Model run by stephane.hess using Apollo 0.3.6 on R 4.5.1 for Darwin. Please acknowledge the use of Apollo by citing Hess & Palma (2019) DOI 10.1016/j.jocm.2019.100170 www.ApolloChoiceModelling.com Model name : LC_MMNL Model description : Latent class with continuous random parameters on Swiss route choice data Model run at : 2025-09-19 12:54:27.111012 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -6.107961 reciprocal of condition number : 5.28191e-05 Number of individuals : 388 Number of rows in database : 3492 Number of modelled outcomes : 3492 Number of cores used : 4 Number of inter-individual draws : 500 (halton) LL(start) : -2370.05 LL (whole model) at equal shares, LL(0) : -2420.47 LL (whole model) at observed shares, LL(C) : -2420.39 LL(final, whole model) : -1497.87 Rho-squared vs equal shares : 0.3812 Adj.Rho-squared vs equal shares : 0.3754 Rho-squared vs observed shares : 0.3811 Adj.Rho-squared vs observed shares : 0.3762 AIC : 3023.74 BIC : 3109.96 LL(0,Class_1) : -2420.47 LL(final,Class_1) : -1704.92 LL(0,Class_2) : -2420.47 LL(final,Class_2) : -2028.16 Estimated parameters : 14 Time taken (hh:mm:ss) : 00:01:5.18 pre-estimation : 00:00:7.58 estimation : 00:00:14.3 post-estimation : 00:00:43.3 Iterations : 25 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc1 -0.03015 0.052845 -0.5705 0.058601 -0.5145 asc2 0.00000 NA NA NA NA log_tt_a_mu -3.13439 0.207627 -15.0963 0.249298 -12.5729 log_tt_b_mu -1.59919 0.157053 -10.1825 0.231674 -6.9028 log_tt_a_sig 0.74595 0.145392 5.1306 0.139433 5.3499 log_tt_b_sig 0.57190 0.090383 6.3275 0.109002 5.2467 tc_a -0.08389 0.019637 -4.2718 0.017864 -4.6959 tc_b -0.81829 0.141382 -5.7878 0.317745 -2.5753 hw_a -0.04267 0.004030 -10.5888 0.008255 -5.1691 hw_b -0.05601 0.005594 -10.0118 0.008377 -6.6863 ch_a -0.70310 0.112427 -6.2539 0.231054 -3.0430 ch_b -2.94513 0.302290 -9.7427 0.347463 -8.4761 delta_a -0.34005 0.272101 -1.2497 0.396539 -0.8575 gamma_commute_a -0.11024 0.344940 -0.3196 0.396214 -0.2782 gamma_car_av_a 0.49175 0.293570 1.6751 0.330205 1.4892 delta_b 0.00000 NA NA NA NA gamma_commute_b 0.00000 NA NA NA NA gamma_car_av_b 0.00000 NA NA NA NA Summary of class allocation for model component : Mean prob. Class_1 0.4544 Class_2 0.5456 Overview of choices for MNL model component Class_1: alt1 alt2 Times available 3492.00 3492.00 Times chosen 1734.00 1758.00 Percentage chosen overall 49.66 50.34 Percentage chosen when available 49.66 50.34 Overview of choices for MNL model component Class_2: alt1 alt2 Times available 3492.00 3492.00 Times chosen 1734.00 1758.00 Percentage chosen overall 49.66 50.34 Percentage chosen when available 49.66 50.34 Classical covariance matrix: asc1 log_tt_a_mu log_tt_b_mu log_tt_a_sig log_tt_b_sig asc1 0.002793 7.507e-05 -5.681e-05 2.241e-05 4.173e-05 log_tt_a_mu 7.507e-05 0.043109 1.0474e-04 -0.014641 -8.6913e-04 log_tt_b_mu -5.681e-05 1.0474e-04 0.024666 0.002446 -0.005002 log_tt_a_sig 2.241e-05 -0.014641 0.002446 0.021139 -0.004617 log_tt_b_sig 4.173e-05 -8.6913e-04 -0.005002 -0.004617 0.008169 tc_a -2.054e-05 -0.002799 -4.4935e-04 6.8999e-04 1.1779e-04 tc_b -1.044e-05 -0.005888 -0.018260 -6.3643e-04 0.002850 hw_a -7.774e-07 -2.8933e-04 -1.0947e-04 9.300e-06 1.374e-05 hw_b 2.866e-06 2.0128e-04 -1.7996e-04 -1.502e-05 -4.341e-05 ch_a -4.717e-06 -0.008018 -0.008343 -3.4109e-04 0.001326 ch_b 4.8437e-04 -0.002346 -0.031435 -0.002751 0.002619 delta_a -1.2433e-04 0.011376 0.020631 0.002348 -0.004441 gamma_commute_a -7.748e-05 0.003060 0.002806 -0.001397 0.001636 gamma_car_av_a 1.770e-06 0.005615 -0.002679 -1.8213e-04 -0.001423 tc_a tc_b hw_a hw_b ch_a asc1 -2.054e-05 -1.044e-05 -7.774e-07 2.866e-06 -4.717e-06 log_tt_a_mu -0.002799 -0.005888 -2.8933e-04 2.0128e-04 -0.008018 log_tt_b_mu -4.4935e-04 -0.018260 -1.0947e-04 -1.7996e-04 -0.008343 log_tt_a_sig 6.8999e-04 -6.3643e-04 9.300e-06 -1.502e-05 -3.4109e-04 log_tt_b_sig 1.1779e-04 0.002850 1.374e-05 -4.341e-05 0.001326 tc_a 3.8562e-04 5.8676e-04 2.239e-05 -9.375e-06 7.6063e-04 tc_b 5.8676e-04 0.019989 1.9700e-04 9.356e-05 0.010112 hw_a 2.239e-05 1.9700e-04 1.624e-05 -8.392e-06 2.5706e-04 hw_b -9.375e-06 9.356e-05 -8.392e-06 3.130e-05 -1.2483e-04 ch_a 7.6063e-04 0.010112 2.5706e-04 -1.2483e-04 0.012640 ch_b 0.001265 0.024009 9.842e-05 5.0546e-04 0.013566 delta_a -0.001479 -0.022005 -3.0204e-04 1.920e-05 -0.018549 gamma_commute_a -4.5133e-04 -4.2219e-04 -1.8896e-04 1.8648e-04 -0.004910 gamma_car_av_a -1.2148e-04 -3.2388e-04 -1.1499e-04 2.3238e-04 -0.001451 ch_b delta_a gamma_commute_a gamma_car_av_a asc1 4.8437e-04 -1.2433e-04 -7.748e-05 1.770e-06 log_tt_a_mu -0.002346 0.011376 0.003060 0.005615 log_tt_b_mu -0.031435 0.020631 0.002806 -0.002679 log_tt_a_sig -0.002751 0.002348 -0.001397 -1.8213e-04 log_tt_b_sig 0.002619 -0.004441 0.001636 -0.001423 tc_a 0.001265 -0.001479 -4.5133e-04 -1.2148e-04 tc_b 0.024009 -0.022005 -4.2219e-04 -3.2388e-04 hw_a 9.842e-05 -3.0204e-04 -1.8896e-04 -1.1499e-04 hw_b 5.0546e-04 1.920e-05 1.8648e-04 2.3238e-04 ch_a 0.013566 -0.018549 -0.004910 -0.001451 ch_b 0.091379 -0.039849 -0.022157 0.010788 delta_a -0.039849 0.074039 -0.016505 -0.032490 gamma_commute_a -0.022157 -0.016505 0.118984 -0.005939 gamma_car_av_a 0.010788 -0.032490 -0.005939 0.086184 Robust covariance matrix: asc1 log_tt_a_mu log_tt_b_mu log_tt_a_sig log_tt_b_sig asc1 0.003434 0.001972 6.1611e-04 -1.7465e-04 -3.803e-05 log_tt_a_mu 0.001972 0.062149 0.024361 -0.012727 -0.002489 log_tt_b_mu 6.1611e-04 0.024361 0.053673 -2.1497e-04 -0.008642 log_tt_a_sig -1.7465e-04 -0.012727 -2.1497e-04 0.019441 -0.006345 log_tt_b_sig -3.803e-05 -0.002489 -0.008642 -0.006345 0.011881 tc_a -1.4876e-04 -0.003159 -0.001461 5.3861e-04 1.7588e-04 tc_b -0.001659 -0.049905 -0.064888 0.005644 0.005783 hw_a -7.333e-05 -0.001454 -0.001056 1.2854e-04 6.886e-05 hw_b 5.082e-05 0.001166 5.7825e-04 -9.994e-05 -1.1084e-04 ch_a -0.001391 -0.038057 -0.040305 0.002691 0.003522 ch_b 0.002280 0.002833 -0.038055 -0.005016 0.004844 delta_a 0.001600 0.046898 0.070622 -0.001877 -0.008112 gamma_commute_a 7.9616e-04 0.005653 -0.006624 -0.003126 0.005058 gamma_car_av_a -7.1059e-04 0.034719 0.012214 -1.2156e-04 -0.006121 tc_a tc_b hw_a hw_b ch_a asc1 -1.4876e-04 -0.001659 -7.333e-05 5.082e-05 -0.001391 log_tt_a_mu -0.003159 -0.049905 -0.001454 0.001166 -0.038057 log_tt_b_mu -0.001461 -0.064888 -0.001056 5.7825e-04 -0.040305 log_tt_a_sig 5.3861e-04 0.005644 1.2854e-04 -9.994e-05 0.002691 log_tt_b_sig 1.7588e-04 0.005783 6.886e-05 -1.1084e-04 0.003522 tc_a 3.1912e-04 0.002425 7.864e-05 -6.560e-05 0.001995 tc_b 0.002425 0.100962 0.001868 -0.001210 0.063395 hw_a 7.864e-05 0.001868 6.815e-05 -4.748e-05 0.001591 hw_b -6.560e-05 -0.001210 -4.748e-05 7.017e-05 -0.001179 ch_a 0.001995 0.063395 0.001591 -0.001179 0.053386 ch_b 9.2202e-04 0.022181 3.1765e-04 3.131e-05 0.022461 delta_a -0.002610 -0.100836 -0.001947 0.001362 -0.075483 gamma_commute_a -0.001298 0.016251 -5.8094e-04 7.6419e-04 -0.006094 gamma_car_av_a -0.001580 -0.031805 -0.001126 0.001112 -0.023786 ch_b delta_a gamma_commute_a gamma_car_av_a asc1 0.002280 0.001600 7.9616e-04 -7.1059e-04 log_tt_a_mu 0.002833 0.046898 0.005653 0.034719 log_tt_b_mu -0.038055 0.070622 -0.006624 0.012214 log_tt_a_sig -0.005016 -0.001877 -0.003126 -1.2156e-04 log_tt_b_sig 0.004844 -0.008112 0.005058 -0.006121 tc_a 9.2202e-04 -0.002610 -0.001298 -0.001580 tc_b 0.022181 -0.100836 0.016251 -0.031805 hw_a 3.1765e-04 -0.001947 -5.8094e-04 -0.001126 hw_b 3.131e-05 0.001362 7.6419e-04 0.001112 ch_a 0.022461 -0.075483 -0.006094 -0.023786 ch_b 0.120731 -0.055284 -0.046242 0.023796 delta_a -0.055284 0.157243 -0.020675 -0.004564 gamma_commute_a -0.046242 -0.020675 0.156985 -0.009704 gamma_car_av_a 0.023796 -0.004564 -0.009704 0.109036 Classical correlation matrix: asc1 log_tt_a_mu log_tt_b_mu log_tt_a_sig log_tt_b_sig asc1 1.000000 0.006842 -0.006845 0.002917 0.008736 log_tt_a_mu 0.006842 1.000000 0.003212 -0.485011 -0.046314 log_tt_b_mu -0.006845 0.003212 1.000000 0.107102 -0.352346 log_tt_a_sig 0.002917 -0.485011 0.107102 1.000000 -0.351371 log_tt_b_sig 0.008736 -0.046314 -0.352346 -0.351371 1.000000 tc_a -0.019795 -0.686615 -0.145700 0.241670 0.066363 tc_b -0.001397 -0.200586 -0.822351 -0.030961 0.223064 hw_a -0.003650 -0.345792 -0.172963 0.015873 0.037736 hw_b 0.009694 0.173283 -0.204824 -0.018470 -0.085860 ch_a -7.9400e-04 -0.343482 -0.472509 -0.020867 0.130459 ch_b 0.030322 -0.037371 -0.662121 -0.062602 0.095852 delta_a -0.008646 0.201368 0.482766 0.059362 -0.180585 gamma_commute_a -0.004250 0.042726 0.051792 -0.027855 0.052487 gamma_car_av_a 1.1411e-04 0.092113 -0.058107 -0.004267 -0.053640 tc_a tc_b hw_a hw_b ch_a asc1 -0.01980 -0.001397 -0.003650 0.009694 -7.9400e-04 log_tt_a_mu -0.68661 -0.200586 -0.345792 0.173283 -0.34348 log_tt_b_mu -0.14570 -0.822351 -0.172963 -0.204824 -0.47251 log_tt_a_sig 0.24167 -0.030961 0.015873 -0.018470 -0.02087 log_tt_b_sig 0.06636 0.223064 0.037736 -0.085860 0.13046 tc_a 1.00000 0.211342 0.282874 -0.085337 0.34453 tc_b 0.21134 1.000000 0.345763 0.118284 0.63618 hw_a 0.28287 0.345763 1.000000 -0.372215 0.56739 hw_b -0.08534 0.118284 -0.372215 1.000000 -0.19847 ch_a 0.34453 0.636180 0.567389 -0.198473 1.00000 ch_b 0.21318 0.561759 0.080791 0.298885 0.39918 delta_a -0.27686 -0.572001 -0.275451 0.012611 -0.60635 gamma_commute_a -0.06663 -0.008657 -0.135934 0.096632 -0.12660 gamma_car_av_a -0.02107 -0.007803 -0.097200 0.141491 -0.04397 ch_b delta_a gamma_commute_a gamma_car_av_a asc1 0.03032 -0.008646 -0.004250 1.1411e-04 log_tt_a_mu -0.03737 0.201368 0.042726 0.092113 log_tt_b_mu -0.66212 0.482766 0.051792 -0.058107 log_tt_a_sig -0.06260 0.059362 -0.027855 -0.004267 log_tt_b_sig 0.09585 -0.180585 0.052487 -0.053640 tc_a 0.21318 -0.276862 -0.066629 -0.021072 tc_b 0.56176 -0.572001 -0.008657 -0.007803 hw_a 0.08079 -0.275451 -0.135934 -0.097200 hw_b 0.29889 0.012611 0.096632 0.141491 ch_a 0.39918 -0.606346 -0.126600 -0.043973 ch_b 1.00000 -0.484464 -0.212488 0.121568 delta_a -0.48446 1.000000 -0.175852 -0.406729 gamma_commute_a -0.21249 -0.175852 1.000000 -0.058652 gamma_car_av_a 0.12157 -0.406729 -0.058652 1.000000 Robust correlation matrix: asc1 log_tt_a_mu log_tt_b_mu log_tt_a_sig log_tt_b_sig asc1 1.000000 0.13497 0.045381 -0.021374 -0.005953 log_tt_a_mu 0.134967 1.00000 0.421790 -0.366143 -0.091594 log_tt_b_mu 0.045381 0.42179 1.000000 -0.006655 -0.342232 log_tt_a_sig -0.021374 -0.36614 -0.006655 1.000000 -0.417458 log_tt_b_sig -0.005953 -0.09159 -0.342232 -0.417458 1.000000 tc_a -0.142100 -0.70939 -0.353001 0.216238 0.090323 tc_b -0.089085 -0.63001 -0.881477 0.127398 0.166979 hw_a -0.151592 -0.70645 -0.551925 0.111676 0.076522 hw_b 0.103523 0.55824 0.297959 -0.085566 -0.121387 ch_a -0.102753 -0.66069 -0.752953 0.083538 0.139848 ch_b 0.111958 0.03270 -0.472739 -0.103539 0.127887 delta_a 0.068847 0.47440 0.768739 -0.033951 -0.187669 gamma_commute_a 0.034290 0.05724 -0.072161 -0.056576 0.117126 gamma_car_av_a -0.036722 0.42176 0.159664 -0.002640 -0.170071 tc_a tc_b hw_a hw_b ch_a asc1 -0.14210 -0.08909 -0.15159 0.10352 -0.10275 log_tt_a_mu -0.70939 -0.63001 -0.70645 0.55824 -0.66069 log_tt_b_mu -0.35300 -0.88148 -0.55193 0.29796 -0.75295 log_tt_a_sig 0.21624 0.12740 0.11168 -0.08557 0.08354 log_tt_b_sig 0.09032 0.16698 0.07652 -0.12139 0.13985 tc_a 1.00000 0.42728 0.53322 -0.43838 0.48341 tc_b 0.42728 1.00000 0.71202 -0.45472 0.86350 hw_a 0.53322 0.71202 1.00000 -0.68665 0.83422 hw_b -0.43838 -0.45472 -0.68665 1.00000 -0.60917 ch_a 0.48341 0.86350 0.83422 -0.60917 1.00000 ch_b 0.14854 0.20090 0.11074 0.01076 0.27977 delta_a -0.36850 -0.80030 -0.59484 0.41008 -0.82386 gamma_commute_a -0.18343 0.12909 -0.17761 0.23024 -0.06656 gamma_car_av_a -0.26789 -0.30313 -0.41310 0.40183 -0.31176 ch_b delta_a gamma_commute_a gamma_car_av_a asc1 0.11196 0.06885 0.03429 -0.036722 log_tt_a_mu 0.03270 0.47440 0.05724 0.421761 log_tt_b_mu -0.47274 0.76874 -0.07216 0.159664 log_tt_a_sig -0.10354 -0.03395 -0.05658 -0.002640 log_tt_b_sig 0.12789 -0.18767 0.11713 -0.170071 tc_a 0.14854 -0.36850 -0.18343 -0.267890 tc_b 0.20090 -0.80030 0.12909 -0.303131 hw_a 0.11074 -0.59484 -0.17761 -0.413097 hw_b 0.01076 0.41008 0.23024 0.401830 ch_a 0.27977 -0.82386 -0.06656 -0.311757 ch_b 1.00000 -0.40124 -0.33589 0.207405 delta_a -0.40124 1.00000 -0.13160 -0.034856 gamma_commute_a -0.33589 -0.13160 1.00000 -0.074172 gamma_car_av_a 0.20741 -0.03486 -0.07417 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 22580 0.2765765 23205 0.2985798 16489 0.3092563 14802 0.3161355 22961 0.3232602 15174 0.3275266 76862 0.3551667 20100 0.3571509 16178 0.3591877 22278 0.3626430 18219 0.3714968 21623 0.3797078 13863 0.3862454 25041 0.3922504 16617 0.3926943 82613 0.3965016 22820 0.3970021 15056 0.4039123 24627 0.4081025 12534 0.4134810 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Latent class with continuous random parameters on Swiss route choice data" indivID "ID" nCores "4" outputDirectory "output/" mixing "TRUE" debug "FALSE" modelName "LC_MMNL" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian --------------------------------- Value asc1 0.03014885 log_tt_a_mu 3.13439209 log_tt_b_mu 1.59919173 log_tt_a_sig 0.74594598 log_tt_b_sig 0.57190318 tc_a 0.08388729 tc_b 0.81829012 hw_a 0.04267168 hw_b 0.05601039 ch_a 0.70310212 ch_b 2.94512978 delta_a 0.34005083 gamma_commute_a 0.11023515 gamma_car_av_a 0.49174913 apollo_randCoeff ------------------ function(apollo_beta, apollo_inputs){ randcoeff = list() randcoeff[["tt_a"]] = -exp(log_tt_a_mu + log_tt_a_sig*draws_tt) randcoeff[["tt_b"]] = -exp(log_tt_b_mu + log_tt_b_sig*draws_tt) return(randcoeff) } apollo_lcPars --------------- function(apollo_beta, apollo_inputs){ lcpars = list() lcpars[["tt"]] = list(tt_a, tt_b) lcpars[["tc"]] = list(tc_a, tc_b) lcpars[["hw"]] = list(hw_a, hw_b) lcpars[["ch"]] = list(ch_a, ch_b) V=list() V[["class_a"]] = delta_a + gamma_commute_a*commute + gamma_car_av_a*car_availability V[["class_b"]] = delta_b + gamma_commute_b*commute + gamma_car_av_b*car_availability classAlloc_settings = list( classes = c(class_a=1, class_b=2), utilities = V ) lcpars[["pi_values"]] = apollo_classAlloc(classAlloc_settings) return(lcpars) } 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 settings for MNL model component that are generic across classes mnl_settings = list( alternatives = c(alt1=1, alt2=2), avail = list(alt1=1, alt2=1), choiceVar = choice ) ### Loop over classes for(s in 1:2){ ### Compute class-specific utilities V=list() V[["alt1"]] = asc1 + tc[[s]]*tc1 + tt[[s]]*tt1 + hw[[s]]*hw1 + ch[[s]]*ch1 V[["alt2"]] = asc2 + tc[[s]]*tc2 + tt[[s]]*tt2 + hw[[s]]*hw2 + ch[[s]]*ch2 mnl_settings$utilities = V ### Compute within-class choice probabilities using MNL model P[[paste0("Class_",s)]] = apollo_mnl(mnl_settings, functionality) ### Take product across observation for same individual P[[paste0("Class_",s)]] = apollo_panelProd(P[[paste0("Class_",s)]], apollo_inputs ,functionality) ### Average across inter-individual draws within classes P[[paste0("Class_",s)]] = apollo_avgInterDraws(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) }