Model run by stephane.hess using Apollo 0.3.5 on R 4.4.0 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_covariates Model description : MNL model with socio-demographics on mode choice SP data Model run at : 2025-03-10 17:01:17.784179 Estimation method : bgw Model diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -2.818749 reciprocal of condition number : 2.9745e-08 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) : -5598.9 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : -6706.94 LL(final) : -4830.94 Rho-squared vs equal shares : 0.4106 Adj.Rho-squared vs equal shares : 0.4085 Rho-squared vs observed shares : 0.2797 Adj.Rho-squared vs observed shares : 0.2776 AIC : 9695.89 BIC : 9812.4 Estimated parameters : 17 Time taken (hh:mm:ss) : 00:00:1.96 pre-estimation : 00:00:0.32 estimation : 00:00:0.25 post-estimation : 00:00:1.4 Iterations : 8 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_car 0.000000 NA NA NA NA asc_bus 0.286354 0.582952 0.4912 0.549513 0.5211 asc_air -0.903377 0.373537 -2.4184 0.361570 -2.4985 asc_rail -2.092701 0.353360 -5.9223 0.351092 -5.9606 asc_bus_interaction_female 0.340193 0.132783 2.5620 0.145286 2.3415 asc_air_interaction_female 0.268174 0.091507 2.9307 0.095283 2.8145 asc_rail_interaction_female 0.189612 0.073759 2.5707 0.078168 2.4257 b_tt_car -0.013107 7.3440e-04 -17.8475 7.6776e-04 -17.0722 b_tt_bus -0.021265 0.001598 -13.3107 0.001518 -14.0090 b_tt_air -0.016578 0.002774 -5.9770 0.002671 -6.2074 b_tt_rail -0.007051 0.001811 -3.8929 0.001765 -3.9959 b_tt_interaction_business -0.006234 6.0074e-04 -10.3772 5.9078e-04 -10.5520 b_access -0.021152 0.002865 -7.3842 0.002706 -7.8156 b_cost -0.076188 0.002097 -36.3304 0.002095 -36.3623 b_cost_interaction_business 0.033379 0.002739 12.1847 0.002572 12.9786 cost_income_elast -0.613821 0.030094 -20.3970 0.030605 -20.0562 b_no_frills 0.000000 NA NA NA NA b_wifi 1.026711 0.056142 18.2877 0.057815 17.7587 b_food 0.422072 0.055027 7.6703 0.056464 7.4750 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 asc_bus_interaction_female asc_bus 0.339833 0.035794 0.032560 -0.010455 asc_air 0.035794 0.139530 0.060929 -0.001527 asc_rail 0.032560 0.060929 0.124863 -0.001253 asc_bus_interaction_female -0.010455 -0.001527 -0.001253 0.017631 asc_air_interaction_female -0.001257 -0.004050 -0.001955 0.003078 asc_rail_interaction_female -0.001425 -0.001491 -0.002759 0.002836 b_tt_car 1.0409e-04 1.6569e-04 1.6552e-04 -6.434e-07 b_tt_bus -8.3297e-04 6.772e-05 5.662e-05 3.862e-06 b_tt_air -1.647e-05 -7.2502e-04 -3.614e-05 -1.279e-06 b_tt_rail 1.105e-05 2.427e-05 -4.7570e-04 -1.719e-06 b_tt_interaction_business 7.427e-06 1.031e-05 1.915e-05 1.057e-06 b_access -2.550e-05 -6.0646e-04 -4.581e-05 3.162e-06 b_cost 1.247e-05 -5.521e-05 -3.943e-05 -9.239e-06 b_cost_interaction_business 3.794e-05 -6.534e-05 2.268e-05 1.371e-05 cost_income_elast -9.9051e-04 0.001332 5.5312e-04 -1.6237e-04 b_wifi -3.6571e-04 -0.002675 -0.001880 1.645e-05 b_food -3.2660e-04 -0.001676 -0.001756 -6.063e-06 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus -0.001257 -0.001425 1.0409e-04 -8.3297e-04 asc_air -0.004050 -0.001491 1.6569e-04 6.772e-05 asc_rail -0.001955 -0.002759 1.6552e-04 5.662e-05 asc_bus_interaction_female 0.003078 0.002836 -6.434e-07 3.862e-06 asc_air_interaction_female 0.008373 0.003520 -1.002e-06 -1.690e-06 asc_rail_interaction_female 0.003520 0.005440 -6.108e-07 -5.672e-07 b_tt_car -1.002e-06 -6.108e-07 5.393e-07 2.066e-07 b_tt_bus -1.690e-06 -5.672e-07 2.066e-07 2.552e-06 b_tt_air -2.576e-07 -2.066e-06 -6.577e-08 -5.452e-08 b_tt_rail 1.554e-07 2.437e-08 -1.587e-08 2.637e-08 b_tt_interaction_business -8.549e-07 -3.060e-07 -3.669e-08 -7.175e-08 b_access -3.012e-06 -3.483e-06 -7.030e-08 -2.594e-07 b_cost -5.141e-06 -3.640e-06 4.869e-07 6.144e-07 b_cost_interaction_business 2.978e-08 1.414e-06 -4.371e-07 -7.186e-07 cost_income_elast 7.665e-06 6.540e-06 -6.251e-07 3.189e-06 b_wifi 7.076e-05 1.602e-05 -6.794e-06 -6.054e-06 b_food 4.013e-05 -4.551e-07 -3.611e-06 -2.639e-06 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -1.647e-05 1.105e-05 7.427e-06 -2.550e-05 asc_air -7.2502e-04 2.427e-05 1.031e-05 -6.0646e-04 asc_rail -3.614e-05 -4.7570e-04 1.915e-05 -4.581e-05 asc_bus_interaction_female -1.279e-06 -1.719e-06 1.057e-06 3.162e-06 asc_air_interaction_female -2.576e-07 1.554e-07 -8.549e-07 -3.012e-06 asc_rail_interaction_female -2.066e-06 2.437e-08 -3.060e-07 -3.483e-06 b_tt_car -6.577e-08 -1.587e-08 -3.669e-08 -7.030e-08 b_tt_bus -5.452e-08 2.637e-08 -7.175e-08 -2.594e-07 b_tt_air 7.693e-06 -2.687e-07 -6.894e-08 2.660e-06 b_tt_rail -2.687e-07 3.281e-06 -1.200e-07 -7.041e-07 b_tt_interaction_business -6.894e-08 -1.200e-07 3.609e-07 9.492e-08 b_access 2.660e-06 -7.041e-07 9.492e-08 8.206e-06 b_cost 1.095e-06 8.953e-07 -3.916e-07 5.331e-07 b_cost_interaction_business -1.221e-07 -6.923e-07 1.187e-06 5.588e-07 cost_income_elast -9.570e-06 -3.335e-06 2.742e-07 -7.526e-06 b_wifi -4.592e-06 -1.038e-05 -2.226e-06 -5.615e-06 b_food -6.300e-06 -4.684e-06 -7.860e-07 -4.785e-06 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 1.247e-05 3.794e-05 -9.9051e-04 -3.6571e-04 asc_air -5.521e-05 -6.534e-05 0.001332 -0.002675 asc_rail -3.943e-05 2.268e-05 5.5312e-04 -0.001880 asc_bus_interaction_female -9.239e-06 1.371e-05 -1.6237e-04 1.645e-05 asc_air_interaction_female -5.141e-06 2.978e-08 7.665e-06 7.076e-05 asc_rail_interaction_female -3.640e-06 1.414e-06 6.540e-06 1.602e-05 b_tt_car 4.869e-07 -4.371e-07 -6.251e-07 -6.794e-06 b_tt_bus 6.144e-07 -7.186e-07 3.189e-06 -6.054e-06 b_tt_air 1.095e-06 -1.221e-07 -9.570e-06 -4.592e-06 b_tt_rail 8.953e-07 -6.923e-07 -3.335e-06 -1.038e-05 b_tt_interaction_business -3.916e-07 1.187e-06 2.742e-07 -2.226e-06 b_access 5.331e-07 5.588e-07 -7.526e-06 -5.615e-06 b_cost 4.398e-06 -3.560e-06 -2.175e-05 -2.211e-05 b_cost_interaction_business -3.560e-06 7.505e-06 3.246e-06 -8.056e-07 cost_income_elast -2.175e-05 3.246e-06 9.0563e-04 1.1251e-04 b_wifi -2.211e-05 -8.056e-07 1.1251e-04 0.003152 b_food -1.225e-05 -5.286e-07 8.494e-05 0.001697 b_food asc_bus -3.2660e-04 asc_air -0.001676 asc_rail -0.001756 asc_bus_interaction_female -6.063e-06 asc_air_interaction_female 4.013e-05 asc_rail_interaction_female -4.551e-07 b_tt_car -3.611e-06 b_tt_bus -2.639e-06 b_tt_air -6.300e-06 b_tt_rail -4.684e-06 b_tt_interaction_business -7.860e-07 b_access -4.785e-06 b_cost -1.225e-05 b_cost_interaction_business -5.286e-07 cost_income_elast 8.494e-05 b_wifi 0.001697 b_food 0.003028 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 0.301965 0.032922 0.034678 -0.011775 asc_air 0.032922 0.130733 0.063502 -0.001594 asc_rail 0.034678 0.063502 0.123265 -6.4128e-04 asc_bus_interaction_female -0.011775 -0.001594 -6.4128e-04 0.021108 asc_air_interaction_female 0.001991 -0.003464 -0.004467 0.003662 asc_rail_interaction_female -0.001727 -0.001676 -0.003047 0.004167 b_tt_car 1.0523e-04 1.7340e-04 1.7304e-04 8.862e-07 b_tt_bus -7.2893e-04 7.999e-05 5.225e-05 5.421e-06 b_tt_air -5.126e-05 -6.3102e-04 -1.928e-05 2.231e-05 b_tt_rail 2.853e-08 1.500e-05 -4.4346e-04 -4.034e-06 b_tt_interaction_business 2.474e-05 3.201e-05 4.088e-05 3.043e-06 b_access 9.425e-05 -5.2315e-04 -4.849e-05 -1.149e-05 b_cost -2.840e-05 -3.853e-05 -5.651e-05 -1.634e-05 b_cost_interaction_business 1.2179e-04 -4.336e-05 9.718e-05 1.524e-05 cost_income_elast -0.001429 0.001669 9.9155e-04 1.8796e-04 b_wifi -0.002178 -0.002232 -0.001700 -4.409e-05 b_food 9.602e-05 -0.001198 -0.001348 4.8058e-04 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 0.001991 -0.001727 1.0523e-04 -7.2893e-04 asc_air -0.003464 -0.001676 1.7340e-04 7.999e-05 asc_rail -0.004467 -0.003047 1.7304e-04 5.225e-05 asc_bus_interaction_female 0.003662 0.004167 8.862e-07 5.421e-06 asc_air_interaction_female 0.009079 0.004621 -3.048e-06 -1.200e-05 asc_rail_interaction_female 0.004621 0.006110 9.531e-07 4.476e-07 b_tt_car -3.048e-06 9.531e-07 5.894e-07 2.419e-07 b_tt_bus -1.200e-05 4.476e-07 2.419e-07 2.304e-06 b_tt_air -7.852e-07 7.604e-06 2.344e-08 9.275e-08 b_tt_rail 1.572e-05 6.855e-06 3.566e-08 1.314e-07 b_tt_interaction_business 6.045e-07 6.700e-07 1.025e-09 -9.351e-08 b_access -1.234e-05 -4.683e-06 -3.243e-08 -5.197e-07 b_cost -2.071e-05 -1.090e-05 4.971e-07 7.365e-07 b_cost_interaction_business 2.164e-05 1.750e-05 -3.569e-07 -8.566e-07 cost_income_elast 2.1864e-04 2.0130e-04 1.046e-06 5.538e-06 b_wifi -1.6434e-04 -1.1758e-04 -6.929e-06 -2.114e-06 b_food -2.7891e-04 -9.338e-05 -4.688e-06 -5.589e-06 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -5.126e-05 2.853e-08 2.474e-05 9.425e-05 asc_air -6.3102e-04 1.500e-05 3.201e-05 -5.2315e-04 asc_rail -1.928e-05 -4.4346e-04 4.088e-05 -4.849e-05 asc_bus_interaction_female 2.231e-05 -4.034e-06 3.043e-06 -1.149e-05 asc_air_interaction_female -7.852e-07 1.572e-05 6.045e-07 -1.234e-05 asc_rail_interaction_female 7.604e-06 6.855e-06 6.700e-07 -4.683e-06 b_tt_car 2.344e-08 3.566e-08 1.025e-09 -3.243e-08 b_tt_bus 9.275e-08 1.314e-07 -9.351e-08 -5.197e-07 b_tt_air 7.133e-06 -1.306e-07 -1.442e-07 2.213e-06 b_tt_rail -1.306e-07 3.114e-06 -1.772e-07 -5.463e-07 b_tt_interaction_business -1.442e-07 -1.772e-07 3.490e-07 7.609e-08 b_access 2.213e-06 -5.463e-07 7.609e-08 7.325e-06 b_cost 9.231e-07 1.048e-06 -4.534e-07 5.359e-07 b_cost_interaction_business -5.059e-10 -1.048e-06 1.010e-06 4.409e-07 cost_income_elast -9.515e-06 -3.789e-06 3.972e-07 -5.408e-06 b_wifi -1.463e-05 -1.245e-05 -2.784e-06 1.771e-06 b_food -1.693e-05 -9.011e-06 -9.263e-07 -1.814e-06 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -2.840e-05 1.2179e-04 -0.001429 -0.002178 asc_air -3.853e-05 -4.336e-05 0.001669 -0.002232 asc_rail -5.651e-05 9.718e-05 9.9155e-04 -0.001700 asc_bus_interaction_female -1.634e-05 1.524e-05 1.8796e-04 -4.409e-05 asc_air_interaction_female -2.071e-05 2.164e-05 2.1864e-04 -1.6434e-04 asc_rail_interaction_female -1.090e-05 1.750e-05 2.0130e-04 -1.1758e-04 b_tt_car 4.971e-07 -3.569e-07 1.046e-06 -6.929e-06 b_tt_bus 7.365e-07 -8.566e-07 5.538e-06 -2.114e-06 b_tt_air 9.231e-07 -5.059e-10 -9.515e-06 -1.463e-05 b_tt_rail 1.048e-06 -1.048e-06 -3.789e-06 -1.245e-05 b_tt_interaction_business -4.534e-07 1.010e-06 3.972e-07 -2.784e-06 b_access 5.359e-07 4.409e-07 -5.408e-06 1.771e-06 b_cost 4.390e-06 -3.638e-06 -1.958e-05 -2.386e-05 b_cost_interaction_business -3.638e-06 6.615e-06 2.968e-06 2.023e-07 cost_income_elast -1.958e-05 2.968e-06 9.3666e-04 5.121e-05 b_wifi -2.386e-05 2.023e-07 5.121e-05 0.003343 b_food -1.647e-05 1.747e-06 -2.370e-05 0.001794 b_food asc_bus 9.602e-05 asc_air -0.001198 asc_rail -0.001348 asc_bus_interaction_female 4.8058e-04 asc_air_interaction_female -2.7891e-04 asc_rail_interaction_female -9.338e-05 b_tt_car -4.688e-06 b_tt_bus -5.589e-06 b_tt_air -1.693e-05 b_tt_rail -9.011e-06 b_tt_interaction_business -9.263e-07 b_access -1.814e-06 b_cost -1.647e-05 b_cost_interaction_business 1.747e-06 cost_income_elast -2.370e-05 b_wifi 0.001794 b_food 0.003188 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.00000 0.16438 0.15807 -0.135073 asc_air 0.16438 1.00000 0.46161 -0.030797 asc_rail 0.15807 0.46161 1.00000 -0.026705 asc_bus_interaction_female -0.13507 -0.03080 -0.02671 1.000000 asc_air_interaction_female -0.02357 -0.11848 -0.06047 0.253329 asc_rail_interaction_female -0.03315 -0.05411 -0.10585 0.289616 b_tt_car 0.24314 0.60398 0.63780 -0.006598 b_tt_bus -0.89438 0.11347 0.10030 0.018204 b_tt_air -0.01019 -0.69979 -0.03688 -0.003472 b_tt_rail 0.01046 0.03587 -0.74326 -0.007148 b_tt_interaction_business 0.02121 0.04596 0.09022 0.013251 b_access -0.01527 -0.56678 -0.04525 0.008314 b_cost 0.01020 -0.07048 -0.05321 -0.033180 b_cost_interaction_business 0.02376 -0.06385 0.02343 0.037692 cost_income_elast -0.05646 0.11845 0.05201 -0.040634 b_wifi -0.01117 -0.12756 -0.09475 0.002207 b_food -0.01018 -0.08156 -0.09031 -8.2979e-04 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus -0.023569 -0.033152 0.243139 -0.894383 asc_air -0.118476 -0.054110 0.603979 0.113472 asc_rail -0.060472 -0.105852 0.637801 0.100299 asc_bus_interaction_female 0.253329 0.289616 -0.006598 0.018204 asc_air_interaction_female 1.000000 0.521489 -0.014909 -0.011562 asc_rail_interaction_female 0.521489 1.000000 -0.011275 -0.004814 b_tt_car -0.014909 -0.011275 1.000000 0.176045 b_tt_bus -0.011562 -0.004814 0.176045 1.000000 b_tt_air -0.001015 -0.010101 -0.032289 -0.012304 b_tt_rail 9.3745e-04 1.8245e-04 -0.011928 0.009112 b_tt_interaction_business -0.015551 -0.006905 -0.083166 -0.074757 b_access -0.011492 -0.016487 -0.033418 -0.056673 b_cost -0.026793 -0.023534 0.316136 0.183396 b_cost_interaction_business 1.1881e-04 0.006995 -0.217243 -0.164195 cost_income_elast 0.002783 0.002946 -0.028283 0.066338 b_wifi 0.013773 0.003869 -0.164784 -0.067502 b_food 0.007970 -1.1214e-04 -0.089357 -0.030019 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -0.010189 0.010462 0.021207 -0.015270 asc_air -0.699795 0.035873 0.045961 -0.566781 asc_rail -0.036878 -0.743261 0.090217 -0.045255 asc_bus_interaction_female -0.003472 -0.007148 0.013251 0.008314 asc_air_interaction_female -0.001015 9.3745e-04 -0.015551 -0.011492 asc_rail_interaction_female -0.010101 1.8245e-04 -0.006905 -0.016487 b_tt_car -0.032289 -0.011928 -0.083166 -0.033418 b_tt_bus -0.012304 0.009112 -0.074757 -0.056673 b_tt_air 1.000000 -0.053495 -0.041374 0.334810 b_tt_rail -0.053495 1.000000 -0.110296 -0.135703 b_tt_interaction_business -0.041374 -0.110296 1.000000 0.055160 b_access 0.334810 -0.135703 0.055160 1.000000 b_cost 0.188331 0.235713 -0.310832 0.088748 b_cost_interaction_business -0.016069 -0.139532 0.721311 0.071210 cost_income_elast -0.114657 -0.061191 0.015166 -0.087306 b_wifi -0.029491 -0.102070 -0.065995 -0.034912 b_food -0.041281 -0.046996 -0.023777 -0.030355 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 0.01020 0.023759 -0.056462 -0.011174 asc_air -0.07048 -0.063850 0.118454 -0.127563 asc_rail -0.05321 0.023434 0.052015 -0.094750 asc_bus_interaction_female -0.03318 0.037692 -0.040634 0.002207 asc_air_interaction_female -0.02679 1.1881e-04 0.002783 0.013773 asc_rail_interaction_female -0.02353 0.006995 0.002946 0.003869 b_tt_car 0.31614 -0.217243 -0.028283 -0.164784 b_tt_bus 0.18340 -0.164195 0.066338 -0.067502 b_tt_air 0.18833 -0.016069 -0.114657 -0.029491 b_tt_rail 0.23571 -0.139532 -0.061191 -0.102070 b_tt_interaction_business -0.31083 0.721311 0.015166 -0.065995 b_access 0.08875 0.071210 -0.087306 -0.034912 b_cost 1.00000 -0.619616 -0.344667 -0.187813 b_cost_interaction_business -0.61962 1.000000 0.039380 -0.005238 cost_income_elast -0.34467 0.039380 1.000000 0.066591 b_wifi -0.18781 -0.005238 0.066591 1.000000 b_food -0.10618 -0.003507 0.051293 0.549323 b_food asc_bus -0.010181 asc_air -0.081557 asc_rail -0.090312 asc_bus_interaction_female -8.2979e-04 asc_air_interaction_female 0.007970 asc_rail_interaction_female -1.1214e-04 b_tt_car -0.089357 b_tt_bus -0.030019 b_tt_air -0.041281 b_tt_rail -0.046996 b_tt_interaction_business -0.023777 b_access -0.030355 b_cost -0.106180 b_cost_interaction_business -0.003507 cost_income_elast 0.051293 b_wifi 0.549323 b_food 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.000000 0.16570 0.17974 -0.147490 asc_air 0.165696 1.00000 0.50023 -0.030338 asc_rail 0.179743 0.50023 1.00000 -0.012572 asc_bus_interaction_female -0.147490 -0.03034 -0.01257 1.000000 asc_air_interaction_female 0.038030 -0.10055 -0.13352 0.264553 asc_rail_interaction_female -0.040194 -0.05931 -0.11104 0.366935 b_tt_car 0.249427 0.62466 0.64195 0.007945 b_tt_bus -0.873861 0.14575 0.09804 0.024582 b_tt_air -0.034928 -0.65348 -0.02056 0.057491 b_tt_rail 2.942e-05 0.02351 -0.71581 -0.015735 b_tt_interaction_business 0.076194 0.14985 0.19708 0.035452 b_access 0.063371 -0.53461 -0.05103 -0.029221 b_cost -0.024663 -0.05086 -0.07682 -0.053677 b_cost_interaction_business 0.086178 -0.04663 0.10762 0.040773 cost_income_elast -0.084968 0.15079 0.09228 0.042271 b_wifi -0.068548 -0.10680 -0.08375 -0.005249 b_food 0.003095 -0.05870 -0.06801 0.058583 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 0.038030 -0.040194 0.249427 -0.873861 asc_air -0.100553 -0.059311 0.624662 0.145747 asc_rail -0.133517 -0.111037 0.641953 0.098036 asc_bus_interaction_female 0.264553 0.366935 0.007945 0.024582 asc_air_interaction_female 1.000000 0.620377 -0.041667 -0.082986 asc_rail_interaction_female 0.620377 1.000000 0.015881 0.003772 b_tt_car -0.041667 0.015881 1.000000 0.207566 b_tt_bus -0.082986 0.003772 0.207566 1.000000 b_tt_air -0.003085 0.036422 0.011431 0.022877 b_tt_rail 0.093479 0.049695 0.026321 0.049066 b_tt_interaction_business 0.010739 0.014508 0.002260 -0.104269 b_access -0.047856 -0.022136 -0.015607 -0.126492 b_cost -0.103758 -0.066562 0.309044 0.231558 b_cost_interaction_business 0.088305 0.087026 -0.180772 -0.219416 cost_income_elast 0.074975 0.084144 0.044536 0.119215 b_wifi -0.029832 -0.026018 -0.156102 -0.024089 b_food -0.051841 -0.021157 -0.108144 -0.065202 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -0.034928 2.942e-05 0.076194 0.06337 asc_air -0.653477 0.02351 0.149849 -0.53461 asc_rail -0.020559 -0.71581 0.197081 -0.05103 asc_bus_interaction_female 0.057491 -0.01573 0.035452 -0.02922 asc_air_interaction_female -0.003085 0.09348 0.010739 -0.04786 asc_rail_interaction_female 0.036422 0.04970 0.014508 -0.02214 b_tt_car 0.011431 0.02632 0.002260 -0.01561 b_tt_bus 0.022877 0.04907 -0.104269 -0.12649 b_tt_air 1.000000 -0.02771 -0.091423 0.30612 b_tt_rail -0.027714 1.00000 -0.169969 -0.11439 b_tt_interaction_business -0.091423 -0.16997 1.000000 0.04759 b_access 0.306117 -0.11439 0.047588 1.00000 b_cost 0.164962 0.28349 -0.366279 0.09451 b_cost_interaction_business -7.365e-05 -0.23093 0.664397 0.06335 cost_income_elast -0.116409 -0.07016 0.021971 -0.06529 b_wifi -0.094765 -0.12205 -0.081514 0.01132 b_food -0.112237 -0.09044 -0.027768 -0.01187 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -0.02466 0.086178 -0.08497 -0.068548 asc_air -0.05086 -0.046628 0.15079 -0.106796 asc_rail -0.07682 0.107621 0.09228 -0.083747 asc_bus_interaction_female -0.05368 0.040773 0.04227 -0.005249 asc_air_interaction_female -0.10376 0.088305 0.07498 -0.029832 asc_rail_interaction_female -0.06656 0.087026 0.08414 -0.026018 b_tt_car 0.30904 -0.180772 0.04454 -0.156102 b_tt_bus 0.23156 -0.219416 0.11921 -0.024089 b_tt_air 0.16496 -7.365e-05 -0.11641 -0.094765 b_tt_rail 0.28349 -0.230931 -0.07016 -0.122048 b_tt_interaction_business -0.36628 0.664397 0.02197 -0.081514 b_access 0.09451 0.063349 -0.06529 0.011317 b_cost 1.00000 -0.675147 -0.30527 -0.196966 b_cost_interaction_business -0.67515 1.000000 0.03771 0.001361 cost_income_elast -0.30527 0.037712 1.00000 0.028943 b_wifi -0.19697 0.001361 0.02894 1.000000 b_food -0.13918 0.012033 -0.01371 0.549573 b_food asc_bus 0.003095 asc_air -0.058698 asc_rail -0.068010 asc_bus_interaction_female 0.058583 asc_air_interaction_female -0.051841 asc_rail_interaction_female -0.021157 b_tt_car -0.108144 b_tt_bus -0.065202 b_tt_air -0.112237 b_tt_rail -0.090442 b_tt_interaction_business -0.027768 b_access -0.011874 b_cost -0.139182 b_cost_interaction_business 0.012033 cost_income_elast -0.013715 b_wifi 0.549573 b_food 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2353159 464 0.2378514 146 0.2461400 181 0.2489964 293 0.2527721 186 0.2576655 276 0.2616345 307 0.2693801 367 0.2717657 441 0.2744234 498 0.2809933 317 0.2816537 434 0.2857819 161 0.2870151 259 0.2980537 133 0.3012292 183 0.3032729 147 0.3048912 447 0.3085425 370 0.3092381 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.062410 0.286354 0.223943 asc_air 0.238276 -0.903377 -1.141654 asc_rail -1.481369 -2.092701 -0.611332 asc_bus_interaction_female 0.000000 0.340193 0.340193 asc_air_interaction_female 0.000000 0.268174 0.268174 asc_rail_interaction_female 0.000000 0.189612 0.189612 b_tt_car -0.011602 -0.013107 -0.001505 b_tt_bus -0.017368 -0.021265 -0.003897 b_tt_air -0.019483 -0.016578 0.002905 b_tt_rail -0.006365 -0.007051 -6.8594e-04 b_tt_interaction_business 0.000000 -0.006234 -0.006234 b_access -0.023193 -0.021152 0.002040 b_cost -0.058756 -0.076188 -0.017432 b_cost_interaction_business 0.000000 0.033379 0.033379 cost_income_elast 0.000000 -0.613821 -0.613821 b_no_frills 0.000000 0.000000 0.000000 b_wifi 0.937555 1.026711 0.089156 b_food 0.409560 0.422072 0.012512 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "MNL model with socio-demographics on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "MNL_SP_covariates" 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 0.286353751 asc_air 0.903377425 asc_rail 2.092701250 asc_bus_interaction_female 0.340193244 asc_air_interaction_female 0.268173658 asc_rail_interaction_female 0.189612394 b_tt_car 0.013107303 b_tt_bus 0.021265325 b_tt_air 0.016578014 b_tt_rail 0.007050876 b_tt_interaction_business 0.006233935 b_access 0.021152371 b_cost 0.076187537 b_cost_interaction_business 0.033379435 cost_income_elast 0.613820749 b_wifi 1.026711292 b_food 0.422071502 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() ### Create alternative specific constants and coefficients using interactions with socio-demographics asc_bus_value = asc_bus + asc_bus_interaction_female * female asc_air_value = asc_air + asc_air_interaction_female * female asc_rail_value = asc_rail + asc_rail_interaction_female * female b_tt_car_value = b_tt_car + b_tt_interaction_business * business b_tt_bus_value = b_tt_bus + b_tt_interaction_business * business b_tt_air_value = b_tt_air + b_tt_interaction_business * business b_tt_rail_value = b_tt_rail + b_tt_interaction_business * business b_cost_value = ( b_cost + b_cost_interaction_business * business ) * ( income / mean_income ) ^ cost_income_elast ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant V = list() V[["car"]] = asc_car + b_tt_car_value * time_car + b_cost_value * cost_car V[["bus"]] = asc_bus_value + b_tt_bus_value * time_bus + b_access * access_bus + b_cost_value * cost_bus V[["air"]] = asc_air_value + b_tt_air_value * time_air + b_access * access_air + b_cost_value * cost_air + b_no_frills * ( service_air == 1 ) + b_wifi * ( service_air == 2 ) + b_food * ( service_air == 3 ) V[["rail"]] = asc_rail_value + b_tt_rail_value * time_rail + b_access * access_rail + b_cost_value * cost_rail + b_no_frills * ( service_rail == 1 ) + b_wifi * ( service_rail == 2 ) + b_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) }