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Latent Class Joint Model

http://apollochoicemodelling.com/forum/viewtopic.php?t=229

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Re: Latent Class Joint Model

Posted: 10 Jun 2021, 15:34
by cybey
Estimation starts and the model converges after 150 to 200 iterations, depending on the exact model specification. In my experience, however, this does not necessarily mean that there is not an error somewhere in the code. To my knowledge, there are only a few papers which use a LC-HCM. For example:
  • Pan, Long; Yao, Enjian; MacKenzie, Don (2019): Modeling EV charging choice considering risk attitudes and attribute non-attendance. In: Transportation Research Part C: Emerging Technologies 102, S. 60–72. DOI: 10.1016/j.trc.2019.03.007.
  • Mariel, Petr; Meyerhoff, Jürgen; Hess, Stephane (2015): Heterogeneous preferences toward landscape externalities of wind turbines – combining choices and attitudes in a hybrid model. In: Renewable and Sustainable Energy Reviews 41, S. 647–657. DOI: 10.1016/j.rser.2014.08.074.
Yet, the code used is not publicly available. Anyway, below are the results of two model specifications using 2000 Sobol Owen draws. The first one is without the dual response part, the second model with dual response. Unlike the usual approach, we did not present a dichotomous choice situation in the dual response part, but instead queried the decision for or against an alternative using a 7-point Likert scale. In this case, we set the cutoff at 7 for "Yes, I would choose this option".

Without dual response (=without free choices)

Code: Select all

Model run using Apollo for R, version 0.2.5 on Windows by 
www.ApolloChoiceModelling.com

Model name                       : ICLV_LC_3Classes_DR0_SO2000
Model description                : Latent class model on panel data (classical estimation)
Model run at                     : 2021-05-21 13:19:14
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 1034
Number of rows in database       : 31020
Number of modelled outcomes      : 37224
               NACount_r1_NACount: 1034
               NACount_r2_NACount: 1034
               NACount_r3_NACount: 1034
               NACount_r4_NACount: 1034
               NACount_r5_NACount: 1034
               NACount_r6_NACount: 1034
         NADuration_r1_NADuration: 1034
         NADuration_r2_NADuration: 1034
         NADuration_r3_NADuration: 1034
         NADuration_r4_NADuration: 1034
         NADuration_r5_NADuration: 1034
         NADuration_r6_NADuration: 1034
             NAPeriod_r1_NAPeriod: 1034
             NAPeriod_r2_NAPeriod: 1034
             NAPeriod_r3_NAPeriod: 1034
             NAPeriod_r4_NAPeriod: 1034
             NAPeriod_r5_NAPeriod: 1034
             NAPeriod_r6_NAPeriod: 1034
       NACompensation_r1_NACompen: 1034
       NACompensation_r2_NACompen: 1034
       NACompensation_r3_NACompen: 1034
       NACompensation_r4_NACompen: 1034
       NACompensation_r5_NACompen: 1034
       NACompensation_r6_NACompen: 1034
                         LC_model: 12408

Number of cores used             :  11 
Number of inter-individual draws : 2000 (sobolOwen)

LL(start)                        : -54539.29
LL(0, whole model)               : Not applicable
LL(final, whole model)           : -52570.18
Rho-square (0)                   : Not applicable
Adj.Rho-square (0)               : Not applicable
AIC                              :  105366.4 
BIC                              :  106329.6 

LL(0,indic_NACount_NACount_r1)   : Not applicable
LL(final,indic_NACount_NACount_r1): -1976.472
LL(0,indic_NACount_NACount_r2)   : Not applicable
LL(final,indic_NACount_NACount_r2): -1959.603
LL(0,indic_NACount_NACount_r3)   : Not applicable
LL(final,indic_NACount_NACount_r3): -1984.101
LL(0,indic_NACount_NACount_r4)   : Not applicable
LL(final,indic_NACount_NACount_r4): -1904.185
LL(0,indic_NACount_NACount_r5)   : Not applicable
LL(final,indic_NACount_NACount_r5): -2146.41
LL(0,indic_NACount_NACount_r6)   : Not applicable
LL(final,indic_NACount_NACount_r6): -2176.484
LL(0,indic_NADuration_NADuration_r1): Not applicable
LL(final,indic_NADuration_NADuration_r1): -1890.559
LL(0,indic_NADuration_NADuration_r2): Not applicable
LL(final,indic_NADuration_NADuration_r2): -1884.196
LL(0,indic_NADuration_NADuration_r3): Not applicable
LL(final,indic_NADuration_NADuration_r3): -1863.505
LL(0,indic_NADuration_NADuration_r4): Not applicable
LL(final,indic_NADuration_NADuration_r4): -1815.395
LL(0,indic_NADuration_NADuration_r5): Not applicable
LL(final,indic_NADuration_NADuration_r5): -2082.593
LL(0,indic_NADuration_NADuration_r6): Not applicable
LL(final,indic_NADuration_NADuration_r6): -2098.595
LL(0,indic_NAPeriod_NAPeriod_r1) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r1): -1814.391
LL(0,indic_NAPeriod_NAPeriod_r2) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r2): -1801.61
LL(0,indic_NAPeriod_NAPeriod_r3) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r3): -1732.198
LL(0,indic_NAPeriod_NAPeriod_r4) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r4): -1727.614
LL(0,indic_NAPeriod_NAPeriod_r5) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r5): -1841.999
LL(0,indic_NAPeriod_NAPeriod_r6) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r6): -1808.092
LL(0,indic_NACompensation_NACompensation_r1): Not applicable
LL(final,indic_NACompensation_NACompensation_r1): -1906.686
LL(0,indic_NACompensation_NACompensation_r2): Not applicable
LL(final,indic_NACompensation_NACompensation_r2): -1889.431
LL(0,indic_NACompensation_NACompensation_r3): Not applicable
LL(final,indic_NACompensation_NACompensation_r3): -1973.553
LL(0,indic_NACompensation_NACompensation_r4): Not applicable
LL(final,indic_NACompensation_NACompensation_r4): -1857.076
LL(0,indic_NACompensation_NACompensation_r5): Not applicable
LL(final,indic_NACompensation_NACompensation_r5): -2132.703
LL(0,indic_NACompensation_NACompensation_r6): Not applicable
LL(final,indic_NACompensation_NACompensation_r6): -2144.094
LL(0,Measurement_model)          : Not applicable
LL(final,Measurement_model)      : -41638.16
LL(0,LC_model)                   : -13631.58
LL(final,LC_model)               : -11026.07

Estimated parameters             :  113
Time taken (hh:mm:ss)            :  436:09:21 
     pre-estimation              :  00:51:27.31 
     estimation                  :  174:21:53.65 
     post-estimation             :  260:56:0.04 
Iterations                       :  152  
Min abs eigenvalue of Hessian    :  0.111192 

Estimates:
                                                        Estimate        s.e.   t.rat.(0)  p(1-sided)    Rob.s.e. Rob.t.rat.(0)  p(1-sided)
b_asc_1                                                 0.013120     0.02646     0.49587    0.309992     0.02872       0.45684    0.323893
b_asc_2                                                 0.049940     0.02646     1.88770    0.029533     0.02774       1.80043    0.035897
b_asc_3                                                 0.000000          NA          NA          NA          NA            NA          NA
delta_A                                                 0.000000          NA          NA          NA          NA            NA          NA
gamma_A_NACount                                         0.000000          NA          NA          NA          NA            NA          NA
gamma_A_NADuration                                      0.000000          NA          NA          NA          NA            NA          NA
gamma_A_NAPeriod                                        0.000000          NA          NA          NA          NA            NA          NA
gamma_A_NACompensation                                  0.000000          NA          NA          NA          NA            NA          NA
delta_B                                                 1.005664     0.20721     4.85333   6.070e-07     0.36667       2.74271    0.003047
gamma_B_NACount                                         0.221836     0.17525     1.26582    0.102788     0.20311       1.09218    0.137376
gamma_B_NADuration                                      0.226123     0.22583     1.00129    0.158343     0.34550       0.65448    0.256402
gamma_B_NAPeriod                                       -0.727808     0.24470    -2.97426    0.001468     0.40720      -1.78737    0.036939
gamma_B_NACompensation                                  0.004471     0.05543     0.08066    0.467855     0.09259       0.04829    0.480741
delta_C                                                 0.696977     0.20354     3.42432  3.0817e-04     0.36295       1.92030    0.027410
gamma_C_NACount                                         0.200559     0.16322     1.22879    0.109576     0.19508       1.02809    0.151955
gamma_C_NADuration                                      0.253307     0.24333     1.04102    0.148934     0.35946       0.70468    0.240505
gamma_C_NAPeriod                                        0.034956     0.20179     0.17323    0.431234     0.32748       0.10674    0.457496
gamma_C_NACompensation                                 -0.317195     0.13463    -2.35602    0.009236     0.17499      -1.81264    0.034943
A_b_Quota_Count                                        -0.683468     0.03982   -17.16286    0.000000     0.07584      -9.01143    0.000000
A_b_Quota_Max_Duration                                 -0.617936     0.04168   -14.82458    0.000000     0.06256      -9.87745    0.000000
A_b_Quota_Period_midmorning                             0.503257     0.11499     4.37635   6.034e-06     0.23397       2.15098    0.015739
A_b_Quota_Period_afternoon                              0.013146     0.12056     0.10904    0.456585     0.22963       0.05725    0.477173
A_b_Quota_Period_evening                               -0.079417     0.11257    -0.70549    0.240253     0.16337      -0.48611    0.313444
A_b_Quota_Period_night                                  1.275524     0.14957     8.52802    0.000000     0.34930       3.65162  1.3030e-04
A_b_Quota_Compensation                                  0.677489     0.07183     9.43191    0.000000     0.09326       7.26447   1.873e-13
B_b_Quota_Count                                        -0.182653     0.02547    -7.17080   3.728e-13     0.04470      -4.08638   2.191e-05
B_b_Quota_Max_Duration                                 -0.254260     0.03155    -8.05838   3.331e-16     0.05079      -5.00611   2.777e-07
B_b_Quota_Period_midmorning                            -0.925891     0.09470    -9.77682    0.000000     0.23912      -3.87210   5.395e-05
B_b_Quota_Period_afternoon                             -1.590658     0.11679   -13.62021    0.000000     0.29323      -5.42467   2.903e-08
B_b_Quota_Period_evening                               -1.246933     0.09846   -12.66447    0.000000     0.23597      -5.28420   6.313e-08
B_b_Quota_Period_night                                  1.894139     0.10282    18.42220    0.000000     0.20830       9.09347    0.000000
B_b_Quota_Compensation                                  0.579954     0.05614    10.33069    0.000000     0.08313       6.97628   1.515e-12
C_b_Quota_Count                                        -0.038316     0.01968    -1.94682    0.025778     0.02942      -1.30241    0.096389
C_b_Quota_Max_Duration                                 -0.015148     0.02204    -0.68716    0.245990     0.02876      -0.52663    0.299227
C_b_Quota_Period_midmorning                            -0.728280     0.07606    -9.57471    0.000000     0.13986      -5.20705   9.593e-08
C_b_Quota_Period_afternoon                             -0.785071     0.07587   -10.34811    0.000000     0.15340      -5.11791   1.545e-07
C_b_Quota_Period_evening                               -0.006914     0.06730    -0.10273    0.459090     0.15047      -0.04595    0.481677
C_b_Quota_Period_night                                  0.043975     0.06804     0.64627    0.259051     0.09736       0.45167    0.325754
C_b_Quota_Compensation                                  0.789275     0.04770    16.54510    0.000000     0.07463      10.57534    0.000000
lambda_NACountComplexityCosts_NACount                   1.000000          NA          NA          NA          NA            NA          NA
lambda_NACountIrrelevance_NACount                       3.042678     2.70003     1.12690    0.129891     3.06417       0.99299    0.160358
lambda_NADurationComplexityCosts_NADuration             1.000000          NA          NA          NA          NA            NA          NA
lambda_NADurationIrrelevance_NADuration                 2.390138     2.58649     0.92409    0.177721     3.61345       0.66146    0.254160
lambda_NAPeriodComplexityCosts_NAPeriod                 1.000000          NA          NA          NA          NA            NA          NA
lambda_NAPeriodIrrelevance_NAPeriod                     0.225187     0.31318     0.71903    0.236061     0.43974       0.51209    0.304294
lambda_NACompensationComplexityCosts_NACompensation     1.000000          NA          NA          NA          NA            NA          NA
lambda_NACompensationIrrelevance_NACompensation         1.651350     0.79794     2.06952    0.019249     0.92110       1.79280    0.036502
sigma_NACount_r1                                        1.202463     0.03112    38.64235    0.000000     0.03902      30.81825    0.000000
sigma_NACount_r2                                        1.062134     0.03055    34.76672    0.000000     0.04621      22.98733    0.000000
sigma_NACount_r3                                        1.174063     0.03206    36.61528    0.000000     0.05278      22.24590    0.000000
sigma_NACount_r4                                        1.040344     0.02895    35.93137    0.000000     0.04507      23.08146    0.000000
sigma_NACount_r5                                        1.350430     0.05133    26.30674    0.000000     0.10736      12.57869    0.000000
sigma_NACount_r6                                        1.408362     0.05410    26.03241    0.000000     0.11573      12.16905    0.000000
sigma_NADuration_r1                                     1.048855     0.02661    39.41898    0.000000     0.04710      22.27000    0.000000
sigma_NADuration_r2                                     0.900890     0.02506    35.94939    0.000000     0.05197      17.33516    0.000000
sigma_NADuration_r3                                     0.860154     0.02344    36.68868    0.000000     0.04156      20.69842    0.000000
sigma_NADuration_r4                                     0.792300     0.02310    34.29485    0.000000     0.03994      19.83924    0.000000
sigma_NADuration_r5                                     1.111542     0.04160    26.71891    0.000000     0.07875      14.11409    0.000000
sigma_NADuration_r6                                     1.133506     0.03856    29.39420    0.000000     0.05994      18.90962    0.000000
sigma_NAPeriod_r1                                       0.959717     0.02404    39.91365    0.000000     0.04844      19.81409    0.000000
sigma_NAPeriod_r2                                       0.760163     0.02166    35.09884    0.000000     0.05471      13.89313    0.000000
sigma_NAPeriod_r3                                       0.731487     0.01965    37.21780    0.000000     0.04611      15.86436    0.000000
sigma_NAPeriod_r4                                       0.683174     0.02060    33.16775    0.000000     0.04476      15.26376    0.000000
sigma_NAPeriod_r5                                       1.264088     0.03928    32.18439    0.000000     0.09054      13.96144    0.000000
sigma_NAPeriod_r6                                       1.238458     0.03650    33.93066    0.000000     0.08130      15.23368    0.000000
sigma_NACompensation_r1                                 1.011670     0.02804    36.07819    0.000000     0.04380      23.09493    0.000000
sigma_NACompensation_r2                                 0.917970     0.02823    32.52199    0.000000     0.05349      17.16013    0.000000
sigma_NACompensation_r3                                 1.135474     0.03036    37.40461    0.000000     0.05079      22.35533    0.000000
sigma_NACompensation_r4                                 0.931692     0.02690    34.63994    0.000000     0.05198      17.92378    0.000000
sigma_NACompensation_r5                                 1.298672     0.04460    29.11851    0.000000     0.09445      13.75048    0.000000
sigma_NACompensation_r6                                 1.306434     0.04633    28.19961    0.000000     0.09573      13.64636    0.000000
zeta_NACountComplexityCosts_r1_NACount                  1.000000          NA          NA          NA          NA            NA          NA
zeta_NACountComplexityCosts_r2_NACount                  1.123706     0.05216    21.54223    0.000000     0.04944      22.72740    0.000000
zeta_NACountComplexityCosts_r3_NACount                  1.077476     0.05533    19.47407    0.000000     0.06180      17.43417    0.000000
zeta_NACountComplexityCosts_r4_NACount                  1.044352     0.05060    20.64091    0.000000     0.05316      19.64611    0.000000
zeta_NACountIrrelevance_r5_NACount                      1.000000          NA          NA          NA          NA            NA          NA
zeta_NACountIrrelevance_r6_NACount                      1.009504     0.04884    20.66766    0.000000     0.02609      38.69335    0.000000
zeta_NADurationComplexityCosts_r1_NADuration            1.000000          NA          NA          NA          NA            NA          NA
zeta_NADurationComplexityCosts_r2_NADuration            1.110812     0.04422    25.11997    0.000000     0.04609      24.10067    0.000000
zeta_NADurationComplexityCosts_r3_NADuration            1.106331     0.04404    25.12384    0.000000     0.04921      22.48082    0.000000
zeta_NADurationComplexityCosts_r4_NADuration            1.075954     0.04239    25.38405    0.000000     0.04888      22.01256    0.000000
zeta_NADurationIrrelevance_r5_NADuration                1.000000          NA          NA          NA          NA            NA          NA
zeta_NADurationIrrelevance_r6_NADuration                1.007266     0.03868    26.04421    0.000000     0.03566      28.24898    0.000000
zeta_NAPeriodComplexityCosts_r1_NAPeriod                1.000000          NA          NA          NA          NA            NA          NA
zeta_NAPeriodComplexityCosts_r2_NAPeriod                1.153689     0.04485    25.72220    0.000000     0.05579      20.68094    0.000000
zeta_NAPeriodComplexityCosts_r3_NAPeriod                1.059867     0.04202    25.22470    0.000000     0.05866      18.06651    0.000000
zeta_NAPeriodComplexityCosts_r4_NAPeriod                1.069590     0.04171    25.64058    0.000000     0.05325      20.08675    0.000000
zeta_NAPeriodIrrelevance_r5_NAPeriod                    1.000000          NA          NA          NA          NA            NA          NA
zeta_NAPeriodIrrelevance_r6_NAPeriod                    0.936435     0.07830    11.95882    0.000000     0.04956      18.89632    0.000000
zeta_NACompensationComplexityCosts_r1_NACompensation    1.000000          NA          NA          NA          NA            NA          NA
zeta_NACompensationComplexityCosts_r2_NACompensation    1.059582     0.04198    25.23817    0.000000     0.04122      25.70770    0.000000
zeta_NACompensationComplexityCosts_r3_NACompensation    1.022334     0.04679    21.85024    0.000000     0.04789      21.34581    0.000000
zeta_NACompensationComplexityCosts_r4_NACompensation    0.981437     0.04121    23.81709    0.000000     0.04066      24.13692    0.000000
zeta_NACompensationIrrelevance_r5_NACompensation        1.000000          NA          NA          NA          NA            NA          NA
zeta_NACompensationIrrelevance_r6_NACompensation        1.020095     0.04481    22.76408    0.000000     0.02501      40.78714    0.000000
gamma_Age_NACountComplexityCosts                        0.153442     0.02299     6.67373   1.247e-11     0.04227       3.62994  1.4174e-04
gamma_Education_NACountComplexityCosts                 -0.395474     0.08813    -4.48726   3.607e-06     0.16394      -2.41232    0.007926
gamma_ExistingApps_NACountComplexityCosts               0.076222     0.08490     0.89781    0.184642     0.17077       0.44634    0.327677
sigma_NACountComplexityCosts                            1.191817     0.05191    22.95954    0.000000     0.07197      16.55912    0.000000
gamma_Age_NACountIrrelevance                            0.189643     0.03175     5.97340   1.162e-09     0.04692       4.04207   2.649e-05
gamma_Education_NACountIrrelevance                     -0.789264     0.11793    -6.69256   1.097e-11     0.16013      -4.92876   4.138e-07
gamma_ExistingApps_NACountIrrelevance                   0.219226     0.10948     2.00241    0.022621     0.15448       1.41912    0.077931
sigma_NACountIrrelevance                                1.409391     0.06791    20.75287    0.000000     0.13490      10.44803    0.000000
gamma_Age_NADurationComplexityCosts                     0.138159     0.01985     6.95909   1.712e-12     0.04374       3.15840  7.9318e-04
gamma_Education_NADurationComplexityCosts              -0.403396     0.07523    -5.36211   4.113e-08     0.17468      -2.30931    0.010463
gamma_ExistingApps_NADurationComplexityCosts            0.032180     0.06043     0.53254    0.297177     0.09631       0.33414    0.369138
sigma_NADurationComplexityCosts                         1.245499     0.04970    25.06023    0.000000     0.10270      12.12709    0.000000
gamma_Age_NADurationIrrelevance                         0.173607     0.03100     5.60004   1.071e-08     0.05064       3.42854  3.0342e-04
gamma_Education_NADurationIrrelevance                  -0.651437     0.11773    -5.53354   1.569e-08     0.19457      -3.34801  4.0698e-04
gamma_ExistingApps_NADurationIrrelevance                0.082927     0.11247     0.73730    0.230470     0.19493       0.42541    0.335269
sigma_NADurationIrrelevance                             1.532677     0.05463    28.05560    0.000000     0.08341      18.37460    0.000000
gamma_Age_NAPeriodComplexityCosts                       0.206194     0.02259     9.12896    0.000000     0.06568       3.13960  8.4590e-04
gamma_Education_NAPeriodComplexityCosts                -0.574204     0.07986    -7.19019   3.235e-13     0.21867      -2.62595    0.004320
gamma_ExistingApps_NAPeriodComplexityCosts              0.291217     0.07892     3.68992  1.1216e-04     0.19713       1.47726    0.069803
sigma_NAPeriodComplexityCosts                           1.207774     0.04605    26.22799    0.000000     0.09477      12.74416    0.000000
gamma_Age_NAPeriodIrrelevance                           0.095518     0.02249     4.24789   1.079e-05     0.03099       3.08256    0.001026
gamma_Education_NAPeriodIrrelevance                    -0.615254     0.08964    -6.86376   3.354e-12     0.11701      -5.25822   7.273e-08
gamma_ExistingApps_NAPeriodIrrelevance                  0.091948     0.07659     1.20047    0.114978     0.11037       0.83310    0.202395
sigma_NAPeriodIrrelevance                              -0.708609     0.07022   -10.09134    0.000000     0.16356      -4.33239   7.375e-06
gamma_Gender_NACompensationComplexityCosts             -0.011057     0.06376    -0.17342    0.431161     0.13825      -0.07998    0.468127
gamma_Age_NACompensationComplexityCosts                 0.118157     0.02413     4.89654   4.877e-07     0.04711       2.50824    0.006067
gamma_Education_NACompensationComplexityCosts          -0.191671     0.09337    -2.05276    0.020048     0.17476      -1.09678    0.136370
gamma_Income_NACompensationComplexityCosts             -0.337857     0.06649    -5.08118   1.875e-07     0.14541      -2.32349    0.010076
gamma_CheapTalk_NACompensationComplexityCosts           0.143784     0.06269     2.29346    0.010911     0.13247       1.08541    0.138870
sigma_NACompensationComplexityCosts                     1.314919     0.04745    27.71063    0.000000     0.07124      18.45762    0.000000
gamma_Gender_NACompensationIrrelevance                  0.182947     0.07660     2.38849    0.008459     0.11992       1.52562    0.063552
gamma_Age_NACompensationIrrelevance                     0.189262     0.03245     5.83180   2.742e-09     0.05392       3.51006  2.2400e-04
gamma_Education_NACompensationIrrelevance              -0.318228     0.12436    -2.55885    0.005251     0.21065      -1.51069    0.065434
gamma_Income_NACompensationIrrelevance                 -0.334290     0.08273    -4.04092   2.662e-05     0.13634      -2.45192    0.007105
gamma_CheapTalk_NACompensationIrrelevance               0.241079     0.07817     3.08399    0.001021     0.13091       1.84157    0.032769
sigma_NACompensationIrrelevance                         1.475163     0.06363    23.18444    0.000000     0.11745      12.55998    0.000000


Summary of class allocation for LC model component LC_model:
         Mean prob.
Class_1      0.2288
Class_2      0.4438
Class_3      0.3274
With dual response (=with free choices); cutoff at 7

Code: Select all

Model run using Apollo for R, version 0.2.5 on Windows by
www.ApolloChoiceModelling.com

Model name                       : ICLV_LC_3Classes_DR1_CutOff7_SO2000
Model description                : Latent class model on panel data (classical estimation)
Model run at                     : 2021-05-21 12:19:55
Estimation method                : bfgs
Model diagnosis                  : successful convergence 
Number of individuals            : 1034
Number of rows in database       : 31020
Number of modelled outcomes      : 24816
               NACount_r1_NACount: 1034
               NACount_r2_NACount: 1034
               NACount_r3_NACount: 1034
               NACount_r4_NACount: 1034
               NACount_r5_NACount: 1034
               NACount_r6_NACount: 1034
         NADuration_r1_NADuration: 1034
         NADuration_r2_NADuration: 1034
         NADuration_r3_NADuration: 1034
         NADuration_r4_NADuration: 1034
         NADuration_r5_NADuration: 1034
         NADuration_r6_NADuration: 1034
             NAPeriod_r1_NAPeriod: 1034
             NAPeriod_r2_NAPeriod: 1034
             NAPeriod_r3_NAPeriod: 1034
             NAPeriod_r4_NAPeriod: 1034
             NAPeriod_r5_NAPeriod: 1034
             NAPeriod_r6_NAPeriod: 1034
       NACompensation_r1_NACompen: 1034
       NACompensation_r2_NACompen: 1034
       NACompensation_r3_NACompen: 1034
       NACompensation_r4_NACompen: 1034
       NACompensation_r5_NACompen: 1034
       NACompensation_r6_NACompen: 1034
                         LC_model: 0

Number of cores used             :  27 
Number of inter-individual draws : 2000 (sobolOwen)

LL(start)                        : -59900.83
LL(0, whole model)               : Not applicable
LL(final, whole model)           : -57920.55
Rho-square (0)                   : Not applicable
Adj.Rho-square (0)               : Not applicable
AIC                              :  116073.1 
BIC                              :  117014.9 

LL(0,indic_NACount_NACount_r1)   : Not applicable
LL(final,indic_NACount_NACount_r1): -1975.785
LL(0,indic_NACount_NACount_r2)   : Not applicable
LL(final,indic_NACount_NACount_r2): -1958.468
LL(0,indic_NACount_NACount_r3)   : Not applicable
LL(final,indic_NACount_NACount_r3): -1983.238
LL(0,indic_NACount_NACount_r4)   : Not applicable
LL(final,indic_NACount_NACount_r4): -1903
LL(0,indic_NACount_NACount_r5)   : Not applicable
LL(final,indic_NACount_NACount_r5): -2146.783
LL(0,indic_NACount_NACount_r6)   : Not applicable
LL(final,indic_NACount_NACount_r6): -2176.588
LL(0,indic_NADuration_NADuration_r1): Not applicable
LL(final,indic_NADuration_NADuration_r1): -1890.278
LL(0,indic_NADuration_NADuration_r2): Not applicable
LL(final,indic_NADuration_NADuration_r2): -1884.213
LL(0,indic_NADuration_NADuration_r3): Not applicable
LL(final,indic_NADuration_NADuration_r3): -1863.396
LL(0,indic_NADuration_NADuration_r4): Not applicable
LL(final,indic_NADuration_NADuration_r4): -1815.61
LL(0,indic_NADuration_NADuration_r5): Not applicable
LL(final,indic_NADuration_NADuration_r5): -2082.642
LL(0,indic_NADuration_NADuration_r6): Not applicable
LL(final,indic_NADuration_NADuration_r6): -2098.623
LL(0,indic_NAPeriod_NAPeriod_r1) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r1): -1813.855
LL(0,indic_NAPeriod_NAPeriod_r2) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r2): -1802.174
LL(0,indic_NAPeriod_NAPeriod_r3) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r3): -1732.784
LL(0,indic_NAPeriod_NAPeriod_r4) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r4): -1727.8
LL(0,indic_NAPeriod_NAPeriod_r5) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r5): -1841.899
LL(0,indic_NAPeriod_NAPeriod_r6) : Not applicable
LL(final,indic_NAPeriod_NAPeriod_r6): -1808.057
LL(0,indic_NACompensation_NACompensation_r1): Not applicable
LL(final,indic_NACompensation_NACompensation_r1): -1908.035
LL(0,indic_NACompensation_NACompensation_r2): Not applicable
LL(final,indic_NACompensation_NACompensation_r2): -1891.925
LL(0,indic_NACompensation_NACompensation_r3): Not applicable
LL(final,indic_NACompensation_NACompensation_r3): -1975.475
LL(0,indic_NACompensation_NACompensation_r4): Not applicable
LL(final,indic_NACompensation_NACompensation_r4): -1858.619
LL(0,indic_NACompensation_NACompensation_r5): Not applicable
LL(final,indic_NACompensation_NACompensation_r5): -2132.253
LL(0,indic_NACompensation_NACompensation_r6): Not applicable
LL(final,indic_NACompensation_NACompensation_r6): -2143.708
LL(0,Measurement_model)          : Not applicable
LL(final,Measurement_model)      : -41637.2
LL(0,LC_model)                   : -22232.15
LL(final,LC_model)               : -16376.83

Estimated parameters             :  116
Time taken (hh:mm:ss)            :  195:15:41.03 
     pre-estimation              :  00:24:14.59 
     estimation                  :  82:34:9.74 
     post-estimation             :  112:17:16.7 
Iterations                       :  179  
Min abs eigenvalue of Hessian    :  0.00069 

Estimates:
                                                        Estimate        s.e.   t.rat.(0)  p(1-sided)    Rob.s.e. Rob.t.rat.(0)  p(1-sided)
b_asc_1                                                  0.03462    0.024706      1.4014    0.080543    0.026393        1.3119    0.094781
b_asc_2                                                  0.06231    0.024807      2.5117    0.006007    0.026337        2.3658    0.008995
b_asc_3                                                  0.00000          NA          NA          NA          NA            NA          NA
delta_A                                                  0.00000          NA          NA          NA          NA            NA          NA
gamma_A_NACount                                          0.00000          NA          NA          NA          NA            NA          NA
gamma_A_NADuration                                       0.00000          NA          NA          NA          NA            NA          NA
gamma_A_NAPeriod                                         0.00000          NA          NA          NA          NA            NA          NA
gamma_A_NACompensation                                   0.00000          NA          NA          NA          NA            NA          NA
delta_B                                                  0.45401    0.146268      3.1039  9.5481e-04    0.303098        1.4979    0.067082
gamma_B_NACount                                         -0.94694    0.161717     -5.8555   2.378e-09    0.224996       -4.2087   1.284e-05
gamma_B_NADuration                                   -8.7083e-04    0.004435     -0.1963    0.422174    0.005000       -0.1741    0.430874
gamma_B_NAPeriod                                        -0.53049    0.200711     -2.6431    0.004108    0.334064       -1.5880    0.056143
gamma_B_NACompensation                                   0.07685    0.054910      1.3995    0.080828    0.058475        1.3142    0.094390
delta_C                                                  0.82617    0.165721      4.9853   3.093e-07    0.408576        2.0221    0.021584
gamma_C_NACount                                         -0.33367    0.146696     -2.2746    0.011465    0.199534       -1.6723    0.047236
gamma_C_NADuration                                      -0.01190    0.018996     -0.6266    0.265467    0.006419       -1.8543    0.031851
gamma_C_NAPeriod                                        -0.49810    0.129219     -3.8547   5.794e-05    0.144664       -3.4431  2.8753e-04
gamma_C_NACompensation                                   0.20889    0.130837      1.5966    0.055179    0.153572        1.3602    0.086881
A_b_DR_asc_0                                             0.00000          NA          NA          NA          NA            NA          NA
A_b_DR_asc_1                                            -5.15376    0.271159    -19.0064    0.000000    0.581184       -8.8677    0.000000
A_b_Quota_Count                                         -0.12242    0.026384     -4.6400   1.742e-06    0.059333       -2.0633    0.019540
A_b_Quota_Max_Duration                                  -0.08544    0.031206     -2.7381    0.003090    0.074366       -1.1490    0.125284
A_b_Quota_Period_midmorning                             -0.48241    0.102390     -4.7114   1.230e-06    0.244644       -1.9719    0.024312
A_b_Quota_Period_afternoon                              -0.54703    0.093955     -5.8223   2.903e-09    0.209994       -2.6050    0.004594
A_b_Quota_Period_evening                                 0.17527    0.094669      1.8514    0.032059    0.258637        0.6777    0.248997
A_b_Quota_Period_night                                   0.03783    0.084616      0.4471    0.327397    0.128438        0.2946    0.384165
A_b_Quota_Compensation                                   0.58486    0.048036     12.1752    0.000000    0.075151        7.7824   3.553e-15
B_b_DR_asc_0                                             0.00000          NA          NA          NA          NA            NA          NA
B_b_DR_asc_1                                            -0.35315    0.095742     -3.6885  1.1278e-04    0.148451       -2.3789    0.008683
B_b_Quota_Count                                         -0.12159    0.015171     -8.0144   5.551e-16    0.021538       -5.6452   8.249e-09
B_b_Quota_Max_Duration                                  -0.08804    0.017912     -4.9152   4.435e-07    0.024400       -3.6082  1.5417e-04
B_b_Quota_Period_midmorning                             -0.47463    0.055062     -8.6199    0.000000    0.082283       -5.7683   4.004e-09
B_b_Quota_Period_afternoon                              -0.80101    0.058941    -13.5900    0.000000    0.084185       -9.5149    0.000000
B_b_Quota_Period_evening                                -0.38274    0.050976     -7.5083   2.998e-14    0.078480       -4.8770   5.386e-07
B_b_Quota_Period_night                                   0.78696    0.050937     15.4496    0.000000    0.084878        9.2717    0.000000
B_b_Quota_Compensation                                   0.41022    0.023640     17.3524    0.000000    0.028202       14.5458    0.000000
C_b_DR_asc_0                                             0.00000          NA          NA          NA          NA            NA          NA
C_b_DR_asc_1                                            -3.91162    0.152347    -25.6756    0.000000    0.259224      -15.0897    0.000000
C_b_Quota_Count                                         -0.35380    0.020198    -17.5166    0.000000    0.034168      -10.3548    0.000000
C_b_Quota_Max_Duration                                  -0.36193    0.023221    -15.5865    0.000000    0.032750      -11.0512    0.000000
C_b_Quota_Period_midmorning                             -0.48021    0.074313     -6.4621   5.165e-11    0.169704       -2.8297    0.002329
C_b_Quota_Period_afternoon                              -1.02325    0.077043    -13.2815    0.000000    0.144708       -7.0712   7.683e-13
C_b_Quota_Period_evening                                -0.86115    0.073716    -11.6821    0.000000    0.125429       -6.8657   3.309e-12
C_b_Quota_Period_night                                   1.45638    0.081992     17.7626    0.000000    0.204269        7.1297   5.029e-13
C_b_Quota_Compensation                                   0.42142    0.033855     12.4479    0.000000    0.056810        7.4181   5.940e-14
lambda_NACountComplexityCosts_NACount                    1.00000          NA          NA          NA          NA            NA          NA
lambda_NACountIrrelevance_NACount                       -0.45148    0.105257     -4.2893   8.963e-06    0.126526       -3.5683  1.7968e-04
lambda_NADurationComplexityCosts_NADuration              1.00000          NA          NA          NA          NA            NA          NA
lambda_NADurationIrrelevance_NADuration                 23.97523   38.057312      0.6300    0.264355    6.559687        3.6549  1.2862e-04
lambda_NAPeriodComplexityCosts_NAPeriod                  1.00000          NA          NA          NA          NA            NA          NA
lambda_NAPeriodIrrelevance_NAPeriod                      0.15068    0.601840      0.2504    0.401154    1.076338        0.1400    0.444334
lambda_NACompensationComplexityCosts_NACompensation      1.00000          NA          NA          NA          NA            NA          NA
lambda_NACompensationIrrelevance_NACompensation          2.33587    1.789157      1.3056    0.095849    2.177775        1.0726    0.141726
sigma_NACount_r1                                         1.19913    0.031079     38.5826    0.000000    0.040289       29.7631    0.000000
sigma_NACount_r2                                         1.05365    0.030572     34.4644    0.000000    0.050205       20.9871    0.000000
sigma_NACount_r3                                         1.18319    0.032599     36.2949    0.000000    0.058402       20.2593    0.000000
sigma_NACount_r4                                         1.04535    0.028965     36.0904    0.000000    0.047775       21.8805    0.000000
sigma_NACount_r5                                         1.32717    0.049593     26.7611    0.000000    0.099897       13.2854    0.000000
sigma_NACount_r6                                         1.38894    0.051121     27.1699    0.000000    0.103138       13.4668    0.000000
sigma_NADuration_r1                                      1.04933    0.026930     38.9645    0.000000    0.050050       20.9658    0.000000
sigma_NADuration_r2                                      0.89409    0.025241     35.4219    0.000000    0.054621       16.3688    0.000000
sigma_NADuration_r3                                      0.85859    0.023695     36.2349    0.000000    0.044644       19.2319    0.000000
sigma_NADuration_r4                                      0.78196    0.023578     33.1650    0.000000    0.045060       17.3536    0.000000
sigma_NADuration_r5                                      1.10844    0.042031     26.3718    0.000000    0.078624       14.0979    0.000000
sigma_NADuration_r6                                      1.13683    0.039065     29.1007    0.000000    0.060655       18.7426    0.000000
sigma_NAPeriod_r1                                        0.96346    0.024394     39.4950    0.000000    0.049702       19.3848    0.000000
sigma_NAPeriod_r2                                        0.76138    0.022087     34.4722    0.000000    0.058736       12.9628    0.000000
sigma_NAPeriod_r3                                        0.72911    0.020360     35.8108    0.000000    0.050700       14.3807    0.000000
sigma_NAPeriod_r4                                        0.68403    0.021328     32.0724    0.000000    0.050014       13.6767    0.000000
sigma_NAPeriod_r5                                        1.28110    0.039188     32.6911    0.000000    0.086949       14.7340    0.000000
sigma_NAPeriod_r6                                        1.25178    0.036664     34.1416    0.000000    0.078436       15.9592    0.000000
sigma_NACompensation_r1                                  1.01042    0.027856     36.2725    0.000000    0.043906       23.0134    0.000000
sigma_NACompensation_r2                                  0.91070    0.028341     32.1339    0.000000    0.053795       16.9290    0.000000
sigma_NACompensation_r3                                  1.13340    0.029906     37.8987    0.000000    0.049507       22.8940    0.000000
sigma_NACompensation_r4                                  0.92255    0.026694     34.5604    0.000000    0.052650       17.5223    0.000000
sigma_NACompensation_r5                                  1.32521    0.048108     27.5464    0.000000    0.111062       11.9321    0.000000
sigma_NACompensation_r6                                  1.33830    0.049467     27.0543    0.000000    0.109963       12.1705    0.000000
zeta_NACountComplexityCosts_r1_NACount                   1.00000          NA          NA          NA          NA            NA          NA
zeta_NACountComplexityCosts_r2_NACount                   1.12638    0.052176     21.5878    0.000000    0.055027       20.4696    0.000000
zeta_NACountComplexityCosts_r3_NACount                   1.06591    0.055341     19.2607    0.000000    0.068501       15.5605    0.000000
zeta_NACountComplexityCosts_r4_NACount                   1.03694    0.050217     20.6493    0.000000    0.054701       18.9565    0.000000
zeta_NACountIrrelevance_r5_NACount                       1.00000          NA          NA          NA          NA            NA          NA
zeta_NACountIrrelevance_r6_NACount                       1.00740    0.047153     21.3646    0.000000    0.026696       37.7355    0.000000
zeta_NADurationComplexityCosts_r1_NADuration             1.00000          NA          NA          NA          NA            NA          NA
zeta_NADurationComplexityCosts_r2_NADuration             1.11595    0.044677     24.9782    0.000000    0.053309       20.9339    0.000000
zeta_NADurationComplexityCosts_r3_NADuration             1.10793    0.044659     24.8085    0.000000    0.056829       19.4958    0.000000
zeta_NADurationComplexityCosts_r4_NADuration             1.08277    0.043085     25.1310    0.000000    0.057291       18.8995    0.000000
zeta_NADurationIrrelevance_r5_NADuration                 1.00000          NA          NA          NA          NA            NA          NA
zeta_NADurationIrrelevance_r6_NADuration                 1.00399    0.039004     25.7409    0.000000    0.037280       26.9310    0.000000
zeta_NAPeriodComplexityCosts_r1_NAPeriod                 1.00000          NA          NA          NA          NA            NA          NA
zeta_NAPeriodComplexityCosts_r2_NAPeriod                 1.15714    0.045494     25.4352    0.000000    0.057634       20.0775    0.000000
zeta_NAPeriodComplexityCosts_r3_NAPeriod                 1.06547    0.042825     24.8797    0.000000    0.061131       17.4294    0.000000
zeta_NAPeriodComplexityCosts_r4_NAPeriod                 1.07301    0.042388     25.3139    0.000000    0.055772       19.2391    0.000000
zeta_NAPeriodIrrelevance_r5_NAPeriod                     1.00000          NA          NA          NA          NA            NA          NA
zeta_NAPeriodIrrelevance_r6_NAPeriod                     0.94147    0.081722     11.5204    0.000000    0.049233       19.1230    0.000000
zeta_NACompensationComplexityCosts_r1_NACompensation     1.00000          NA          NA          NA          NA            NA          NA
zeta_NACompensationComplexityCosts_r2_NACompensation     1.06335    0.042045     25.2909    0.000000    0.041860       25.4025    0.000000
zeta_NACompensationComplexityCosts_r3_NACompensation     1.02314    0.046296     22.1002    0.000000    0.047220       21.6676    0.000000
zeta_NACompensationComplexityCosts_r4_NACompensation     0.98704    0.040892     24.1375    0.000000    0.041161       23.9798    0.000000
zeta_NACompensationIrrelevance_r5_NACompensation         1.00000          NA          NA          NA          NA            NA          NA
zeta_NACompensationIrrelevance_r6_NACompensation         1.01713    0.046464     21.8906    0.000000    0.025628       39.6880    0.000000
gamma_Age_NACountComplexityCosts                         0.14989    0.023247      6.4477   5.678e-11    0.043876        3.4162  3.1750e-04
gamma_Education_NACountComplexityCosts                  -0.39293    0.086507     -4.5422   2.783e-06    0.156546       -2.5100    0.006036
gamma_ExistingApps_NACountComplexityCosts                0.04615    0.083990      0.5495    0.291322    0.168785        0.2735    0.392253
sigma_NACountComplexityCosts                             1.17713    0.050177     23.4594    0.000000    0.067207       17.5150    0.000000
gamma_Age_NACountIrrelevance                             0.18041    0.031705      5.6903   6.341e-09    0.047118        3.8289   6.436e-05
gamma_Education_NACountIrrelevance                      -0.75262    0.118963     -6.3265   1.254e-10    0.165512       -4.5472   2.718e-06
gamma_ExistingApps_NACountIrrelevance                    0.22735    0.109171      2.0825    0.018647    0.151989        1.4958    0.067347
sigma_NACountIrrelevance                                 1.44969    0.065055     22.2840    0.000000    0.119201       12.1617    0.000000
gamma_Age_NADurationComplexityCosts                      0.13014    0.020012      6.5032   3.932e-11    0.045369        2.8685    0.002062
gamma_Education_NADurationComplexityCosts               -0.35325    0.075174     -4.6991   1.307e-06    0.179528       -1.9676    0.024555
gamma_ExistingApps_NADurationComplexityCosts             0.05364    0.061807      0.8678    0.192739    0.101242        0.5298    0.298124
sigma_NADurationComplexityCosts                          1.24052    0.051905     23.8996    0.000000    0.122884       10.0950    0.000000
gamma_Age_NADurationIrrelevance                          0.17533    0.031784      5.5163   1.731e-08    0.054155        3.2376  6.0280e-04
gamma_Education_NADurationIrrelevance                   -0.62151    0.119048     -5.2207   8.914e-08    0.195963       -3.1716  7.5809e-04
gamma_ExistingApps_NADurationIrrelevance                 0.10487    0.116361      0.9012    0.183729    0.219697        0.4773    0.316560
sigma_NADurationIrrelevance                              1.53503    0.054946     27.9373    0.000000    0.084441       18.1787    0.000000
gamma_Age_NAPeriodComplexityCosts                        0.20019    0.024453      8.1867   1.110e-16    0.081546        2.4549    0.007046
gamma_Education_NAPeriodComplexityCosts                 -0.56400    0.087648     -6.4348   6.181e-11    0.275475       -2.0474    0.020311
gamma_ExistingApps_NAPeriodComplexityCosts               0.27920    0.079342      3.5189  2.1664e-04    0.203328        1.3731    0.084854
sigma_NAPeriodComplexityCosts                            1.21197    0.048377     25.0526    0.000000    0.115129       10.5271    0.000000
gamma_Age_NAPeriodIrrelevance                            0.09645    0.022315      4.3223   7.719e-06    0.030141        3.2000  6.8704e-04
gamma_Education_NAPeriodIrrelevance                     -0.61846    0.088854     -6.9604   1.697e-12    0.115459       -5.3566   4.241e-08
gamma_ExistingApps_NAPeriodIrrelevance                   0.08122    0.075548      1.0751    0.141160    0.105901        0.7670    0.221548
sigma_NAPeriodIrrelevance                               -0.67293    0.072207     -9.3194    0.000000    0.165972       -4.0545   2.512e-05
gamma_Gender_NACompensationComplexityCosts              -0.02283    0.064385     -0.3545    0.361465    0.140003       -0.1630    0.435240
gamma_Age_NACompensationComplexityCosts                  0.12013    0.023543      5.1024   1.677e-07    0.047580        2.5248    0.005788
gamma_Education_NACompensationComplexityCosts           -0.15170    0.091607     -1.6560    0.048860    0.170265       -0.8910    0.186472
gamma_Income_NACompensationComplexityCosts              -0.37621    0.066082     -5.6931   6.237e-09    0.138877       -2.7090    0.003375
gamma_CheapTalk_NACompensationComplexityCosts            0.14521    0.059725      2.4312    0.007524    0.124825        1.1633    0.122358
sigma_NACompensationComplexityCosts                      1.32738    0.047462     27.9674    0.000000    0.070112       18.9323    0.000000
gamma_Gender_NACompensationIrrelevance                   0.19015    0.077896      2.4411    0.007322    0.128971        1.4744    0.070192
gamma_Age_NACompensationIrrelevance                      0.19228    0.032689      5.8821   2.025e-09    0.057335        3.3536  3.9883e-04
gamma_Education_NACompensationIrrelevance               -0.28467    0.124692     -2.2830    0.011216    0.209088       -1.3615    0.086682
gamma_Income_NACompensationIrrelevance                  -0.35516    0.082948     -4.2818   9.271e-06    0.137231       -2.5881    0.004826
gamma_CheapTalk_NACompensationIrrelevance                0.22544    0.077896      2.8941    0.001901    0.128730        1.7513    0.039948
sigma_NACompensationIrrelevance                          1.43731    0.067503     21.2926    0.000000    0.141528       10.1556    0.000000


Summary of class allocation for LC model component LC_model:
         Mean prob.
Class_1      0.2315
Class_2      0.3252
Class_3      0.4433
With the exception of coefficient lambda_NADurationIrrelevance_NADuration, the results look plausible/normal to me.

Nico

Re: Latent Class Joint Model

Posted: 11 Jun 2021, 13:37
by stephanehess
Nico

the model specification looks fine to me. Did you also see how the results compare to simpler specifications? That is often a good way to ensure that everything is working as expected

Stephane

Re: Latent Class Joint Model

Posted: 16 Jun 2021, 08:37
by cybey
Good morning Stephane,

I have just compared the LC model with the LC-HC model (without the dual response part). The three classes A, B, and C of the two models are quite similar (in terms of the signs of the parameters and their absolute values), which may be a result of the gamma parameters in the LC-HC for class allocation not being significant:

Image

In contrast, when I estimate an HC-MIXL model and use the latent variables directly to explain the utility parameters, almost all are highly significant. For this reason, I tend to use the HC-MIXL model (e.g., with subsequent classification based on the importances), although the HC-LC model has advantages in terms of interpretation. What do you think?

That said, I still have another question for you, Stephane: In one publication you wrote that the same sociodemographic characteristics should be used to explain both the utility parameters and the latent variables, thus separating direct and indirect effects of sociodemographics. Is this also something you would do with the HC-LC model, i.e., to use the same sociodemographic characteristics for class allocation and the latent variables?

Nico

Re: Latent Class Joint Model

Posted: 18 Jun 2021, 11:22
by stephanehess
Nico

this is very much dataset dependent. In some studies, it will make sense to use the LV to explain class allocation, but if the LV is related more to heterogeneity in sensitivities to individual attributes, then including an attribute-specific interaction for the LV will make more sense. That seems to be the case for you here.

And yes, I would still include the same socios also in the class allocation.

Stephane

Re: Latent Class Joint Model

Posted: 18 Jun 2021, 14:21
by cybey
Perfect, thank you so much for your help!
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