Model run by stephane.hess using Apollo 0.2.8 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : MMNL_wtp_space_inter_intra Model description : Mixed logit model on Swiss route choice data, WTP space with correlated and flexible distributions, inter and intra-individual heterogeneity Model run at : 2022-10-08 15:11:39 Estimation method : bfgs Model diagnosis : successful convergence 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 : 100 (halton) Number of intra-individual draws : 100 (mlhs) LL(start) : -2406.92 LL at equal shares, LL(0) : -2420.47 LL at observed shares, LL(C) : -2420.39 LL(final) : -1440.26 Rho-squared vs equal shares : 0.405 Adj.Rho-squared vs equal shares : 0.4 Rho-squared vs observed shares : 0.4049 Adj.Rho-squared vs observed shares : 0.4 AIC : 2904.53 BIC : 2978.43 Estimated parameters : 12 Time taken (hh:mm:ss) : 02:24:46.14 pre-estimation : 00:10:7.81 estimation : 00:52:17.07 post-estimation : 01:22:21.26 Iterations : 51 Min abs eigenvalue of Hessian : 1.59218 Unconstrained optimisation. These outputs have had the scaling used in estimation applied to them. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_1 -0.05709 0.07609 -0.7503 0.08853 -0.6449 asc_2 0.00000 NA NA NA NA mu_log_b_tc -2.57197 0.23103 -11.1328 0.23601 -10.8978 sigma_log_b_tc_inter 5.49614 0.77215 7.1179 0.71355 7.7025 mu_log_v_tt -1.35352 0.05816 -23.2729 0.05314 -25.4697 sigma_log_v_tt_inter 0.61372 0.04681 13.1101 0.03978 15.4281 sigma_log_v_tt_inter_2 0.02520 0.02783 0.9057 0.01940 1.2989 sigma_log_v_tt_intra 0.52126 0.03525 14.7884 0.02345 22.2296 mu_log_v_hw -2.16214 0.09042 -23.9135 0.10806 -20.0079 sigma_log_v_hw_inter -0.92596 0.06590 -14.0508 0.05987 -15.4656 sigma_log_v_hw_v_tt_inter 0.44123 0.05899 7.4799 0.04643 9.5028 v_ch 4.10056 0.31643 12.9587 0.40924 10.0200 gamma_vtt_business 2.33967 0.20141 11.6165 0.14487 16.1498 Overview of choices for MNL model component : 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: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 0.005790 0.001039 -0.004477 mu_log_b_tc 0.001039 0.053374 -0.133603 sigma_log_b_tc_inter -0.004477 -0.133603 0.596220 mu_log_v_tt 7.718e-05 -0.002040 0.001714 sigma_log_v_tt_inter 1.1216e-04 0.001354 -0.003393 sigma_log_v_tt_inter_2 -7.350e-05 -1.7940e-04 0.001050 sigma_log_v_tt_intra -5.064e-05 7.6657e-04 0.001281 mu_log_v_hw 1.1421e-04 -0.005610 -0.001378 sigma_log_v_hw_inter 1.1188e-04 -5.5719e-04 -0.002779 sigma_log_v_hw_v_tt_inter -1.4253e-04 8.1611e-04 0.002034 v_ch 6.780e-05 -0.029610 0.012288 gamma_vtt_business -1.0340e-04 -0.001392 -0.002440 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 7.718e-05 1.1216e-04 -7.350e-05 mu_log_b_tc -0.002040 0.001354 -1.7940e-04 sigma_log_b_tc_inter 0.001714 -0.003393 0.001050 mu_log_v_tt 0.003382 -3.5206e-04 -6.7123e-04 sigma_log_v_tt_inter -3.5206e-04 0.002191 -9.9860e-04 sigma_log_v_tt_inter_2 -6.7123e-04 -9.9860e-04 7.7428e-04 sigma_log_v_tt_intra -0.001014 5.140e-05 1.1627e-04 mu_log_v_hw 9.7550e-04 -4.4446e-04 4.289e-05 sigma_log_v_hw_inter 7.8819e-04 1.6502e-04 -3.0079e-04 sigma_log_v_hw_v_tt_inter -7.9105e-04 -4.4397e-04 6.0680e-04 v_ch 0.003700 -0.001831 -5.119e-05 gamma_vtt_business -0.006149 5.2916e-04 0.001371 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 -5.064e-05 1.1421e-04 1.1188e-04 mu_log_b_tc 7.6657e-04 -0.005610 -5.5719e-04 sigma_log_b_tc_inter 0.001281 -0.001378 -0.002779 mu_log_v_tt -0.001014 9.7550e-04 7.8819e-04 sigma_log_v_tt_inter 5.140e-05 -4.4446e-04 1.6502e-04 sigma_log_v_tt_inter_2 1.1627e-04 4.289e-05 -3.0079e-04 sigma_log_v_tt_intra 0.001242 -5.6540e-04 -3.6934e-04 mu_log_v_hw -5.6540e-04 0.008175 0.003532 sigma_log_v_hw_inter -3.6934e-04 0.003532 0.004343 sigma_log_v_hw_v_tt_inter -3.3766e-04 -0.001158 -0.001396 v_ch -4.6345e-04 0.017329 0.002356 gamma_vtt_business 8.6414e-04 8.5926e-04 -0.004072 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 -1.4253e-04 6.780e-05 -1.0340e-04 mu_log_b_tc 8.1611e-04 -0.029610 -0.001392 sigma_log_b_tc_inter 0.002034 0.012288 -0.002440 mu_log_v_tt -7.9105e-04 0.003700 -0.006149 sigma_log_v_tt_inter -4.4397e-04 -0.001831 5.2916e-04 sigma_log_v_tt_inter_2 6.0680e-04 -5.119e-05 0.001371 sigma_log_v_tt_intra -3.3766e-04 -4.6345e-04 8.6414e-04 mu_log_v_hw -0.001158 0.017329 8.5926e-04 sigma_log_v_hw_inter -0.001396 0.002356 -0.004072 sigma_log_v_hw_v_tt_inter 0.003480 -0.005783 0.003310 v_ch -0.005783 0.100129 0.006836 gamma_vtt_business 0.003310 0.006836 0.040566 Robust covariance matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 0.007838 0.006549 -0.017523 mu_log_b_tc 0.006549 0.055699 -0.122179 sigma_log_b_tc_inter -0.017523 -0.122179 0.509152 mu_log_v_tt -3.0188e-04 -0.003807 0.004857 sigma_log_v_tt_inter 1.9115e-04 0.003870 -0.007199 sigma_log_v_tt_inter_2 -4.791e-06 -9.4093e-04 0.002339 sigma_log_v_tt_intra 5.108e-05 0.001031 -9.4139e-04 mu_log_v_hw -7.6915e-04 -0.013169 0.011056 sigma_log_v_hw_inter -3.0519e-04 -0.003042 -3.4868e-04 sigma_log_v_hw_v_tt_inter 2.7931e-04 0.003047 -8.1683e-04 v_ch -0.004047 -0.059059 0.068318 gamma_vtt_business 5.5464e-04 -0.001365 -8.286e-05 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -3.0188e-04 1.9115e-04 -4.791e-06 mu_log_b_tc -0.003807 0.003870 -9.4093e-04 sigma_log_b_tc_inter 0.004857 -0.007199 0.002339 mu_log_v_tt 0.002824 -8.5221e-04 -2.7539e-04 sigma_log_v_tt_inter -8.5221e-04 0.001582 -5.8235e-04 sigma_log_v_tt_inter_2 -2.7539e-04 -5.8235e-04 3.7647e-04 sigma_log_v_tt_intra -7.4499e-04 1.3506e-04 6.927e-05 mu_log_v_hw 0.001984 -0.002135 5.6769e-04 sigma_log_v_hw_inter 0.001114 -3.2158e-04 -1.3598e-04 sigma_log_v_hw_v_tt_inter -0.001296 2.7840e-04 2.6320e-04 v_ch 0.008839 -0.009115 0.002109 gamma_vtt_business -0.004763 2.9896e-04 0.001124 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 5.108e-05 -7.6915e-04 -3.0519e-04 mu_log_b_tc 0.001031 -0.013169 -0.003042 sigma_log_b_tc_inter -9.4139e-04 0.011056 -3.4868e-04 mu_log_v_tt -7.4499e-04 0.001984 0.001114 sigma_log_v_tt_inter 1.3506e-04 -0.002135 -3.2158e-04 sigma_log_v_tt_inter_2 6.927e-05 5.6769e-04 -1.3598e-04 sigma_log_v_tt_intra 5.4985e-04 -7.6346e-04 -3.6357e-04 mu_log_v_hw -7.6346e-04 0.011678 0.004598 sigma_log_v_hw_inter -3.6357e-04 0.004598 0.003585 sigma_log_v_hw_v_tt_inter -3.702e-05 -0.002566 -0.001692 v_ch -0.001559 0.035241 0.008792 gamma_vtt_business 5.1862e-04 6.3057e-04 -0.003562 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 2.7931e-04 -0.004047 5.5464e-04 mu_log_b_tc 0.003047 -0.059059 -0.001365 sigma_log_b_tc_inter -8.1683e-04 0.068318 -8.286e-05 mu_log_v_tt -0.001296 0.008839 -0.004763 sigma_log_v_tt_inter 2.7840e-04 -0.009115 2.9896e-04 sigma_log_v_tt_inter_2 2.6320e-04 0.002109 0.001124 sigma_log_v_tt_intra -3.702e-05 -0.001559 5.1862e-04 mu_log_v_hw -0.002566 0.035241 6.3057e-04 sigma_log_v_hw_inter -0.001692 0.008792 -0.003562 sigma_log_v_hw_v_tt_inter 0.002156 -0.010421 0.003324 v_ch -0.010421 0.167475 0.004761 gamma_vtt_business 0.003324 0.004761 0.020988 Classical correlation matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 1.000000 0.05912 -0.07620 mu_log_b_tc 0.059123 1.00000 -0.74894 sigma_log_b_tc_inter -0.076203 -0.74894 1.00000 mu_log_v_tt 0.017439 -0.15184 0.03817 sigma_log_v_tt_inter 0.031486 0.12515 -0.09386 sigma_log_v_tt_inter_2 -0.034713 -0.02791 0.04885 sigma_log_v_tt_intra -0.018879 0.09414 0.04706 mu_log_v_hw 0.016600 -0.26856 -0.01974 sigma_log_v_hw_inter 0.022310 -0.03660 -0.05461 sigma_log_v_hw_v_tt_inter -0.031755 0.05988 0.04465 v_ch 0.002816 -0.40504 0.05029 gamma_vtt_business -0.006747 -0.02992 -0.01569 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 0.01744 0.03149 -0.034713 mu_log_b_tc -0.15184 0.12515 -0.027908 sigma_log_b_tc_inter 0.03817 -0.09386 0.048852 mu_log_v_tt 1.00000 -0.12931 -0.414772 sigma_log_v_tt_inter -0.12931 1.00000 -0.766620 sigma_log_v_tt_inter_2 -0.41477 -0.76662 1.000000 sigma_log_v_tt_intra -0.49485 0.03115 0.118544 mu_log_v_hw 0.18551 -0.10501 0.017048 sigma_log_v_hw_inter 0.20565 0.05349 -0.164027 sigma_log_v_hw_v_tt_inter -0.23058 -0.16078 0.369681 v_ch 0.20105 -0.12363 -0.005814 gamma_vtt_business -0.52496 0.05612 0.244588 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 -0.01888 0.01660 0.02231 mu_log_b_tc 0.09414 -0.26856 -0.03660 sigma_log_b_tc_inter 0.04706 -0.01974 -0.05461 mu_log_v_tt -0.49485 0.18551 0.20565 sigma_log_v_tt_inter 0.03115 -0.10501 0.05349 sigma_log_v_tt_inter_2 0.11854 0.01705 -0.16403 sigma_log_v_tt_intra 1.00000 -0.17741 -0.15900 mu_log_v_hw -0.17741 1.00000 0.59274 sigma_log_v_hw_inter -0.15900 0.59274 1.00000 sigma_log_v_hw_v_tt_inter -0.16240 -0.21717 -0.35903 v_ch -0.04155 0.60571 0.11299 gamma_vtt_business 0.12172 0.04719 -0.30682 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 -0.03175 0.002816 -0.006747 mu_log_b_tc 0.05988 -0.405041 -0.029922 sigma_log_b_tc_inter 0.04465 0.050292 -0.015691 mu_log_v_tt -0.23058 0.201049 -0.524962 sigma_log_v_tt_inter -0.16078 -0.123629 0.056123 sigma_log_v_tt_inter_2 0.36968 -0.005814 0.244588 sigma_log_v_tt_intra -0.16240 -0.041551 0.121722 mu_log_v_hw -0.21717 0.605710 0.047185 sigma_log_v_hw_inter -0.35903 0.112991 -0.306824 sigma_log_v_hw_v_tt_inter 1.00000 -0.309802 0.278584 v_ch -0.30980 1.000000 0.107265 gamma_vtt_business 0.27858 0.107265 1.000000 Robust correlation matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 1.000000 0.31344 -0.277373 mu_log_b_tc 0.313441 1.00000 -0.725517 sigma_log_b_tc_inter -0.277373 -0.72552 1.000000 mu_log_v_tt -0.064164 -0.30357 0.128096 sigma_log_v_tt_inter 0.054275 0.41224 -0.253626 sigma_log_v_tt_inter_2 -0.002789 -0.20548 0.168916 sigma_log_v_tt_intra 0.024606 0.18636 -0.056263 mu_log_v_hw -0.080393 -0.51633 0.143385 sigma_log_v_hw_inter -0.057576 -0.21528 -0.008162 sigma_log_v_hw_v_tt_inter 0.067946 0.27806 -0.024654 v_ch -0.111687 -0.61149 0.233958 gamma_vtt_business 0.043243 -0.03993 -8.0157e-04 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -0.06416 0.05427 -0.002789 mu_log_b_tc -0.30357 0.41224 -0.205477 sigma_log_b_tc_inter 0.12810 -0.25363 0.168916 mu_log_v_tt 1.00000 -0.40313 -0.267082 sigma_log_v_tt_inter -0.40313 1.00000 -0.754494 sigma_log_v_tt_inter_2 -0.26708 -0.75449 1.000000 sigma_log_v_tt_intra -0.59784 0.14479 0.152246 mu_log_v_hw 0.34546 -0.49672 0.270744 sigma_log_v_hw_inter 0.35019 -0.13502 -0.117056 sigma_log_v_hw_v_tt_inter -0.52504 0.15073 0.292150 v_ch 0.40644 -0.55995 0.265588 gamma_vtt_business -0.61869 0.05188 0.399903 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 0.02461 -0.08039 -0.057576 mu_log_b_tc 0.18636 -0.51633 -0.215284 sigma_log_b_tc_inter -0.05626 0.14338 -0.008162 mu_log_v_tt -0.59784 0.34546 0.350187 sigma_log_v_tt_inter 0.14479 -0.49672 -0.135022 sigma_log_v_tt_inter_2 0.15225 0.27074 -0.117056 sigma_log_v_tt_intra 1.00000 -0.30129 -0.258963 mu_log_v_hw -0.30129 1.00000 0.710620 sigma_log_v_hw_inter -0.25896 0.71062 1.000000 sigma_log_v_hw_v_tt_inter -0.03400 -0.51142 -0.608743 v_ch -0.16245 0.79688 0.358831 gamma_vtt_business 0.15266 0.04028 -0.410704 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 0.06795 -0.11169 0.04324 mu_log_b_tc 0.27806 -0.61149 -0.03993 sigma_log_b_tc_inter -0.02465 0.23396 -8.0157e-04 mu_log_v_tt -0.52504 0.40644 -0.61869 sigma_log_v_tt_inter 0.15073 -0.55995 0.05188 sigma_log_v_tt_inter_2 0.29215 0.26559 0.39990 sigma_log_v_tt_intra -0.03400 -0.16245 0.15266 mu_log_v_hw -0.51142 0.79688 0.04028 sigma_log_v_hw_inter -0.60874 0.35883 -0.41070 sigma_log_v_hw_v_tt_inter 1.00000 -0.54842 0.49418 v_ch -0.54842 1.00000 0.08030 gamma_vtt_business 0.49418 0.08030 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 23205 0.3600248 15174 0.3607308 76862 0.3780058 16178 0.3784190 14802 0.3856454 22580 0.3870223 22820 0.3935983 15056 0.3973955 22278 0.4008852 82613 0.4020978 16489 0.4026935 18219 0.4059001 80546 0.4061969 20323 0.4114278 20063 0.4151377 22961 0.4183713 14353 0.4200617 17645 0.4219161 21922 0.4231423 12534 0.4253272 Changes in parameter estimates from starting values: Initial Estimate Difference asc_1 0.000 -0.05709 -0.05709 asc_2 0.000 0.00000 0.00000 mu_log_b_tc -3.000 -2.57197 0.42803 sigma_log_b_tc_inter 0.000 5.49614 5.49614 mu_log_v_tt -3.000 -1.35352 1.64648 sigma_log_v_tt_inter 0.000 0.61372 0.61372 sigma_log_v_tt_inter_2 0.000 0.02520 0.02520 sigma_log_v_tt_intra 0.000 0.52126 0.52126 mu_log_v_hw -3.000 -2.16214 0.83786 sigma_log_v_hw_inter 0.000 -0.92596 -0.92596 sigma_log_v_hw_v_tt_inter 0.000 0.44123 0.44123 v_ch 0.000 4.10056 4.10056 gamma_vtt_business 0.000 2.33967 2.33967 Settings and functions used in model definition: apollo_control -------------- Value modelName "MMNL_wtp_space_inter_intra" modelDescr "Mixed logit model on Swiss route choice data, WTP space with correlated and flexible distributions, inter and intra-individual heterogeneity" indivID "ID" mixing "TRUE" nCores "4" analyticGrad "TRUE" outputDirectory "output/" debug "FALSE" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad_manualSet "TRUE" Hessian routines attempted -------------- numerical jacobian of LL analytical gradient Scaling in estimation -------------- Value asc_1 0.05709482 mu_log_b_tc 2.57197408 sigma_log_b_tc_inter 5.49613341 mu_log_v_tt 1.35351085 sigma_log_v_tt_inter 0.61372119 sigma_log_v_tt_inter_2 0.02520204 sigma_log_v_tt_intra 0.52126332 mu_log_v_hw 2.16215829 sigma_log_v_hw_inter 0.92595472 sigma_log_v_hw_v_tt_inter 0.44123031 v_ch 4.10055185 gamma_vtt_business 2.33967051 Scaling used in computing Hessian -------------- Value asc_1 0.05709482 mu_log_b_tc 2.57197258 sigma_log_b_tc_inter 5.49613811 mu_log_v_tt 1.35352078 sigma_log_v_tt_inter 0.61371891 sigma_log_v_tt_inter_2 0.02520203 sigma_log_v_tt_intra 0.52126249 mu_log_v_hw 2.16214443 sigma_log_v_hw_inter 0.92595994 sigma_log_v_hw_v_tt_inter 0.44123070 v_ch 4.10055742 gamma_vtt_business 2.33967325 apollo_randCoeff ---------------- function(apollo_beta, apollo_inputs){ randcoeff = list() randcoeff[["b_tc"]] = -exp( mu_log_b_tc + sigma_log_b_tc_inter * draws_tc_inter ) randcoeff[["v_tt"]] = ( exp( mu_log_v_tt + sigma_log_v_tt_inter * draws_tt_inter + sigma_log_v_tt_inter_2 * draws_tt_inter ^ 2 + sigma_log_v_tt_intra * draws_tt_intra ) * ( gamma_vtt_business * business + ( 1 - business ) ) ) randcoeff[["v_hw"]] = exp( mu_log_v_hw + sigma_log_v_hw_inter * draws_hw_inter + sigma_log_v_hw_v_tt_inter * draws_tt_inter ) return(randcoeff) } apollo_probabilities -------------------- function(apollo_beta, apollo_inputs, functionality="estimate"){ ### Function initialisation: do not change the following three commands ### 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() ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant V = list() V[["alt1"]] = asc_1 + b_tc*(v_tt*tt1 + tc1 + v_hw*hw1 + v_ch*ch1) V[["alt2"]] = asc_2 + b_tc*(v_tt*tt2 + tc2 + v_hw*hw2 + v_ch*ch2) ### Define settings for MNL model component mnl_settings = list( alternatives = c(alt1=1, alt2=2), avail = list(alt1=1, alt2=1), choiceVar = choice, utilities = V ) ### Compute probabilities using MNL model P[["model"]] = apollo_mnl(mnl_settings, functionality) ### Average across intra-individual draws P = apollo_avgIntraDraws(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) }