Model run using Apollo for R, version 0.2.6 on Darwin by stephane.hess 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 : 2021-11-04 19:08:38 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 : 50 (halton) Number of intra-individual draws : 50 (mlhs) LL(start) : -2406.92 LL(0) : -2420.47 LL(C) : -2420.387 LL(final) : -1440.927 Rho-square (0) : 0.4047 Adj.Rho-square (0) : 0.3997 Rho-square (C) : 0.4047 Adj.Rho-square (C) : 0.3997 AIC : 2905.85 BIC : 2979.75 Estimated parameters : 12 Time taken (hh:mm:ss) : 00:25:50.33 pre-estimation : 00:02:14.99 estimation : 00:15:14.67 post-estimation : 00:08:20.67 Iterations : 86 Min abs eigenvalue of Hessian : 0.78487 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_1 -0.07875 0.079728 -0.9877 0.092858 -0.8481 asc_2 0.00000 NA NA NA NA mu_log_b_tc 3.68996 0.719739 5.1268 0.618523 5.9658 sigma_log_b_tc_inter -6.24878 0.875672 -7.1360 0.745521 -8.3818 mu_log_v_tt -1.37987 0.034290 -40.2407 0.024151 -57.1343 sigma_log_v_tt_inter 0.58903 0.017220 34.2057 0.008225 71.6174 sigma_log_v_tt_inter_2 0.07290 0.009095 8.0146 0.003095 23.5545 sigma_log_v_tt_intra -0.53578 0.019882 -26.9473 0.010158 -52.7457 mu_log_v_hw -2.28476 0.065159 -35.0644 0.051295 -44.5416 sigma_log_v_hw_inter -1.02125 0.047248 -21.6148 0.029825 -34.2410 sigma_log_v_hw_v_tt_inter 0.63548 0.031713 20.0384 0.017565 36.1786 v_ch 3.80049 0.181661 20.9208 0.146945 25.8633 gamma_vtt_business 2.30433 0.092465 24.9211 0.034776 66.2628 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 0.006357 -0.005544 0.006651 mu_log_b_tc -0.005544 0.518025 -0.619194 sigma_log_b_tc_inter 0.006651 -0.619194 0.766802 mu_log_v_tt 1.0054e-04 -0.002565 0.002064 sigma_log_v_tt_inter -2.023e-05 3.6979e-04 -2.8794e-04 sigma_log_v_tt_inter_2 -1.691e-05 3.6352e-04 -4.2306e-04 sigma_log_v_tt_intra 4.758e-05 -0.001347 0.001424 mu_log_v_hw 6.444e-05 -0.004017 0.002840 sigma_log_v_hw_inter 3.990e-05 -0.002952 0.003330 sigma_log_v_hw_v_tt_inter -5.092e-05 0.001566 -0.001395 v_ch 5.4183e-04 -0.007224 -0.001653 gamma_vtt_business 2.029e-05 6.5823e-04 -0.001808 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 1.0054e-04 -2.023e-05 -1.691e-05 mu_log_b_tc -0.002565 3.6979e-04 3.6352e-04 sigma_log_b_tc_inter 0.002064 -2.8794e-04 -4.2306e-04 mu_log_v_tt 0.001176 -2.6190e-04 -1.4240e-04 sigma_log_v_tt_inter -2.6190e-04 2.9654e-04 -1.954e-05 sigma_log_v_tt_inter_2 -1.4240e-04 -1.954e-05 8.273e-05 sigma_log_v_tt_intra 4.2429e-04 -1.4838e-04 -3.963e-05 mu_log_v_hw 3.2534e-04 7.673e-05 -2.537e-05 sigma_log_v_hw_inter -6.179e-05 -4.654e-06 3.250e-05 sigma_log_v_hw_v_tt_inter -3.2095e-04 1.3847e-04 1.5380e-04 v_ch 0.001988 -6.121e-05 2.152e-05 gamma_vtt_business -4.6862e-04 1.1568e-04 -1.665e-05 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 4.758e-05 6.444e-05 3.990e-05 mu_log_b_tc -0.001347 -0.004017 -0.002952 sigma_log_b_tc_inter 0.001424 0.002840 0.003330 mu_log_v_tt 4.2429e-04 3.2534e-04 -6.179e-05 sigma_log_v_tt_inter -1.4838e-04 7.673e-05 -4.654e-06 sigma_log_v_tt_inter_2 -3.963e-05 -2.537e-05 3.250e-05 sigma_log_v_tt_intra 3.9531e-04 -2.6575e-04 -2.2190e-04 mu_log_v_hw -2.6575e-04 0.004246 0.002028 sigma_log_v_hw_inter -2.2190e-04 0.002028 0.002232 sigma_log_v_hw_v_tt_inter -6.261e-05 -0.001010 -1.7513e-04 v_ch -2.7912e-04 0.004708 3.3861e-04 gamma_vtt_business -1.5624e-04 -2.5669e-04 -0.001135 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 -5.092e-05 5.4183e-04 2.029e-05 mu_log_b_tc 0.001566 -0.007224 6.5823e-04 sigma_log_b_tc_inter -0.001395 -0.001653 -0.001808 mu_log_v_tt -3.2095e-04 0.001988 -4.6862e-04 sigma_log_v_tt_inter 1.3847e-04 -6.121e-05 1.1568e-04 sigma_log_v_tt_inter_2 1.5380e-04 2.152e-05 -1.665e-05 sigma_log_v_tt_intra -6.261e-05 -2.7912e-04 -1.5624e-04 mu_log_v_hw -0.001010 0.004708 -2.5669e-04 sigma_log_v_hw_inter -1.7513e-04 3.3861e-04 -0.001135 sigma_log_v_hw_v_tt_inter 0.001006 -8.8207e-04 1.6878e-04 v_ch -8.8207e-04 0.033001 0.003401 gamma_vtt_business 1.6878e-04 0.003401 0.008550 Robust covariance matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 0.008623 -0.015390 0.021412 mu_log_b_tc -0.015390 0.382570 -0.452834 sigma_log_b_tc_inter 0.021412 -0.452834 0.555802 mu_log_v_tt 1.035e-05 -0.002103 0.001769 sigma_log_v_tt_inter -7.192e-06 4.7348e-04 -3.6645e-04 sigma_log_v_tt_inter_2 -9.981e-06 3.9263e-04 -4.4768e-04 sigma_log_v_tt_intra 4.571e-05 -0.001163 0.001335 mu_log_v_hw -1.5570e-04 -0.001030 -2.9746e-04 sigma_log_v_hw_inter 2.209e-05 -0.001662 0.001503 sigma_log_v_hw_v_tt_inter 3.414e-05 9.0606e-04 -6.4885e-04 v_ch -6.6468e-04 0.006710 -0.014194 gamma_vtt_business -4.207e-07 0.001348 -0.002060 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 1.035e-05 -7.192e-06 -9.981e-06 mu_log_b_tc -0.002103 4.7348e-04 3.9263e-04 sigma_log_b_tc_inter 0.001769 -3.6645e-04 -4.4768e-04 mu_log_v_tt 5.8328e-04 -1.6819e-04 -4.948e-05 sigma_log_v_tt_inter -1.6819e-04 6.765e-05 1.148e-05 sigma_log_v_tt_inter_2 -4.948e-05 1.148e-05 9.578e-06 sigma_log_v_tt_intra 1.8773e-04 -5.709e-05 -2.013e-05 mu_log_v_hw 2.9639e-04 -7.261e-05 -1.451e-05 sigma_log_v_hw_inter -2.330e-05 -4.596e-06 1.302e-05 sigma_log_v_hw_v_tt_inter -2.0163e-04 6.457e-05 2.892e-05 v_ch 0.002083 -5.3343e-04 -3.974e-05 gamma_vtt_business 9.995e-05 -1.751e-05 -9.854e-06 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 4.571e-05 -1.5570e-04 2.209e-05 mu_log_b_tc -0.001163 -0.001030 -0.001662 sigma_log_b_tc_inter 0.001335 -2.9746e-04 0.001503 mu_log_v_tt 1.8773e-04 2.9639e-04 -2.330e-05 sigma_log_v_tt_inter -5.709e-05 -7.261e-05 -4.596e-06 sigma_log_v_tt_inter_2 -2.013e-05 -1.451e-05 1.302e-05 sigma_log_v_tt_intra 1.0318e-04 -1.3384e-04 -1.2575e-04 mu_log_v_hw -1.3384e-04 0.002631 0.001277 sigma_log_v_hw_inter -1.2575e-04 0.001277 8.8955e-04 sigma_log_v_hw_v_tt_inter -1.856e-05 -7.4058e-04 -2.7889e-04 v_ch 1.2349e-04 0.003570 7.8671e-04 gamma_vtt_business 3.190e-05 -1.9249e-04 -4.1251e-04 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 3.414e-05 -6.6468e-04 -4.207e-07 mu_log_b_tc 9.0606e-04 0.006710 0.001348 sigma_log_b_tc_inter -6.4885e-04 -0.014194 -0.002060 mu_log_v_tt -2.0163e-04 0.002083 9.995e-05 sigma_log_v_tt_inter 6.457e-05 -5.3343e-04 -1.751e-05 sigma_log_v_tt_inter_2 2.892e-05 -3.974e-05 -9.854e-06 sigma_log_v_tt_intra -1.856e-05 1.2349e-04 3.190e-05 mu_log_v_hw -7.4058e-04 0.003570 -1.9249e-04 sigma_log_v_hw_inter -2.7889e-04 7.8671e-04 -4.1251e-04 sigma_log_v_hw_v_tt_inter 3.0853e-04 -9.7955e-04 3.632e-05 v_ch -9.7955e-04 0.021593 0.001827 gamma_vtt_business 3.632e-05 0.001827 0.001209 Classical correlation matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 1.000000 -0.096618 0.09526 mu_log_b_tc -0.096618 1.000000 -0.98245 sigma_log_b_tc_inter 0.095263 -0.982449 1.00000 mu_log_v_tt 0.036774 -0.103922 0.06875 sigma_log_v_tt_inter -0.014734 0.029836 -0.01910 sigma_log_v_tt_inter_2 -0.023320 0.055531 -0.05312 sigma_log_v_tt_intra 0.030016 -0.094136 0.08179 mu_log_v_hw 0.012404 -0.085652 0.04978 sigma_log_v_hw_inter 0.010592 -0.086796 0.08049 sigma_log_v_hw_v_tt_inter -0.020139 0.068588 -0.05022 v_ch 0.037410 -0.055248 -0.01039 gamma_vtt_business 0.002753 0.009891 -0.02233 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 0.03677 -0.014734 -0.02332 mu_log_b_tc -0.10392 0.029836 0.05553 sigma_log_b_tc_inter 0.06875 -0.019095 -0.05312 mu_log_v_tt 1.00000 -0.443539 -0.45657 sigma_log_v_tt_inter -0.44354 1.000000 -0.12473 sigma_log_v_tt_inter_2 -0.45657 -0.124726 1.00000 sigma_log_v_tt_intra 0.62234 -0.433382 -0.21915 mu_log_v_hw 0.14561 0.068384 -0.04281 sigma_log_v_hw_inter -0.03814 -0.005720 0.07562 sigma_log_v_hw_v_tt_inter -0.29514 0.253552 0.53321 v_ch 0.31914 -0.019567 0.01303 gamma_vtt_business -0.14780 0.072648 -0.01980 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 0.03002 0.01240 0.010592 mu_log_b_tc -0.09414 -0.08565 -0.086796 sigma_log_b_tc_inter 0.08179 0.04978 0.080491 mu_log_v_tt 0.62234 0.14561 -0.038138 sigma_log_v_tt_inter -0.43338 0.06838 -0.005720 sigma_log_v_tt_inter_2 -0.21915 -0.04281 0.075619 sigma_log_v_tt_intra 1.00000 -0.20513 -0.236221 mu_log_v_hw -0.20513 1.00000 0.658693 sigma_log_v_hw_inter -0.23622 0.65869 1.000000 sigma_log_v_hw_v_tt_inter -0.09930 -0.48863 -0.116878 v_ch -0.07728 0.39771 0.039451 gamma_vtt_business -0.08499 -0.04260 -0.259702 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 -0.02014 0.03741 0.002753 mu_log_b_tc 0.06859 -0.05525 0.009891 sigma_log_b_tc_inter -0.05022 -0.01039 -0.022329 mu_log_v_tt -0.29514 0.31914 -0.147799 sigma_log_v_tt_inter 0.25355 -0.01957 0.072648 sigma_log_v_tt_inter_2 0.53321 0.01303 -0.019798 sigma_log_v_tt_intra -0.09930 -0.07728 -0.084988 mu_log_v_hw -0.48863 0.39771 -0.042605 sigma_log_v_hw_inter -0.11688 0.03945 -0.259702 sigma_log_v_hw_v_tt_inter 1.00000 -0.15311 0.057559 v_ch -0.15311 1.00000 0.202468 gamma_vtt_business 0.05756 0.20247 1.000000 Robust correlation matrix: asc_1 mu_log_b_tc sigma_log_b_tc_inter asc_1 1.000000 -0.26796 0.309295 mu_log_b_tc -0.267955 1.00000 -0.982026 sigma_log_b_tc_inter 0.309295 -0.98203 1.000000 mu_log_v_tt 0.004615 -0.14075 0.098254 sigma_log_v_tt_inter -0.009417 0.09307 -0.059763 sigma_log_v_tt_inter_2 -0.034732 0.20512 -0.194032 sigma_log_v_tt_intra 0.048456 -0.18518 0.176318 mu_log_v_hw -0.032688 -0.03246 -0.007779 sigma_log_v_hw_inter 0.007976 -0.09011 0.067573 sigma_log_v_hw_v_tt_inter 0.020930 0.08340 -0.049549 v_ch -0.048713 0.07382 -0.129567 gamma_vtt_business -1.3027e-04 0.06268 -0.079449 mu_log_v_tt sigma_log_v_tt_inter sigma_log_v_tt_inter_2 asc_1 0.004615 -0.009417 -0.03473 mu_log_b_tc -0.140751 0.093073 0.20512 sigma_log_b_tc_inter 0.098254 -0.059763 -0.19403 mu_log_v_tt 1.000000 -0.846727 -0.66197 sigma_log_v_tt_inter -0.846727 1.000000 0.45111 sigma_log_v_tt_inter_2 -0.661971 0.451105 1.00000 sigma_log_v_tt_intra 0.765259 -0.683393 -0.64023 mu_log_v_hw 0.239246 -0.172105 -0.09138 sigma_log_v_hw_inter -0.032341 -0.018736 0.14105 sigma_log_v_hw_v_tt_inter -0.475290 0.446978 0.53200 v_ch 0.587070 -0.441367 -0.08739 gamma_vtt_business 0.119010 -0.061210 -0.09156 sigma_log_v_tt_intra mu_log_v_hw sigma_log_v_hw_inter asc_1 0.04846 -0.032688 0.007976 mu_log_b_tc -0.18518 -0.032465 -0.090108 sigma_log_b_tc_inter 0.17632 -0.007779 0.067573 mu_log_v_tt 0.76526 0.239246 -0.032341 sigma_log_v_tt_inter -0.68339 -0.172105 -0.018736 sigma_log_v_tt_inter_2 -0.64023 -0.091380 0.141046 sigma_log_v_tt_intra 1.00000 -0.256874 -0.415071 mu_log_v_hw -0.25687 1.000000 0.834860 sigma_log_v_hw_inter -0.41507 0.834860 1.000000 sigma_log_v_hw_v_tt_inter -0.10402 -0.821960 -0.532352 v_ch 0.08274 0.473681 0.179504 gamma_vtt_business 0.09029 -0.107907 -0.397716 sigma_log_v_hw_v_tt_inter v_ch gamma_vtt_business asc_1 0.02093 -0.04871 -1.3027e-04 mu_log_b_tc 0.08340 0.07382 0.06268 sigma_log_b_tc_inter -0.04955 -0.12957 -0.07945 mu_log_v_tt -0.47529 0.58707 0.11901 sigma_log_v_tt_inter 0.44698 -0.44137 -0.06121 sigma_log_v_tt_inter_2 0.53200 -0.08739 -0.09156 sigma_log_v_tt_intra -0.10402 0.08274 0.09029 mu_log_v_hw -0.82196 0.47368 -0.10791 sigma_log_v_hw_inter -0.53235 0.17950 -0.39772 sigma_log_v_hw_v_tt_inter 1.00000 -0.37951 0.05946 v_ch -0.37951 1.00000 0.35748 gamma_vtt_business 0.05946 0.35748 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 15174 0.3663412 23205 0.3680467 16178 0.3753270 76862 0.3789581 15056 0.3876963 22580 0.3902836 22820 0.3904880 80546 0.3910808 14802 0.3930404 20323 0.3959449 16489 0.3980594 22278 0.4020066 18219 0.4058422 20063 0.4082317 14353 0.4110310 82613 0.4128862 15489 0.4158176 17645 0.4170158 21922 0.4172146 12534 0.4207158 Changes in parameter estimates from starting values: Initial Estimate Difference asc_1 0.000 -0.07875 -0.07875 asc_2 0.000 0.00000 0.00000 mu_log_b_tc -3.000 3.68996 6.68996 sigma_log_b_tc_inter 0.000 -6.24878 -6.24878 mu_log_v_tt -3.000 -1.37987 1.62013 sigma_log_v_tt_inter 0.000 0.58903 0.58903 sigma_log_v_tt_inter_2 0.000 0.07290 0.07290 sigma_log_v_tt_intra 0.000 -0.53578 -0.53578 mu_log_v_hw -3.000 -2.28476 0.71524 sigma_log_v_hw_inter 0.000 -1.02125 -1.02125 sigma_log_v_hw_v_tt_inter 0.000 0.63548 0.63548 v_ch 0.000 3.80049 3.80049 gamma_vtt_business 0.000 2.30433 2.30433 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 0.07874885 mu_log_b_tc 3.68992345 sigma_log_b_tc_inter 6.24885922 mu_log_v_tt 1.37987765 sigma_log_v_tt_inter 0.58903942 sigma_log_v_tt_inter_2 0.07289609 sigma_log_v_tt_intra 0.53577862 mu_log_v_hw 2.28475790 sigma_log_v_hw_inter 1.02125114 sigma_log_v_hw_v_tt_inter 0.63547481 v_ch 3.80046308 gamma_vtt_business 2.30431151 Scaling used in computing Hessian -------------- Value asc_1 0.07874885 mu_log_b_tc 3.68995794 sigma_log_b_tc_inter 6.24877794 mu_log_v_tt 1.37986661 sigma_log_v_tt_inter 0.58903066 sigma_log_v_tt_inter_2 0.07289610 sigma_log_v_tt_intra 0.53577654 mu_log_v_hw 2.28475608 sigma_log_v_hw_inter 1.02124910 sigma_log_v_hw_v_tt_inter 0.63547931 v_ch 3.80048625 gamma_vtt_business 2.30433393 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) }