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 : MNL_SP_WTP_space Model description : MNL model on mode choice SP data, in WTP space Model run at : 2025-09-19 11:36:33.797232 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -0.816606 reciprocal of condition number : 3.32466e-07 Number of individuals : 500 Number of rows in database : 7000 Number of modelled outcomes : 7000 Number of cores used : 1 Model without mixing LL(start) : -8196.02 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : -6706.94 LL(final) : -5598.9 Rho-squared vs equal shares : 0.3169 Adj.Rho-squared vs equal shares : 0.3155 Rho-squared vs observed shares : 0.1652 Adj.Rho-squared vs observed shares : 0.164 AIC : 11219.8 BIC : 11295.19 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:00:1.05 pre-estimation : 00:00:0.19 estimation : 00:00:0.16 post-estimation : 00:00:0.7 Iterations : 11 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_car 0.00000 NA NA NA NA asc_bus 0.06241 0.538550 0.1159 0.533037 0.1171 asc_air 0.23828 0.340124 0.7006 0.329272 0.7236 asc_rail -1.48137 0.327325 -4.5257 0.309844 -4.7810 wtp_tt_car 0.19746 0.010970 18.0006 0.011068 17.8407 wtp_tt_bus 0.29560 0.024965 11.8408 0.025314 11.6774 wtp_tt_air 0.33160 0.042851 7.7383 0.041592 7.9727 wtp_tt_rail 0.10833 0.028564 3.7924 0.027288 3.9697 wtp_access 0.39473 0.045270 8.7195 0.044973 8.7770 b_cost -0.05876 0.001487 -39.5176 0.001660 -35.3946 wtp_no_frills 0.00000 NA NA NA NA wtp_wifi -15.95678 0.897545 -17.7782 0.989345 -16.1286 wtp_food -6.97052 0.881668 -7.9061 0.889295 -7.8383 Overview of choices for MNL model component : car bus air rail Times available 5446.00 6314.00 5264.00 6118.00 Times chosen 1946.00 358.00 1522.00 3174.00 Percentage chosen overall 27.80 5.11 21.74 45.34 Percentage chosen when available 35.73 5.67 28.91 51.88 Classical covariance matrix: asc_bus asc_air asc_rail wtp_tt_car wtp_tt_bus wtp_tt_air wtp_tt_rail asc_bus 0.290036 0.033491 0.027795 -0.001543 0.012243 5.1094e-04 -2.8817e-04 asc_air 0.033491 0.115685 0.049672 -0.002523 -0.001047 0.010205 -4.4534e-04 asc_rail 0.027795 0.049672 0.107142 -0.002473 -9.2076e-04 2.9851e-04 0.007186 wtp_tt_car -0.001543 -0.002523 -0.002473 1.2034e-04 3.620e-05 -4.983e-05 -3.838e-05 wtp_tt_bus 0.012243 -0.001047 -9.2076e-04 3.620e-05 6.2325e-04 -4.556e-05 -4.663e-05 wtp_tt_air 5.1094e-04 0.010205 2.9851e-04 -4.983e-05 -4.556e-05 0.001836 -1.2815e-04 wtp_tt_rail -2.8817e-04 -4.4534e-04 0.007186 -3.838e-05 -4.663e-05 -1.2815e-04 8.1593e-04 wtp_access 9.6917e-04 0.008399 4.0577e-04 -1.970e-05 -3.649e-05 5.9457e-04 -2.2359e-04 b_cost 2.028e-05 -8.220e-05 -3.463e-05 3.229e-06 6.820e-06 -2.888e-06 -4.815e-06 wtp_wifi 6.1630e-04 0.061753 0.035229 -0.001513 -0.001736 0.001634 -8.9141e-04 wtp_food 0.001278 0.034251 0.029389 -6.6041e-04 -6.0850e-04 -1.5138e-04 -3.5736e-04 wtp_access b_cost wtp_wifi wtp_food asc_bus 9.6917e-04 2.028e-05 6.1630e-04 0.001278 asc_air 0.008399 -8.220e-05 0.061753 0.034251 asc_rail 4.0577e-04 -3.463e-05 0.035229 0.029389 wtp_tt_car -1.970e-05 3.229e-06 -0.001513 -6.6041e-04 wtp_tt_bus -3.649e-05 6.820e-06 -0.001736 -6.0850e-04 wtp_tt_air 5.9457e-04 -2.888e-06 0.001634 -1.5138e-04 wtp_tt_rail -2.2359e-04 -4.815e-06 -8.9141e-04 -3.5736e-04 wtp_access 0.002049 4.118e-06 -2.1028e-04 -5.0198e-04 b_cost 4.118e-06 2.211e-06 -2.8638e-04 -8.324e-05 wtp_wifi -2.1028e-04 -2.8638e-04 0.805587 0.426521 wtp_food -5.0198e-04 -8.324e-05 0.426521 0.777339 Robust covariance matrix: asc_bus asc_air asc_rail wtp_tt_car wtp_tt_bus wtp_tt_air wtp_tt_rail asc_bus 0.284129 0.025233 0.020214 -0.001353 0.012138 8.0849e-04 -7.2242e-04 asc_air 0.025233 0.108420 0.043448 -0.002318 -0.001137 0.008903 -0.001016 asc_rail 0.020214 0.043448 0.096003 -0.002195 -9.1285e-04 -4.3904e-04 0.006083 wtp_tt_car -0.001353 -0.002318 -0.002195 1.2250e-04 4.927e-05 -8.333e-06 -2.376e-06 wtp_tt_bus 0.012138 -0.001137 -9.1285e-04 4.927e-05 6.4081e-04 1.960e-05 -2.245e-05 wtp_tt_air 8.0849e-04 0.008903 -4.3904e-04 -8.333e-06 1.960e-05 0.001730 -1.2607e-04 wtp_tt_rail -7.2242e-04 -0.001016 0.006083 -2.376e-06 -2.245e-05 -1.2607e-04 7.4466e-04 wtp_access -9.6063e-04 0.008491 7.8189e-04 -3.323e-05 -1.2567e-04 4.9490e-04 -2.1977e-04 b_cost 4.522e-05 -8.022e-07 2.027e-05 3.028e-06 8.890e-06 3.821e-06 -2.547e-06 wtp_wifi 0.035251 0.031682 0.016253 -0.002125 -0.001303 -0.003962 -0.002961 wtp_food -0.016186 0.019644 0.026599 -0.001040 -0.001841 -0.003854 -9.9402e-04 wtp_access b_cost wtp_wifi wtp_food asc_bus -9.6063e-04 4.522e-05 0.035251 -0.016186 asc_air 0.008491 -8.022e-07 0.031682 0.019644 asc_rail 7.8189e-04 2.027e-05 0.016253 0.026599 wtp_tt_car -3.323e-05 3.028e-06 -0.002125 -0.001040 wtp_tt_bus -1.2567e-04 8.890e-06 -0.001303 -0.001841 wtp_tt_air 4.9490e-04 3.821e-06 -0.003962 -0.003854 wtp_tt_rail -2.1977e-04 -2.547e-06 -0.002961 -9.9402e-04 wtp_access 0.002023 8.936e-06 -7.3859e-04 -0.001540 b_cost 8.936e-06 2.756e-06 -5.5224e-04 -1.1525e-04 wtp_wifi -7.3859e-04 -5.5224e-04 0.978805 0.468936 wtp_food -0.001540 -1.1525e-04 0.468936 0.790846 Classical correlation matrix: asc_bus asc_air asc_rail wtp_tt_car wtp_tt_bus wtp_tt_air wtp_tt_rail asc_bus 1.000000 0.18284 0.15767 -0.26119 0.91058 0.022140 -0.01873 asc_air 0.182838 1.00000 0.44617 -0.67618 -0.12335 0.700199 -0.04584 asc_rail 0.157673 0.44617 1.00000 -0.68872 -0.11268 0.021282 0.76860 wtp_tt_car -0.261190 -0.67618 -0.68872 1.00000 0.13220 -0.105997 -0.12248 wtp_tt_bus 0.910581 -0.12335 -0.11268 0.13220 1.00000 -0.042586 -0.06539 wtp_tt_air 0.022140 0.70020 0.02128 -0.10600 -0.04259 1.000000 -0.10470 wtp_tt_rail -0.018732 -0.04584 0.76860 -0.12248 -0.06539 -0.104699 1.00000 wtp_access 0.039752 0.54545 0.02738 -0.03966 -0.03228 0.306496 -0.17291 b_cost 0.025330 -0.16254 -0.07115 0.19800 0.18373 -0.045326 -0.11338 wtp_wifi 0.001275 0.20229 0.11991 -0.15365 -0.07747 0.042486 -0.03477 wtp_food 0.002692 0.11422 0.10184 -0.06828 -0.02765 -0.004007 -0.01419 wtp_access b_cost wtp_wifi wtp_food asc_bus 0.039752 0.02533 0.001275 0.002692 asc_air 0.545450 -0.16254 0.202286 0.114218 asc_rail 0.027383 -0.07115 0.119912 0.101837 wtp_tt_car -0.039664 0.19800 -0.153645 -0.068282 wtp_tt_bus -0.032284 0.18373 -0.077468 -0.027646 wtp_tt_air 0.306496 -0.04533 0.042486 -0.004007 wtp_tt_rail -0.172911 -0.11338 -0.034769 -0.014190 wtp_access 1.000000 0.06118 -0.005175 -0.012577 b_cost 0.061185 1.00000 -0.214597 -0.063500 wtp_wifi -0.005175 -0.21460 1.000000 0.538988 wtp_food -0.012577 -0.06350 0.538988 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail wtp_tt_car wtp_tt_bus wtp_tt_air wtp_tt_rail asc_bus 1.00000 0.143765 0.12239 -0.229366 0.89956 0.03647 -0.049666 asc_air 0.14376 1.000000 0.42586 -0.636031 -0.13641 0.65007 -0.113049 asc_rail 0.12239 0.425861 1.00000 -0.640023 -0.11638 -0.03407 0.719490 wtp_tt_car -0.22937 -0.636031 -0.64002 1.000000 0.17584 -0.01810 -0.007865 wtp_tt_bus 0.89956 -0.136412 -0.11638 0.175836 1.00000 0.01861 -0.032501 wtp_tt_air 0.03647 0.650072 -0.03407 -0.018102 0.01861 1.00000 -0.111072 wtp_tt_rail -0.04967 -0.113049 0.71949 -0.007865 -0.03250 -0.11107 1.000000 wtp_access -0.04007 0.573357 0.05611 -0.066748 -0.11039 0.26457 -0.179078 b_cost 0.05110 -0.001468 0.03941 0.164790 0.21156 0.05534 -0.056217 wtp_wifi 0.06684 0.097256 0.05302 -0.194028 -0.05203 -0.09629 -0.109675 wtp_food -0.03415 0.067086 0.09653 -0.105709 -0.08176 -0.10419 -0.040961 wtp_access b_cost wtp_wifi wtp_food asc_bus -0.04007 0.051103 0.06684 -0.03415 asc_air 0.57336 -0.001468 0.09726 0.06709 asc_rail 0.05611 0.039408 0.05302 0.09653 wtp_tt_car -0.06675 0.164790 -0.19403 -0.10571 wtp_tt_bus -0.11039 0.211563 -0.05203 -0.08176 wtp_tt_air 0.26457 0.055344 -0.09629 -0.10419 wtp_tt_rail -0.17908 -0.056217 -0.10968 -0.04096 wtp_access 1.00000 0.119700 -0.01660 -0.03850 b_cost 0.11970 1.000000 -0.33625 -0.07807 wtp_wifi -0.01660 -0.336253 1.00000 0.53299 wtp_food -0.03850 -0.078067 0.53299 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.1815920 272 0.2158480 457 0.2243954 82 0.2251270 151 0.2385036 263 0.2422002 186 0.2425681 196 0.2428432 278 0.2514740 77 0.2541713 147 0.2563694 146 0.2608293 276 0.2617144 293 0.2647152 25 0.2674995 400 0.2683087 369 0.2688813 309 0.2704938 304 0.2708669 446 0.2711952 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "MNL model on mode choice SP data, in WTP space" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "MNL_SP_WTP_space" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" 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 asc_bus 0.06240912 asc_air 0.23827639 asc_rail 1.48137010 wtp_tt_car 0.19746405 wtp_tt_bus 0.29560344 wtp_tt_air 0.33159830 wtp_tt_rail 0.10832827 wtp_access 0.39472896 b_cost 0.05875594 wtp_wifi 15.95677813 wtp_food 6.97052401 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() ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant V = list() V[["car"]] = asc_car + b_cost * ( wtp_tt_car * time_car + cost_car ) V[["bus"]] = asc_bus + b_cost * ( wtp_tt_bus * time_bus + wtp_access * access_bus + cost_bus ) V[["air"]] = asc_air + b_cost * ( wtp_tt_air * time_air + wtp_access * access_air + cost_air + wtp_no_frills * ( service_air == 1 ) + wtp_wifi * ( service_air == 2 ) + wtp_food * ( service_air == 3 ) ) V[["rail"]] = asc_rail + b_cost * ( wtp_tt_rail * time_rail + wtp_access * access_rail + cost_rail + wtp_no_frills * ( service_rail == 1 ) + wtp_wifi * ( service_rail == 2 ) + wtp_food * ( service_rail == 3 ) ) ### Define settings for MNL model component mnl_settings = list( alternatives = c(car=1, bus=2, air=3, rail=4), avail = list(car=av_car, bus=av_bus, air=av_air, rail=av_rail), choiceVar = choice, utilities = V ) ### Compute probabilities using MNL model P[["model"]] = apollo_mnl(mnl_settings, functionality) ### Take product across observation for same individual P = apollo_panelProd(P, apollo_inputs, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }