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 : 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 : 2025-09-19 12:03:27.859272 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -1.103722 reciprocal of condition number : 3.95643e-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 : 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) : -1438.15 Rho-squared vs equal shares : 0.4058 Adj.Rho-squared vs equal shares : 0.4009 Rho-squared vs observed shares : 0.4058 Adj.Rho-squared vs observed shares : 0.4013 AIC : 2900.3 BIC : 2974.2 Estimated parameters : 12 Time taken (hh:mm:ss) : 00:13:27.76 pre-estimation : 00:01:4.35 estimation : 00:03:8.07 post-estimation : 00:09:15.34 Iterations : 23 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_1 -0.06281 0.07890 -0.7961 0.09206 -0.6823 asc_2 0.00000 NA NA NA NA mu_log_b_tc -2.58540 0.24147 -10.7070 0.28091 -9.2036 sigma_log_b_tc_inter 6.01816 0.92857 6.4811 0.90641 6.6396 mu_log_v_tt -1.37562 0.04864 -28.2816 0.05754 -23.9064 sigma_log_v_tt_inter -0.58667 0.03963 -14.8053 0.03338 -17.5748 sigma_log_v_tt_inter_2 0.02368 0.01945 1.2171 0.01173 2.0182 sigma_log_v_tt_intra 0.53996 0.02500 21.5993 0.02977 18.1349 mu_log_v_hw -2.20340 0.09089 -24.2436 0.16199 -13.6020 sigma_log_v_hw_inter -1.05285 0.07136 -14.7535 0.06968 -15.1095 sigma_log_v_hw_v_tt_inter -0.47387 0.07705 -6.1499 0.18051 -2.6252 v_ch 3.93243 0.37418 10.5094 0.87046 4.5177 gamma_vtt_business 2.35055 0.60485 3.8862 1.46632 1.6030 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 asc_1 0.006225 0.001401 mu_log_b_tc 0.001401 0.058306 sigma_log_b_tc_inter -0.007543 -0.157904 mu_log_v_tt 1.1582e-04 -0.002286 sigma_log_v_tt_inter -4.087e-05 -9.8645e-04 sigma_log_v_tt_inter_2 -4.025e-05 -1.7052e-04 sigma_log_v_tt_intra -7.152e-05 9.3324e-04 mu_log_v_hw 1.6281e-04 -0.004518 sigma_log_v_hw_inter 8.016e-05 5.7640e-04 sigma_log_v_hw_v_tt_inter 1.0780e-04 -0.004775 v_ch 7.9824e-04 -0.030366 gamma_vtt_business -7.8112e-04 0.039725 sigma_log_b_tc_inter mu_log_v_tt asc_1 -0.007543 1.1582e-04 mu_log_b_tc -0.157904 -0.002286 sigma_log_b_tc_inter 0.862239 -0.001421 mu_log_v_tt -0.001421 0.002366 sigma_log_v_tt_inter 0.001410 4.0972e-04 sigma_log_v_tt_inter_2 6.5737e-04 -2.7127e-04 sigma_log_v_tt_intra 0.002735 -8.7094e-04 mu_log_v_hw -0.016255 0.001312 sigma_log_v_hw_inter -0.013334 1.4973e-04 sigma_log_v_hw_v_tt_inter -0.010615 0.001349 v_ch -0.052268 0.007336 gamma_vtt_business 0.067283 -0.012889 sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -4.087e-05 -4.025e-05 mu_log_b_tc -9.8645e-04 -1.7052e-04 sigma_log_b_tc_inter 0.001410 6.5737e-04 mu_log_v_tt 4.0972e-04 -2.7127e-04 sigma_log_v_tt_inter 0.001570 6.1541e-04 sigma_log_v_tt_inter_2 6.1541e-04 3.7838e-04 sigma_log_v_tt_intra 1.605e-05 1.5334e-04 mu_log_v_hw -7.123e-05 -1.4756e-04 sigma_log_v_hw_inter -3.1748e-04 -1.6780e-04 sigma_log_v_hw_v_tt_inter 4.3662e-04 3.022e-05 v_ch 0.002239 3.1359e-04 gamma_vtt_business -0.003736 -3.2047e-04 sigma_log_v_tt_intra mu_log_v_hw asc_1 -7.152e-05 1.6281e-04 mu_log_b_tc 9.3324e-04 -0.004518 sigma_log_b_tc_inter 0.002735 -0.016255 mu_log_v_tt -8.7094e-04 0.001312 sigma_log_v_tt_inter 1.605e-05 -7.123e-05 sigma_log_v_tt_inter_2 1.5334e-04 -1.4756e-04 sigma_log_v_tt_intra 6.2495e-04 -7.0029e-04 mu_log_v_hw -7.0029e-04 0.008260 sigma_log_v_hw_inter -1.6920e-04 0.004293 sigma_log_v_hw_v_tt_inter -7.7553e-04 0.004473 v_ch -0.003888 0.024036 gamma_vtt_business 0.007339 -0.028123 sigma_log_v_hw_inter sigma_log_v_hw_v_tt_inter asc_1 8.016e-05 1.0780e-04 mu_log_b_tc 5.7640e-04 -0.004775 sigma_log_b_tc_inter -0.013334 -0.010615 mu_log_v_tt 1.4973e-04 0.001349 sigma_log_v_tt_inter -3.1748e-04 4.3662e-04 sigma_log_v_tt_inter_2 -1.6780e-04 3.022e-05 sigma_log_v_tt_intra -1.6920e-04 -7.7553e-04 mu_log_v_hw 0.004293 0.004473 sigma_log_v_hw_inter 0.005093 0.001391 sigma_log_v_hw_v_tt_inter 0.001391 0.005937 v_ch 0.004620 0.023572 gamma_vtt_business -0.004547 -0.041989 v_ch gamma_vtt_business asc_1 7.9824e-04 -7.8112e-04 mu_log_b_tc -0.030366 0.039725 sigma_log_b_tc_inter -0.052268 0.067283 mu_log_v_tt 0.007336 -0.012889 sigma_log_v_tt_inter 0.002239 -0.003736 sigma_log_v_tt_inter_2 3.1359e-04 -3.2047e-04 sigma_log_v_tt_intra -0.003888 0.007339 mu_log_v_hw 0.024036 -0.028123 sigma_log_v_hw_inter 0.004620 -0.004547 sigma_log_v_hw_v_tt_inter 0.023572 -0.041989 v_ch 0.140011 -0.184367 gamma_vtt_business -0.184367 0.365838 Robust covariance matrix: asc_1 mu_log_b_tc asc_1 0.008474 0.008035 mu_log_b_tc 0.008035 0.078912 sigma_log_b_tc_inter -0.024044 -0.079229 mu_log_v_tt -2.6645e-04 -0.009772 sigma_log_v_tt_inter -1.1647e-04 -0.004456 sigma_log_v_tt_inter_2 -2.141e-05 -0.001075 sigma_log_v_tt_intra 1.0752e-04 0.005260 mu_log_v_hw -7.4588e-04 -0.028363 sigma_log_v_hw_inter -1.4433e-04 -0.005466 sigma_log_v_hw_v_tt_inter -8.3120e-04 -0.034169 v_ch -0.004188 -0.169070 gamma_vtt_business 0.006624 0.278491 sigma_log_b_tc_inter mu_log_v_tt asc_1 -0.024044 -2.6645e-04 mu_log_b_tc -0.079229 -0.009772 sigma_log_b_tc_inter 0.821574 -0.012822 mu_log_v_tt -0.012822 0.003311 sigma_log_v_tt_inter -0.003101 0.001329 sigma_log_v_tt_inter_2 -3.0018e-04 1.8488e-04 sigma_log_v_tt_intra 0.008656 -0.001614 mu_log_v_hw -0.056056 0.007276 sigma_log_v_hw_inter -0.026145 0.001595 sigma_log_v_hw_v_tt_inter -0.055003 0.008579 v_ch -0.252147 0.042254 gamma_vtt_business 0.418551 -0.070030 sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -1.1647e-04 -2.141e-05 mu_log_b_tc -0.004456 -0.001075 sigma_log_b_tc_inter -0.003101 -3.0018e-04 mu_log_v_tt 0.001329 1.8488e-04 sigma_log_v_tt_inter 0.001114 3.3332e-04 sigma_log_v_tt_inter_2 3.3332e-04 1.3761e-04 sigma_log_v_tt_intra -5.4026e-04 -6.586e-05 mu_log_v_hw 0.002774 5.7006e-04 sigma_log_v_hw_inter 3.8827e-04 2.986e-05 sigma_log_v_hw_v_tt_inter 0.003459 7.8779e-04 v_ch 0.017710 0.004055 gamma_vtt_business -0.028045 -0.006342 sigma_log_v_tt_intra mu_log_v_hw asc_1 1.0752e-04 -7.4588e-04 mu_log_b_tc 0.005260 -0.028363 sigma_log_b_tc_inter 0.008656 -0.056056 mu_log_v_tt -0.001614 0.007276 sigma_log_v_tt_inter -5.4026e-04 0.002774 sigma_log_v_tt_inter_2 -6.586e-05 5.7006e-04 sigma_log_v_tt_intra 8.8653e-04 -0.004147 mu_log_v_hw -0.004147 0.026241 sigma_log_v_hw_inter -9.8394e-04 0.008707 sigma_log_v_hw_v_tt_inter -0.004945 0.027351 v_ch -0.023866 0.132409 gamma_vtt_business 0.040405 -0.213834 sigma_log_v_hw_inter sigma_log_v_hw_v_tt_inter asc_1 -1.4433e-04 -8.3120e-04 mu_log_b_tc -0.005466 -0.034169 sigma_log_b_tc_inter -0.026145 -0.055003 mu_log_v_tt 0.001595 0.008579 sigma_log_v_tt_inter 3.8827e-04 0.003459 sigma_log_v_tt_inter_2 2.986e-05 7.8779e-04 sigma_log_v_tt_intra -9.8394e-04 -0.004945 mu_log_v_hw 0.008707 0.027351 sigma_log_v_hw_inter 0.004855 0.006982 sigma_log_v_hw_v_tt_inter 0.006982 0.032583 v_ch 0.032183 0.155257 gamma_vtt_business -0.049203 -0.263290 v_ch gamma_vtt_business asc_1 -0.004188 0.006624 mu_log_b_tc -0.169070 0.278491 sigma_log_b_tc_inter -0.252147 0.418551 mu_log_v_tt 0.042254 -0.070030 sigma_log_v_tt_inter 0.017710 -0.028045 sigma_log_v_tt_inter_2 0.004055 -0.006342 sigma_log_v_tt_intra -0.023866 0.040405 mu_log_v_hw 0.132409 -0.213834 sigma_log_v_hw_inter 0.032183 -0.049203 sigma_log_v_hw_v_tt_inter 0.155257 -0.263290 v_ch 0.757695 -1.254375 gamma_vtt_business -1.254375 2.150092 Classical correlation matrix: asc_1 mu_log_b_tc asc_1 1.00000 0.07353 mu_log_b_tc 0.07353 1.00000 sigma_log_b_tc_inter -0.10296 -0.70424 mu_log_v_tt 0.03018 -0.19465 sigma_log_v_tt_inter -0.01307 -0.10310 sigma_log_v_tt_inter_2 -0.02622 -0.03630 sigma_log_v_tt_intra -0.03626 0.15460 mu_log_v_hw 0.02271 -0.20588 sigma_log_v_hw_inter 0.01424 0.03345 sigma_log_v_hw_v_tt_inter 0.01773 -0.25664 v_ch 0.02704 -0.33608 gamma_vtt_business -0.01637 0.27199 sigma_log_b_tc_inter mu_log_v_tt asc_1 -0.10296 0.03018 mu_log_b_tc -0.70424 -0.19465 sigma_log_b_tc_inter 1.00000 -0.03147 mu_log_v_tt -0.03147 1.00000 sigma_log_v_tt_inter 0.03832 0.21258 sigma_log_v_tt_inter_2 0.03639 -0.28671 sigma_log_v_tt_intra 0.11781 -0.71626 mu_log_v_hw -0.19261 0.29671 sigma_log_v_hw_inter -0.20122 0.04314 sigma_log_v_hw_v_tt_inter -0.14835 0.35989 v_ch -0.15043 0.40307 gamma_vtt_business 0.11980 -0.43809 sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -0.01307 -0.02622 mu_log_b_tc -0.10310 -0.03630 sigma_log_b_tc_inter 0.03832 0.03639 mu_log_v_tt 0.21258 -0.28671 sigma_log_v_tt_inter 1.00000 0.79841 sigma_log_v_tt_inter_2 0.79841 1.00000 sigma_log_v_tt_intra 0.01620 0.31534 mu_log_v_hw -0.01978 -0.08347 sigma_log_v_hw_inter -0.11227 -0.12088 sigma_log_v_hw_v_tt_inter 0.14300 0.02016 v_ch 0.15103 0.04308 gamma_vtt_business -0.15586 -0.02724 sigma_log_v_tt_intra mu_log_v_hw asc_1 -0.03626 0.02271 mu_log_b_tc 0.15460 -0.20588 sigma_log_b_tc_inter 0.11781 -0.19261 mu_log_v_tt -0.71626 0.29671 sigma_log_v_tt_inter 0.01620 -0.01978 sigma_log_v_tt_inter_2 0.31534 -0.08347 sigma_log_v_tt_intra 1.00000 -0.30822 mu_log_v_hw -0.30822 1.00000 sigma_log_v_hw_inter -0.09484 0.66185 sigma_log_v_hw_v_tt_inter -0.40261 0.63872 v_ch -0.41564 0.70678 gamma_vtt_business 0.48536 -0.51160 sigma_log_v_hw_inter sigma_log_v_hw_v_tt_inter asc_1 0.01424 0.01773 mu_log_b_tc 0.03345 -0.25664 sigma_log_b_tc_inter -0.20122 -0.14835 mu_log_v_tt 0.04314 0.35989 sigma_log_v_tt_inter -0.11227 0.14300 sigma_log_v_tt_inter_2 -0.12088 0.02016 sigma_log_v_tt_intra -0.09484 -0.40261 mu_log_v_hw 0.66185 0.63872 sigma_log_v_hw_inter 1.00000 0.25293 sigma_log_v_hw_v_tt_inter 0.25293 1.00000 v_ch 0.17303 0.81757 gamma_vtt_business -0.10533 -0.90095 v_ch gamma_vtt_business asc_1 0.02704 -0.01637 mu_log_b_tc -0.33608 0.27199 sigma_log_b_tc_inter -0.15043 0.11980 mu_log_v_tt 0.40307 -0.43809 sigma_log_v_tt_inter 0.15103 -0.15586 sigma_log_v_tt_inter_2 0.04308 -0.02724 sigma_log_v_tt_intra -0.41564 0.48536 mu_log_v_hw 0.70678 -0.51160 sigma_log_v_hw_inter 0.17303 -0.10533 sigma_log_v_hw_v_tt_inter 0.81757 -0.90095 v_ch 1.00000 -0.81462 gamma_vtt_business -0.81462 1.00000 Robust correlation matrix: asc_1 mu_log_b_tc asc_1 1.00000 0.3107 mu_log_b_tc 0.31073 1.0000 sigma_log_b_tc_inter -0.28816 -0.3112 mu_log_v_tt -0.05030 -0.6045 sigma_log_v_tt_inter -0.03790 -0.4752 sigma_log_v_tt_inter_2 -0.01982 -0.3261 sigma_log_v_tt_intra 0.03923 0.6289 mu_log_v_hw -0.05002 -0.6233 sigma_log_v_hw_inter -0.02250 -0.2793 sigma_log_v_hw_v_tt_inter -0.05002 -0.6738 v_ch -0.05227 -0.6914 gamma_vtt_business 0.04907 0.6761 sigma_log_b_tc_inter mu_log_v_tt asc_1 -0.28816 -0.05030 mu_log_b_tc -0.31116 -0.60453 sigma_log_b_tc_inter 1.00000 -0.24584 mu_log_v_tt -0.24584 1.00000 sigma_log_v_tt_inter -0.10248 0.69178 sigma_log_v_tt_inter_2 -0.02823 0.27390 sigma_log_v_tt_intra 0.32073 -0.94206 mu_log_v_hw -0.38177 0.78053 sigma_log_v_hw_inter -0.41395 0.39787 sigma_log_v_hw_v_tt_inter -0.33618 0.82596 v_ch -0.31958 0.84360 gamma_vtt_business 0.31492 -0.82999 sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 -0.03790 -0.01982 mu_log_b_tc -0.47517 -0.32608 sigma_log_b_tc_inter -0.10248 -0.02823 mu_log_v_tt 0.69178 0.27390 sigma_log_v_tt_inter 1.00000 0.85122 sigma_log_v_tt_inter_2 0.85122 1.00000 sigma_log_v_tt_intra -0.54357 -0.18855 mu_log_v_hw 0.51295 0.29999 sigma_log_v_hw_inter 0.16692 0.03653 sigma_log_v_hw_v_tt_inter 0.57408 0.37204 v_ch 0.60949 0.39712 gamma_vtt_business -0.57297 -0.36868 sigma_log_v_tt_intra mu_log_v_hw asc_1 0.03923 -0.05002 mu_log_b_tc 0.62892 -0.62330 sigma_log_b_tc_inter 0.32073 -0.38177 mu_log_v_tt -0.94206 0.78053 sigma_log_v_tt_inter -0.54357 0.51295 sigma_log_v_tt_inter_2 -0.18855 0.29999 sigma_log_v_tt_intra 1.00000 -0.85987 mu_log_v_hw -0.85987 1.00000 sigma_log_v_hw_inter -0.47425 0.77137 sigma_log_v_hw_v_tt_inter -0.92009 0.93538 v_ch -0.92085 0.93903 gamma_vtt_business 0.92546 -0.90024 sigma_log_v_hw_inter sigma_log_v_hw_v_tt_inter asc_1 -0.02250 -0.05002 mu_log_b_tc -0.27926 -0.67384 sigma_log_b_tc_inter -0.41395 -0.33618 mu_log_v_tt 0.39787 0.82596 sigma_log_v_tt_inter 0.16692 0.57408 sigma_log_v_tt_inter_2 0.03653 0.37204 sigma_log_v_tt_intra -0.47425 -0.92009 mu_log_v_hw 0.77137 0.93538 sigma_log_v_hw_inter 1.00000 0.55508 sigma_log_v_hw_v_tt_inter 0.55508 1.00000 v_ch 0.53060 0.98811 gamma_vtt_business -0.48156 -0.99474 v_ch gamma_vtt_business asc_1 -0.05227 0.04907 mu_log_b_tc -0.69143 0.67610 sigma_log_b_tc_inter -0.31958 0.31492 mu_log_v_tt 0.84360 -0.82999 sigma_log_v_tt_inter 0.60949 -0.57297 sigma_log_v_tt_inter_2 0.39712 -0.36868 sigma_log_v_tt_intra -0.92085 0.92546 mu_log_v_hw 0.93903 -0.90024 sigma_log_v_hw_inter 0.53060 -0.48156 sigma_log_v_hw_v_tt_inter 0.98811 -0.99474 v_ch 1.00000 -0.98277 gamma_vtt_business -0.98277 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 15174 0.3595049 23205 0.3617578 76862 0.3735043 16178 0.3800800 22580 0.3857141 14802 0.3867648 15056 0.3929565 22820 0.3945979 22278 0.3975361 16489 0.4031045 82613 0.4037590 18219 0.4053691 80546 0.4075846 17645 0.4137983 20063 0.4167660 14353 0.4168444 22961 0.4197493 21922 0.4214567 12534 0.4225289 16617 0.4294726 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Mixed logit model on Swiss route choice data, WTP space with correlated and flexible distributions, inter and intra-individual heterogeneity" indivID "ID" nCores "4" analyticGrad "TRUE" outputDirectory "output/" mixing "TRUE" debug "FALSE" modelName "MMNL_wtp_space_inter_intra" workInLogs "FALSE" seed "13" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad_manualSet "TRUE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian --------------------------------- Value asc_1 0.06280816 mu_log_b_tc 2.58540162 sigma_log_b_tc_inter 6.01815708 mu_log_v_tt 1.37562408 sigma_log_v_tt_inter 0.58666795 sigma_log_v_tt_inter_2 0.02367501 sigma_log_v_tt_intra 0.53996024 mu_log_v_hw 2.20339772 sigma_log_v_hw_inter 1.05284943 sigma_log_v_hw_v_tt_inter 0.47386636 v_ch 3.93242764 gamma_vtt_business 2.35054783 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) }