["LV_envEnth"]] = gamma_Male_envEnth*genderCoded + gamma_dailyDistanceAvg_envEnth*dailyDistanceAvg + gamma_ageAvg_envEnth*ageAvg + gamma_knowledgeLow_envEnth*knowledgeLow + gamma_knowledgeMiddle_envEnth*knowledgeMiddle + gamma_knowledgeHigh_envEnth*knowledgeHigh + sigma_eta_envEnth*eta_envEnth
randcoeff[["LV_socIma"]] = gamma_Male_socIma*genderCoded + gamma_dailyDistanceAvg_socIma*dailyDistanceAvg + gamma_ageAvg_socIma*ageAvg + gamma_knowledgeLow_socIma*knowledgeLow + gamma_knowledgeMiddle_socIma*knowledgeMiddle + gamma_knowledgeHigh_socIma*knowledgeHigh + sigma_eta_socIma*eta_socIma
randcoeff[["LV_techEnth"]] = gamma_Male_techEnth*genderCoded + gamma_dailyDistanceAvg_techEnth*dailyDistanceAvg + gamma_ageAvg_techEnth*ageAvg + gamma_knowledgeLow_techEnth*knowledgeLow + gamma_knowledgeMiddle_techEnth*knowledgeMiddle + gamma_knowledgeHigh_techEnth*knowledgeHigh + sigma_eta_techEnth*eta_techEnth
# randcoeff[["LV_monBen"]] = gamma_Male_monBen*genderCoded + gamma_dailyDistanceAvg_monBen*dailyDistanceAvg + gamma_ageAvg_monBen*ageAvg + sigma_eta_monBen*eta_monBen
# randcoeff[["LV_envEnth"]] = gamma_Male_envEnth*genderCoded + gamma_dailyDistanceAvg_envEnth*dailyDistanceAvg + gamma_ageAvg_envEnth*ageAvg + sigma_eta_envEnth*eta_envEnth
# randcoeff[["LV_socIma"]] = gamma_Male_socIma*genderCoded + gamma_dailyDistanceAvg_socIma*dailyDistanceAvg + gamma_ageAvg_socIma*ageAvg + sigma_eta_socIma*eta_socIma
#
return(randcoeff)
}
# ################################################################# #
#### 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()
### Likelihood of indicators
ol_settings1 = list(outcomeOrdered = monBen_1,
V = constant_monBen_1 + zeta_monBen_1*LV_monBen,
tau = list(tau_monBen_1_1, tau_monBen_1_2, tau_monBen_1_3, tau_monBen_1_4),
rows = (task==1),
componentName = "indic_monBen_1")
ol_settings2 = list(outcomeOrdered = monBen_2,
V = constant_monBen_2 + zeta_monBen_2*LV_monBen,
tau = list(tau_monBen_2_1, tau_monBen_2_2, tau_monBen_2_3, tau_monBen_2_4),
rows = (task==1),
componentName = "indic_monBen_2")
ol_settings3 = list(outcomeOrdered = monBen_3,
V = constant_monBen_3 + zeta_monBen_3*LV_monBen,
tau = list(tau_monBen_3_1, tau_monBen_3_2, tau_monBen_3_3, tau_monBen_3_4),
rows = (task==1),
componentName = "indic_monBen_3")
ol_settings5 = list(outcomeOrdered = envEnth_1,
V = constant_envEnth_1 + zeta_envEnth_1*LV_envEnth,
tau = list(tau_envEnth_1_1, tau_envEnth_1_2, tau_envEnth_1_3, tau_envEnth_1_4),
rows = (task==1),
componentName = "indic_envEnth_1")
ol_settings6 = list(outcomeOrdered = envEnth_2,
V = constant_envEnth_2 + zeta_envEnth_2*LV_envEnth,
tau = list(tau_envEnth_2_1, tau_envEnth_2_2, tau_envEnth_2_3, tau_envEnth_2_4),
rows = (task==1),
componentName = "indic_envEnth_2")
ol_settings7 = list(outcomeOrdered = envEnth_3,
V = constant_envEnth_3 + zeta_envEnth_3*LV_envEnth,
tau = list(tau_envEnth_3_1, tau_envEnth_3_2, tau_envEnth_3_3, tau_envEnth_3_4),
rows = (task==1),
componentName = "indic_envEnth_3")
ol_settings8 = list(outcomeOrdered = socIma_1,
V = constant_socIma_1 + zeta_socIma_1*LV_socIma,
tau = list(tau_socIma_1_1, tau_socIma_1_2, tau_socIma_1_3, tau_socIma_1_4),
rows = (task==1),
componentName = "indic_socIma_1")
ol_settings9 = list(outcomeOrdered = socIma_2,
V = constant_socIma_2 + zeta_socIma_2*LV_socIma,
tau = list(tau_socIma_2_1, tau_socIma_2_2, tau_socIma_2_3, tau_socIma_2_4),
rows = (task==1),
componentName = "indic_socIma_2")
ol_settings10 = list(outcomeOrdered = socIma_3,
V = constant_socIma_3 + zeta_socIma_3*LV_socIma,
tau = list(tau_socIma_3_1, tau_socIma_3_2, tau_socIma_3_3, tau_socIma_3_4),
rows = (task==1),
componentName = "indic_socIma_3")
ol_settings11 = list(outcomeOrdered = socIma_4,
V = constant_socIma_4 + zeta_socIma_4*LV_socIma,
tau = list(tau_socIma_4_1, tau_socIma_4_2, tau_socIma_4_3, tau_socIma_4_4),
rows = (task==1),
componentName = "indic_socIma_4")
ol_settings12 = list(outcomeOrdered = techEnth_1,
V = constant_techEnth_1 + zeta_techEnth_1*LV_techEnth,
tau = list(tau_techEnth_1_1, tau_techEnth_1_2, tau_techEnth_1_3, tau_techEnth_1_4),
rows = (task==1),
componentName = "indic_techEnth_1")
ol_settings13 = list(outcomeOrdered = techEnth_2,
V = constant_techEnth_2 + zeta_techEnth_2*LV_techEnth,
tau = list(tau_techEnth_2_1, tau_techEnth_2_2, tau_techEnth_2_3, tau_techEnth_2_4),
rows = (task==1),
componentName = "indic_techEnth_2")
ol_settings14 = list(outcomeOrdered = techEnth_3r,
V = constant_techEnth_3r + zeta_techEnth_3r*LV_techEnth,
tau = list(tau_techEnth_3r_1, tau_techEnth_3r_2, tau_techEnth_3r_3, tau_techEnth_3r_4),
rows = (task==1),
componentName = "indic_techEnth_3r")
P[["indic_monBen_1"]] = apollo_ol(ol_settings1, functionality)
P[["indic_monBen_2"]] = apollo_ol(ol_settings2, functionality)
P[["indic_monBen_3"]] = apollo_ol(ol_settings3, functionality)
P[["indic_envEnth_1"]] = apollo_ol(ol_settings5, functionality)
P[["indic_envEnth_2"]] = apollo_ol(ol_settings6, functionality)
P[["indic_envEnth_3"]] = apollo_ol(ol_settings7, functionality)
P[["indic_socIma_1"]] = apollo_ol(ol_settings8, functionality)
P[["indic_socIma_2"]] = apollo_ol(ol_settings9, functionality)
P[["indic_socIma_3"]] = apollo_ol(ol_settings10, functionality)
P[["indic_socIma_4"]] = apollo_ol(ol_settings11, functionality)
P[["indic_techEnth_1"]] = apollo_ol(ol_settings12, functionality)
P[["indic_techEnth_2"]] = apollo_ol(ol_settings13, functionality)
P[["indic_techEnth_3r"]] = apollo_ol(ol_settings14, functionality)
### Likelihood of choices
### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["alt1"]] = asc_EV + b_pp*(ppEV*(50+20*log(incomeAvg/10000))) + b_oc*ocEV + b_ct*ctEV/60 + b_r*rEV/100 + b_e*eEV + b_cf*cfEV
V[["alt2"]] = asc_CV + b_pp*(ppCV*(50+20*log(incomeAvg/10000))) + b_oc*ocCV + + b_r*rCV/100 + lambda_monBen*LV_monBen + lambda_envEnth*LV_envEnth + lambda_socIma*LV_socIma+ lambda_techEnth*LV_techEnth
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(alt1=1, alt2=2),
avail = list(alt1=1, alt2=1),
choiceVar = choiceVehicle,
utilities = V,
componentName = "choice"
)
### Compute probabilities for MNL model component
P[["choice"]] = apollo_mnl(mnl_settings, functionality)
### Likelihood of the whole model
P = apollo_combineModels(P, apollo_inputs, functionality)
### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)
### Average across inter-individual draws
P = apollo_avgInterDraws(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #
### Optional: calculate LL before model estimation
estimate_settings = list(maxIterations = 250)
### Estimate model
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs, estimate_settings = list(scaleAfterConvergence=FALSE, maxIterations=300))
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model)
apollo_saveOutput(model)
Code: Select all
Estimate Std.err. t-ratio(0) Rob.std.err. Rob.t-ratio(0)
asc_CV 0 NA NA NA NA
asc_EV -0.59573678 0.269435472 -2.21105549 0.282113903 -2.111688841
b_pp -0.006358901 0.001612845 -3.942660019 0.001668805 -3.810452841
b_oc -0.049546163 0.022597885 -2.192513265 0.022738858 -2.178920435
b_ct -0.037256533 0.010417145 -3.576462971 0.010457177 -3.562771446
b_r 0.080633006 0.024266472 3.322815389 0.023659819 3.408014437
b_cf 0.190510673 0.080134178 2.377395989 0.078812924 2.417251668
b_e -0.181431952 0.086086377 -2.107557071 0.085965024 -2.110532218
gamma_Male_monBen 0.321530159 0.099088449 3.244880348 0.11005033 2.921664642
gamma_female_monBen 0 NA NA NA NA
gamma_dailyDistanceAvg_monBen 0.003745347 0.002650187 1.413238758 0.002955031 1.267447567
gamma_ageAvg_monBen -0.015258677 0.006316165 -2.415813667 0.006212439 -2.456149189
gamma_knowledgeLow_monBen -1.30281726 0.181630177 -7.172911895 0.219220532 -5.942952724
gamma_knowledgeMiddle_monBen -1.05425992 0.143579622 -7.342684878 0.163412578 -6.451522493
gamma_knowledgeHigh_monBen 0 NA NA NA NA
gamma_Male_envEnth 0.129809526 0.159836074 0.812141605 0.179754086 0.722150627
gamma_female_envEnth 0 NA NA NA NA
gamma_dailyDistanceAvg_envEnth 0.019616686 0.004815407 4.073734089 0.006157292 3.185927616
gamma_ageAvg_envEnth 0.023104604 0.010428598 2.215504461 0.0111972 2.063426925
gamma_knowledgeLow_envEnth -2.796840308 0.336428648 -8.313323855 0.381945017 -7.322625468
gamma_knowledgeMiddle_envEnth -1.678941848 0.24962377 -6.725889304 0.29606914 -5.670776247
gamma_knowledgeHigh_envEnth 0 NA NA NA NA
gamma_Male_socIma 0.364327729 0.175600742 2.074750507 0.211525279 1.722383868
gamma_female_socIma 0 NA NA NA NA
gamma_dailyDistanceAvg_socIma 0.00231761 0.005286208 0.438425768 0.008313123 0.278789308
gamma_ageAvg_socIma 0.012310484 0.01179855 1.043389583 0.014599164 0.843232177
gamma_knowledgeLow_socIma -2.825684639 0.307476514 -9.189920247 0.369815531 -7.640794949
gamma_knowledgeMiddle_socIma -2.152049378 0.25628739 -8.397016257 0.356471398 -6.037088507
gamma_knowledgeHigh_socIma 0 NA NA NA NA
gamma_Male_techEnth -0.246293578 0.106812928 -2.305840529 0.187857486 -1.311066079
gamma_female_techEnth 0 NA NA NA NA
gamma_dailyDistanceAvg_techEnth 0.015656149 0.003104896 5.042406569 0.004537121 3.450678983
gamma_ageAvg_techEnth 0.00523192 0.006179767 0.846620833 0.007979687 0.655654812
gamma_knowledgeLow_techEnth -1.996899745 0.247917515 -8.054694106 0.403724571 -4.946193237
gamma_knowledgeMiddle_techEnth -1.333132905 0.176882091 -7.536845006 0.243935182 -5.465111234
gamma_knowledgeHigh_techEnth 0 NA NA NA NA
lambda_monBen 0.254160383 0.078850138 3.223334661 0.181683882 1.398915418
sigma_eta_monBen -1.361166532 0.118271786 -11.5088017 0.143919941 -9.457803542
zeta_monBen_1 1 NA NA NA NA
zeta_monBen_2 0.997631834 0.117084495 8.520614412 0.140415926 7.104833933
zeta_monBen_3 1.352306968 0.159870369 8.458771813 0.15406208 8.777675641
constant_monBen_1 7.568757772 0.550120595 13.75836105 0.57077885 13.26040335
constant_monBen_2 5.653364356 0.345999303 16.33923626 0.367900673 15.36655074
constant_monBen_3 6.430064122 0.443642812 14.49378634 0.491376004 13.08583259
tau_monBen_1_1 0 NA NA NA NA
tau_monBen_1_2 1.379945958 0.390334201 3.535293485 0.392709392 3.513911268
tau_monBen_1_3 3.817522484 0.449461294 8.49355113 0.455083073 8.388627733
tau_monBen_1_4 5.92511188 0.465762174 12.72132476 0.479627323 12.35357453
tau_monBen_2_1 0 NA NA NA NA
tau_monBen_2_2 1.399774382 0.163881206 8.541396646 0.163484772 8.562108678
tau_monBen_2_3 3.686988729 0.202757007 18.18427277 0.202952903 18.1667208
tau_monBen_2_4 5.528068535 0.234796138 23.54412039 0.232210559 23.80627543
tau_monBen_3_1 0 NA NA NA NA
tau_monBen_3_2 1.711315309 0.168793958 10.13848676 0.181631538 9.421906159
tau_monBen_3_3 3.486298397 0.214810762 16.22962635 0.253404708 13.75782805
tau_monBen_3_4 5.598748911 0.284276443 19.69473393 0.351293147 15.93754094
lambda_envEnth -0.218759145 0.044067561 -4.964176363 0.076653925 -2.853854448
sigma_eta_envEnth -2.200217149 0.218876462 -10.05232418 0.244922868 -8.983306337
zeta_envEnth_1 1 NA NA NA NA
zeta_envEnth_2 0.647561686 0.08451719 7.661893191 0.092214114 7.022370623
zeta_envEnth_3 0.701127645 0.086795357 8.077939553 0.094458589 7.422592823
constant_envEnth_1 9.226520914 0.908618873 10.15444559 0.969668062 9.515133349
constant_envEnth_2 6.829874937 0.533259507 12.80778842 0.577426209 11.82813462
constant_envEnth_3 5.596193081 0.390286273 14.33868796 0.470144065 11.90314521
tau_envEnth_1_1 0 NA NA NA NA
tau_envEnth_1_2 1.726041505 0.653936005 2.639465469 0.649220999 2.658634745
tau_envEnth_1_3 4.213603486 0.72857954 5.783312942 0.716167565 5.883544146
tau_envEnth_1_4 7.255389137 0.777890638 9.327004061 0.759123005 9.557593553
tau_envEnth_2_1 0 NA NA NA NA
tau_envEnth_2_2 1.534165318 0.39962864 3.838977404 0.394866837 3.88527264
tau_envEnth_2_3 3.375513619 0.445940397 7.569427752 0.441122969 7.652092171
tau_envEnth_2_4 6.024734051 0.467517055 12.88666155 0.462509839 13.0261749
tau_envEnth_3_1 0 NA NA NA NA
tau_envEnth_3_2 1.188999773 0.19626113 6.058253992 0.200625441 5.926465579
tau_envEnth_3_3 3.062984058 0.240430161 12.73959989 0.252052989 12.15214335
tau_envEnth_3_4 5.354125181 0.280026904 19.12003846 0.312602174 17.12760062
lambda_socIma -0.245226372 0.025518903 -9.609596779 0.033768362 -7.262015677
sigma_eta_socIma -2.947583426 0.171804406 -17.15662303 0.205128785 -14.3694286
zeta_socIma_1 1 NA NA NA NA
zeta_socIma_2 0.98722191 0.073323763 13.46387403 0.075709344 13.03963097
zeta_socIma_3 1.136602528 0.090889891 12.50526886 0.095850888 11.85802815
zeta_socIma_4 0.757787827 0.057542627 13.16915586 0.062881535 12.05103897
constant_socIma_1 7.554674209 0.569164367 13.27327333 0.695248986 10.866142
constant_socIma_2 8.09988259 0.58338041 13.8843925 0.723373592 11.19737115
constant_socIma_3 8.030117697 0.634428539 12.65724539 0.803170996 9.998017533
constant_socIma_4 6.184451662 0.430347276 14.37083957 0.559800381 11.04760173
tau_socIma_1_1 0 NA NA NA NA
tau_socIma_1_2 1.16398035 0.182571325 6.375482843 0.176540915 6.593261101
tau_socIma_1_3 4.008461085 0.25725932 15.5814028 0.252440673 15.87882428
tau_socIma_1_4 6.382425365 0.312704209 20.41042361 0.314565123 20.28967897
tau_socIma_2_1 0 NA NA NA NA
tau_socIma_2_2 2.06901135 0.24885579 8.314097696 0.223792486 9.245222608
tau_socIma_2_3 5.478389397 0.315146982 17.383601 0.306252575 17.88846802
tau_socIma_2_4 7.702086785 0.364650269 21.12184591 0.368791713 20.88465255
tau_socIma_3_1 0 NA NA NA NA
tau_socIma_3_2 1.629333358 0.195796813 8.321551965 0.196612894 8.28701173
tau_socIma_3_3 4.987491938 0.287657985 17.33827045 0.313282472 15.92011169
tau_socIma_3_4 7.213076752 0.351499354 20.52088194 0.40020267 18.02355981
tau_socIma_4_1 0 NA NA NA NA
tau_socIma_4_2 1.272880581 0.161654246 7.874093088 0.160058189 7.952611393
tau_socIma_4_3 3.476437667 0.206057384 16.87121132 0.210046331 16.55081357
tau_socIma_4_4 5.764683799 0.244649003 23.56307906 0.25631507 22.49061595
lambda_techEnth 0.705213252 0.123067935 5.73027615 0.283785967 2.485018054
sigma_eta_techEnth -1.087816838 0.110464925 -9.847622092 0.147150143 -7.392563909
zeta_techEnth_1 1 NA NA NA NA
zeta_techEnth_2 0.333837224 0.055299633 6.036879596 0.061242726 5.451050975
zeta_techEnth_3r 0.756805561 0.090654184 8.348269564 0.088762705 8.52616609
constant_techEnth_1 7.644528417 0.658296745 11.61258729 0.705614624 10.83385769
constant_techEnth_2 4.913088406 0.284711272 17.25638882 0.29398337 16.71213038
constant_techEnth_3r 3.27010531 0.214391632 15.25295216 0.281438316 11.61926123
tau_techEnth_1_1 0 NA NA NA NA
tau_techEnth_1_2 1.835772537 0.536040067 3.424692761 0.541228034 3.391865207
tau_techEnth_1_3 3.334966471 0.574921917 5.800729403 0.583007059 5.720284892
tau_techEnth_1_4 6.020193661 0.59303381 10.15151845 0.616122132 9.771104382
tau_techEnth_2_1 0 NA NA NA NA
tau_techEnth_2_2 1.405436946 0.233662044 6.014827757 0.23352352 6.018395694
tau_techEnth_2_3 2.994297633 0.262341155 11.41375485 0.261550969 11.44823759
tau_techEnth_2_4 4.828200254 0.270743108 17.83314189 0.271517748 17.78226392
tau_techEnth_3r_1 0 NA NA NA NA
tau_techEnth_3r_2 1.417625217 0.089907284 15.76763471 0.10202737 13.89455801
tau_techEnth_3r_3 2.367703755 0.108298442 21.86276843 0.140172871 16.89131237
tau_techEnth_3r_4 3.379739277 0.130333843 25.93140191 0.187680246 18.00796486