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_covariates Model description : MNL model with socio-demographics on mode choice SP data Model run at : 2025-09-19 11:38:22.442639 Estimation method : bgw Estimation 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) : 00:00:2.14 pre-estimation : 00:00:0.33 estimation : 00:00:0.2 post-estimation : 00:00:1.62 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_bus 0.339833 0.035794 asc_air 0.035794 0.139530 asc_rail 0.032560 0.060929 asc_bus_interaction_female -0.010455 -0.001527 asc_air_interaction_female -0.001257 -0.004050 asc_rail_interaction_female -0.001425 -0.001491 b_tt_car 1.0409e-04 1.6569e-04 b_tt_bus -8.3297e-04 6.772e-05 b_tt_air -1.647e-05 -7.2502e-04 b_tt_rail 1.105e-05 2.427e-05 b_tt_interaction_business 7.427e-06 1.031e-05 b_access -2.550e-05 -6.0646e-04 b_cost 1.247e-05 -5.521e-05 b_cost_interaction_business 3.794e-05 -6.534e-05 cost_income_elast -9.9051e-04 0.001332 b_wifi -3.6571e-04 -0.002675 b_food -3.2660e-04 -0.001676 asc_rail asc_bus_interaction_female asc_bus 0.032560 -0.010455 asc_air 0.060929 -0.001527 asc_rail 0.124863 -0.001253 asc_bus_interaction_female -0.001253 0.017631 asc_air_interaction_female -0.001955 0.003078 asc_rail_interaction_female -0.002759 0.002836 b_tt_car 1.6552e-04 -6.434e-07 b_tt_bus 5.662e-05 3.862e-06 b_tt_air -3.614e-05 -1.279e-06 b_tt_rail -4.7570e-04 -1.719e-06 b_tt_interaction_business 1.915e-05 1.057e-06 b_access -4.581e-05 3.162e-06 b_cost -3.943e-05 -9.239e-06 b_cost_interaction_business 2.268e-05 1.371e-05 cost_income_elast 5.5312e-04 -1.6237e-04 b_wifi -0.001880 1.645e-05 b_food -0.001756 -6.063e-06 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.001257 -0.001425 asc_air -0.004050 -0.001491 asc_rail -0.001955 -0.002759 asc_bus_interaction_female 0.003078 0.002836 asc_air_interaction_female 0.008373 0.003520 asc_rail_interaction_female 0.003520 0.005440 b_tt_car -1.002e-06 -6.108e-07 b_tt_bus -1.690e-06 -5.672e-07 b_tt_air -2.576e-07 -2.066e-06 b_tt_rail 1.554e-07 2.437e-08 b_tt_interaction_business -8.549e-07 -3.060e-07 b_access -3.012e-06 -3.483e-06 b_cost -5.141e-06 -3.640e-06 b_cost_interaction_business 2.978e-08 1.414e-06 cost_income_elast 7.665e-06 6.540e-06 b_wifi 7.076e-05 1.602e-05 b_food 4.013e-05 -4.551e-07 b_tt_car b_tt_bus asc_bus 1.0409e-04 -8.3297e-04 asc_air 1.6569e-04 6.772e-05 asc_rail 1.6552e-04 5.662e-05 asc_bus_interaction_female -6.434e-07 3.862e-06 asc_air_interaction_female -1.002e-06 -1.690e-06 asc_rail_interaction_female -6.108e-07 -5.672e-07 b_tt_car 5.393e-07 2.066e-07 b_tt_bus 2.066e-07 2.552e-06 b_tt_air -6.577e-08 -5.452e-08 b_tt_rail -1.587e-08 2.637e-08 b_tt_interaction_business -3.669e-08 -7.175e-08 b_access -7.030e-08 -2.594e-07 b_cost 4.869e-07 6.144e-07 b_cost_interaction_business -4.371e-07 -7.186e-07 cost_income_elast -6.251e-07 3.189e-06 b_wifi -6.794e-06 -6.054e-06 b_food -3.611e-06 -2.639e-06 b_tt_air b_tt_rail asc_bus -1.647e-05 1.105e-05 asc_air -7.2502e-04 2.427e-05 asc_rail -3.614e-05 -4.7570e-04 asc_bus_interaction_female -1.279e-06 -1.719e-06 asc_air_interaction_female -2.576e-07 1.554e-07 asc_rail_interaction_female -2.066e-06 2.437e-08 b_tt_car -6.577e-08 -1.587e-08 b_tt_bus -5.452e-08 2.637e-08 b_tt_air 7.693e-06 -2.687e-07 b_tt_rail -2.687e-07 3.281e-06 b_tt_interaction_business -6.894e-08 -1.200e-07 b_access 2.660e-06 -7.041e-07 b_cost 1.095e-06 8.953e-07 b_cost_interaction_business -1.221e-07 -6.923e-07 cost_income_elast -9.570e-06 -3.335e-06 b_wifi -4.592e-06 -1.038e-05 b_food -6.300e-06 -4.684e-06 b_tt_interaction_business b_access asc_bus 7.427e-06 -2.550e-05 asc_air 1.031e-05 -6.0646e-04 asc_rail 1.915e-05 -4.581e-05 asc_bus_interaction_female 1.057e-06 3.162e-06 asc_air_interaction_female -8.549e-07 -3.012e-06 asc_rail_interaction_female -3.060e-07 -3.483e-06 b_tt_car -3.669e-08 -7.030e-08 b_tt_bus -7.175e-08 -2.594e-07 b_tt_air -6.894e-08 2.660e-06 b_tt_rail -1.200e-07 -7.041e-07 b_tt_interaction_business 3.609e-07 9.492e-08 b_access 9.492e-08 8.206e-06 b_cost -3.916e-07 5.331e-07 b_cost_interaction_business 1.187e-06 5.588e-07 cost_income_elast 2.742e-07 -7.526e-06 b_wifi -2.226e-06 -5.615e-06 b_food -7.860e-07 -4.785e-06 b_cost b_cost_interaction_business asc_bus 1.247e-05 3.794e-05 asc_air -5.521e-05 -6.534e-05 asc_rail -3.943e-05 2.268e-05 asc_bus_interaction_female -9.239e-06 1.371e-05 asc_air_interaction_female -5.141e-06 2.978e-08 asc_rail_interaction_female -3.640e-06 1.414e-06 b_tt_car 4.869e-07 -4.371e-07 b_tt_bus 6.144e-07 -7.186e-07 b_tt_air 1.095e-06 -1.221e-07 b_tt_rail 8.953e-07 -6.923e-07 b_tt_interaction_business -3.916e-07 1.187e-06 b_access 5.331e-07 5.588e-07 b_cost 4.398e-06 -3.560e-06 b_cost_interaction_business -3.560e-06 7.505e-06 cost_income_elast -2.175e-05 3.246e-06 b_wifi -2.211e-05 -8.056e-07 b_food -1.225e-05 -5.286e-07 cost_income_elast b_wifi asc_bus -9.9051e-04 -3.6571e-04 asc_air 0.001332 -0.002675 asc_rail 5.5312e-04 -0.001880 asc_bus_interaction_female -1.6237e-04 1.645e-05 asc_air_interaction_female 7.665e-06 7.076e-05 asc_rail_interaction_female 6.540e-06 1.602e-05 b_tt_car -6.251e-07 -6.794e-06 b_tt_bus 3.189e-06 -6.054e-06 b_tt_air -9.570e-06 -4.592e-06 b_tt_rail -3.335e-06 -1.038e-05 b_tt_interaction_business 2.742e-07 -2.226e-06 b_access -7.526e-06 -5.615e-06 b_cost -2.175e-05 -2.211e-05 b_cost_interaction_business 3.246e-06 -8.056e-07 cost_income_elast 9.0563e-04 1.1251e-04 b_wifi 1.1251e-04 0.003152 b_food 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_bus 0.301965 0.032922 asc_air 0.032922 0.130733 asc_rail 0.034678 0.063502 asc_bus_interaction_female -0.011775 -0.001594 asc_air_interaction_female 0.001991 -0.003464 asc_rail_interaction_female -0.001727 -0.001676 b_tt_car 1.0523e-04 1.7340e-04 b_tt_bus -7.2893e-04 7.999e-05 b_tt_air -5.126e-05 -6.3102e-04 b_tt_rail 2.853e-08 1.500e-05 b_tt_interaction_business 2.474e-05 3.201e-05 b_access 9.425e-05 -5.2315e-04 b_cost -2.840e-05 -3.853e-05 b_cost_interaction_business 1.2179e-04 -4.336e-05 cost_income_elast -0.001429 0.001669 b_wifi -0.002178 -0.002232 b_food 9.602e-05 -0.001198 asc_rail asc_bus_interaction_female asc_bus 0.034678 -0.011775 asc_air 0.063502 -0.001594 asc_rail 0.123265 -6.4128e-04 asc_bus_interaction_female -6.4128e-04 0.021108 asc_air_interaction_female -0.004467 0.003662 asc_rail_interaction_female -0.003047 0.004167 b_tt_car 1.7304e-04 8.862e-07 b_tt_bus 5.225e-05 5.421e-06 b_tt_air -1.928e-05 2.231e-05 b_tt_rail -4.4346e-04 -4.034e-06 b_tt_interaction_business 4.088e-05 3.043e-06 b_access -4.849e-05 -1.149e-05 b_cost -5.651e-05 -1.634e-05 b_cost_interaction_business 9.718e-05 1.524e-05 cost_income_elast 9.9155e-04 1.8796e-04 b_wifi -0.001700 -4.409e-05 b_food -0.001348 4.8058e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.001991 -0.001727 asc_air -0.003464 -0.001676 asc_rail -0.004467 -0.003047 asc_bus_interaction_female 0.003662 0.004167 asc_air_interaction_female 0.009079 0.004621 asc_rail_interaction_female 0.004621 0.006110 b_tt_car -3.048e-06 9.531e-07 b_tt_bus -1.200e-05 4.476e-07 b_tt_air -7.852e-07 7.604e-06 b_tt_rail 1.572e-05 6.855e-06 b_tt_interaction_business 6.045e-07 6.700e-07 b_access -1.234e-05 -4.683e-06 b_cost -2.071e-05 -1.090e-05 b_cost_interaction_business 2.164e-05 1.750e-05 cost_income_elast 2.1864e-04 2.0130e-04 b_wifi -1.6434e-04 -1.1758e-04 b_food -2.7891e-04 -9.338e-05 b_tt_car b_tt_bus asc_bus 1.0523e-04 -7.2893e-04 asc_air 1.7340e-04 7.999e-05 asc_rail 1.7304e-04 5.225e-05 asc_bus_interaction_female 8.862e-07 5.421e-06 asc_air_interaction_female -3.048e-06 -1.200e-05 asc_rail_interaction_female 9.531e-07 4.476e-07 b_tt_car 5.894e-07 2.419e-07 b_tt_bus 2.419e-07 2.304e-06 b_tt_air 2.344e-08 9.275e-08 b_tt_rail 3.566e-08 1.314e-07 b_tt_interaction_business 1.025e-09 -9.351e-08 b_access -3.243e-08 -5.197e-07 b_cost 4.971e-07 7.365e-07 b_cost_interaction_business -3.569e-07 -8.566e-07 cost_income_elast 1.046e-06 5.538e-06 b_wifi -6.929e-06 -2.114e-06 b_food -4.688e-06 -5.589e-06 b_tt_air b_tt_rail asc_bus -5.126e-05 2.853e-08 asc_air -6.3102e-04 1.500e-05 asc_rail -1.928e-05 -4.4346e-04 asc_bus_interaction_female 2.231e-05 -4.034e-06 asc_air_interaction_female -7.852e-07 1.572e-05 asc_rail_interaction_female 7.604e-06 6.855e-06 b_tt_car 2.344e-08 3.566e-08 b_tt_bus 9.275e-08 1.314e-07 b_tt_air 7.133e-06 -1.306e-07 b_tt_rail -1.306e-07 3.114e-06 b_tt_interaction_business -1.442e-07 -1.772e-07 b_access 2.213e-06 -5.463e-07 b_cost 9.231e-07 1.048e-06 b_cost_interaction_business -5.059e-10 -1.048e-06 cost_income_elast -9.515e-06 -3.789e-06 b_wifi -1.463e-05 -1.245e-05 b_food -1.693e-05 -9.011e-06 b_tt_interaction_business b_access asc_bus 2.474e-05 9.425e-05 asc_air 3.201e-05 -5.2315e-04 asc_rail 4.088e-05 -4.849e-05 asc_bus_interaction_female 3.043e-06 -1.149e-05 asc_air_interaction_female 6.045e-07 -1.234e-05 asc_rail_interaction_female 6.700e-07 -4.683e-06 b_tt_car 1.025e-09 -3.243e-08 b_tt_bus -9.351e-08 -5.197e-07 b_tt_air -1.442e-07 2.213e-06 b_tt_rail -1.772e-07 -5.463e-07 b_tt_interaction_business 3.490e-07 7.609e-08 b_access 7.609e-08 7.325e-06 b_cost -4.534e-07 5.359e-07 b_cost_interaction_business 1.010e-06 4.409e-07 cost_income_elast 3.972e-07 -5.408e-06 b_wifi -2.784e-06 1.771e-06 b_food -9.263e-07 -1.814e-06 b_cost b_cost_interaction_business asc_bus -2.840e-05 1.2179e-04 asc_air -3.853e-05 -4.336e-05 asc_rail -5.651e-05 9.718e-05 asc_bus_interaction_female -1.634e-05 1.524e-05 asc_air_interaction_female -2.071e-05 2.164e-05 asc_rail_interaction_female -1.090e-05 1.750e-05 b_tt_car 4.971e-07 -3.569e-07 b_tt_bus 7.365e-07 -8.566e-07 b_tt_air 9.231e-07 -5.059e-10 b_tt_rail 1.048e-06 -1.048e-06 b_tt_interaction_business -4.534e-07 1.010e-06 b_access 5.359e-07 4.409e-07 b_cost 4.390e-06 -3.638e-06 b_cost_interaction_business -3.638e-06 6.615e-06 cost_income_elast -1.958e-05 2.968e-06 b_wifi -2.386e-05 2.023e-07 b_food -1.647e-05 1.747e-06 cost_income_elast b_wifi asc_bus -0.001429 -0.002178 asc_air 0.001669 -0.002232 asc_rail 9.9155e-04 -0.001700 asc_bus_interaction_female 1.8796e-04 -4.409e-05 asc_air_interaction_female 2.1864e-04 -1.6434e-04 asc_rail_interaction_female 2.0130e-04 -1.1758e-04 b_tt_car 1.046e-06 -6.929e-06 b_tt_bus 5.538e-06 -2.114e-06 b_tt_air -9.515e-06 -1.463e-05 b_tt_rail -3.789e-06 -1.245e-05 b_tt_interaction_business 3.972e-07 -2.784e-06 b_access -5.408e-06 1.771e-06 b_cost -1.958e-05 -2.386e-05 b_cost_interaction_business 2.968e-06 2.023e-07 cost_income_elast 9.3666e-04 5.121e-05 b_wifi 5.121e-05 0.003343 b_food -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_bus 1.00000 0.16438 asc_air 0.16438 1.00000 asc_rail 0.15807 0.46161 asc_bus_interaction_female -0.13507 -0.03080 asc_air_interaction_female -0.02357 -0.11848 asc_rail_interaction_female -0.03315 -0.05411 b_tt_car 0.24314 0.60398 b_tt_bus -0.89438 0.11347 b_tt_air -0.01019 -0.69979 b_tt_rail 0.01046 0.03587 b_tt_interaction_business 0.02121 0.04596 b_access -0.01527 -0.56678 b_cost 0.01020 -0.07048 b_cost_interaction_business 0.02376 -0.06385 cost_income_elast -0.05646 0.11845 b_wifi -0.01117 -0.12756 b_food -0.01018 -0.08156 asc_rail asc_bus_interaction_female asc_bus 0.15807 -0.135073 asc_air 0.46161 -0.030797 asc_rail 1.00000 -0.026705 asc_bus_interaction_female -0.02671 1.000000 asc_air_interaction_female -0.06047 0.253329 asc_rail_interaction_female -0.10585 0.289616 b_tt_car 0.63780 -0.006598 b_tt_bus 0.10030 0.018204 b_tt_air -0.03688 -0.003472 b_tt_rail -0.74326 -0.007148 b_tt_interaction_business 0.09022 0.013251 b_access -0.04525 0.008314 b_cost -0.05321 -0.033180 b_cost_interaction_business 0.02343 0.037692 cost_income_elast 0.05201 -0.040634 b_wifi -0.09475 0.002207 b_food -0.09031 -8.2979e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.023569 -0.033152 asc_air -0.118476 -0.054110 asc_rail -0.060472 -0.105852 asc_bus_interaction_female 0.253329 0.289616 asc_air_interaction_female 1.000000 0.521489 asc_rail_interaction_female 0.521489 1.000000 b_tt_car -0.014909 -0.011275 b_tt_bus -0.011562 -0.004814 b_tt_air -0.001015 -0.010101 b_tt_rail 9.3745e-04 1.8245e-04 b_tt_interaction_business -0.015551 -0.006905 b_access -0.011492 -0.016487 b_cost -0.026793 -0.023534 b_cost_interaction_business 1.1881e-04 0.006995 cost_income_elast 0.002783 0.002946 b_wifi 0.013773 0.003869 b_food 0.007970 -1.1214e-04 b_tt_car b_tt_bus asc_bus 0.243139 -0.894383 asc_air 0.603979 0.113472 asc_rail 0.637801 0.100299 asc_bus_interaction_female -0.006598 0.018204 asc_air_interaction_female -0.014909 -0.011562 asc_rail_interaction_female -0.011275 -0.004814 b_tt_car 1.000000 0.176045 b_tt_bus 0.176045 1.000000 b_tt_air -0.032289 -0.012304 b_tt_rail -0.011928 0.009112 b_tt_interaction_business -0.083166 -0.074757 b_access -0.033418 -0.056673 b_cost 0.316136 0.183396 b_cost_interaction_business -0.217243 -0.164195 cost_income_elast -0.028283 0.066338 b_wifi -0.164784 -0.067502 b_food -0.089357 -0.030019 b_tt_air b_tt_rail asc_bus -0.010189 0.010462 asc_air -0.699795 0.035873 asc_rail -0.036878 -0.743261 asc_bus_interaction_female -0.003472 -0.007148 asc_air_interaction_female -0.001015 9.3745e-04 asc_rail_interaction_female -0.010101 1.8245e-04 b_tt_car -0.032289 -0.011928 b_tt_bus -0.012304 0.009112 b_tt_air 1.000000 -0.053495 b_tt_rail -0.053495 1.000000 b_tt_interaction_business -0.041374 -0.110296 b_access 0.334810 -0.135703 b_cost 0.188331 0.235713 b_cost_interaction_business -0.016069 -0.139532 cost_income_elast -0.114657 -0.061191 b_wifi -0.029491 -0.102070 b_food -0.041281 -0.046996 b_tt_interaction_business b_access asc_bus 0.021207 -0.015270 asc_air 0.045961 -0.566781 asc_rail 0.090217 -0.045255 asc_bus_interaction_female 0.013251 0.008314 asc_air_interaction_female -0.015551 -0.011492 asc_rail_interaction_female -0.006905 -0.016487 b_tt_car -0.083166 -0.033418 b_tt_bus -0.074757 -0.056673 b_tt_air -0.041374 0.334810 b_tt_rail -0.110296 -0.135703 b_tt_interaction_business 1.000000 0.055160 b_access 0.055160 1.000000 b_cost -0.310832 0.088748 b_cost_interaction_business 0.721311 0.071210 cost_income_elast 0.015166 -0.087306 b_wifi -0.065995 -0.034912 b_food -0.023777 -0.030355 b_cost b_cost_interaction_business asc_bus 0.01020 0.023759 asc_air -0.07048 -0.063850 asc_rail -0.05321 0.023434 asc_bus_interaction_female -0.03318 0.037692 asc_air_interaction_female -0.02679 1.1881e-04 asc_rail_interaction_female -0.02353 0.006995 b_tt_car 0.31614 -0.217243 b_tt_bus 0.18340 -0.164195 b_tt_air 0.18833 -0.016069 b_tt_rail 0.23571 -0.139532 b_tt_interaction_business -0.31083 0.721311 b_access 0.08875 0.071210 b_cost 1.00000 -0.619616 b_cost_interaction_business -0.61962 1.000000 cost_income_elast -0.34467 0.039380 b_wifi -0.18781 -0.005238 b_food -0.10618 -0.003507 cost_income_elast b_wifi asc_bus -0.056462 -0.011174 asc_air 0.118454 -0.127563 asc_rail 0.052015 -0.094750 asc_bus_interaction_female -0.040634 0.002207 asc_air_interaction_female 0.002783 0.013773 asc_rail_interaction_female 0.002946 0.003869 b_tt_car -0.028283 -0.164784 b_tt_bus 0.066338 -0.067502 b_tt_air -0.114657 -0.029491 b_tt_rail -0.061191 -0.102070 b_tt_interaction_business 0.015166 -0.065995 b_access -0.087306 -0.034912 b_cost -0.344667 -0.187813 b_cost_interaction_business 0.039380 -0.005238 cost_income_elast 1.000000 0.066591 b_wifi 0.066591 1.000000 b_food 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_bus 1.000000 0.16570 asc_air 0.165696 1.00000 asc_rail 0.179743 0.50023 asc_bus_interaction_female -0.147490 -0.03034 asc_air_interaction_female 0.038030 -0.10055 asc_rail_interaction_female -0.040194 -0.05931 b_tt_car 0.249427 0.62466 b_tt_bus -0.873861 0.14575 b_tt_air -0.034928 -0.65348 b_tt_rail 2.942e-05 0.02351 b_tt_interaction_business 0.076194 0.14985 b_access 0.063371 -0.53461 b_cost -0.024663 -0.05086 b_cost_interaction_business 0.086178 -0.04663 cost_income_elast -0.084968 0.15079 b_wifi -0.068548 -0.10680 b_food 0.003095 -0.05870 asc_rail asc_bus_interaction_female asc_bus 0.17974 -0.147490 asc_air 0.50023 -0.030338 asc_rail 1.00000 -0.012572 asc_bus_interaction_female -0.01257 1.000000 asc_air_interaction_female -0.13352 0.264553 asc_rail_interaction_female -0.11104 0.366935 b_tt_car 0.64195 0.007945 b_tt_bus 0.09804 0.024582 b_tt_air -0.02056 0.057491 b_tt_rail -0.71581 -0.015735 b_tt_interaction_business 0.19708 0.035452 b_access -0.05103 -0.029221 b_cost -0.07682 -0.053677 b_cost_interaction_business 0.10762 0.040773 cost_income_elast 0.09228 0.042271 b_wifi -0.08375 -0.005249 b_food -0.06801 0.058583 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.038030 -0.040194 asc_air -0.100553 -0.059311 asc_rail -0.133517 -0.111037 asc_bus_interaction_female 0.264553 0.366935 asc_air_interaction_female 1.000000 0.620377 asc_rail_interaction_female 0.620377 1.000000 b_tt_car -0.041667 0.015881 b_tt_bus -0.082986 0.003772 b_tt_air -0.003085 0.036422 b_tt_rail 0.093479 0.049695 b_tt_interaction_business 0.010739 0.014508 b_access -0.047856 -0.022136 b_cost -0.103758 -0.066562 b_cost_interaction_business 0.088305 0.087026 cost_income_elast 0.074975 0.084144 b_wifi -0.029832 -0.026018 b_food -0.051841 -0.021157 b_tt_car b_tt_bus asc_bus 0.249427 -0.873861 asc_air 0.624662 0.145747 asc_rail 0.641953 0.098036 asc_bus_interaction_female 0.007945 0.024582 asc_air_interaction_female -0.041667 -0.082986 asc_rail_interaction_female 0.015881 0.003772 b_tt_car 1.000000 0.207566 b_tt_bus 0.207566 1.000000 b_tt_air 0.011431 0.022877 b_tt_rail 0.026321 0.049066 b_tt_interaction_business 0.002260 -0.104269 b_access -0.015607 -0.126492 b_cost 0.309044 0.231558 b_cost_interaction_business -0.180772 -0.219416 cost_income_elast 0.044536 0.119215 b_wifi -0.156102 -0.024089 b_food -0.108144 -0.065202 b_tt_air b_tt_rail asc_bus -0.034928 2.942e-05 asc_air -0.653477 0.02351 asc_rail -0.020559 -0.71581 asc_bus_interaction_female 0.057491 -0.01573 asc_air_interaction_female -0.003085 0.09348 asc_rail_interaction_female 0.036422 0.04970 b_tt_car 0.011431 0.02632 b_tt_bus 0.022877 0.04907 b_tt_air 1.000000 -0.02771 b_tt_rail -0.027714 1.00000 b_tt_interaction_business -0.091423 -0.16997 b_access 0.306117 -0.11439 b_cost 0.164962 0.28349 b_cost_interaction_business -7.365e-05 -0.23093 cost_income_elast -0.116409 -0.07016 b_wifi -0.094765 -0.12205 b_food -0.112237 -0.09044 b_tt_interaction_business b_access asc_bus 0.076194 0.06337 asc_air 0.149849 -0.53461 asc_rail 0.197081 -0.05103 asc_bus_interaction_female 0.035452 -0.02922 asc_air_interaction_female 0.010739 -0.04786 asc_rail_interaction_female 0.014508 -0.02214 b_tt_car 0.002260 -0.01561 b_tt_bus -0.104269 -0.12649 b_tt_air -0.091423 0.30612 b_tt_rail -0.169969 -0.11439 b_tt_interaction_business 1.000000 0.04759 b_access 0.047588 1.00000 b_cost -0.366279 0.09451 b_cost_interaction_business 0.664397 0.06335 cost_income_elast 0.021971 -0.06529 b_wifi -0.081514 0.01132 b_food -0.027768 -0.01187 b_cost b_cost_interaction_business asc_bus -0.02466 0.086178 asc_air -0.05086 -0.046628 asc_rail -0.07682 0.107621 asc_bus_interaction_female -0.05368 0.040773 asc_air_interaction_female -0.10376 0.088305 asc_rail_interaction_female -0.06656 0.087026 b_tt_car 0.30904 -0.180772 b_tt_bus 0.23156 -0.219416 b_tt_air 0.16496 -7.365e-05 b_tt_rail 0.28349 -0.230931 b_tt_interaction_business -0.36628 0.664397 b_access 0.09451 0.063349 b_cost 1.00000 -0.675147 b_cost_interaction_business -0.67515 1.000000 cost_income_elast -0.30527 0.037712 b_wifi -0.19697 0.001361 b_food -0.13918 0.012033 cost_income_elast b_wifi asc_bus -0.08497 -0.068548 asc_air 0.15079 -0.106796 asc_rail 0.09228 -0.083747 asc_bus_interaction_female 0.04227 -0.005249 asc_air_interaction_female 0.07498 -0.029832 asc_rail_interaction_female 0.08414 -0.026018 b_tt_car 0.04454 -0.156102 b_tt_bus 0.11921 -0.024089 b_tt_air -0.11641 -0.094765 b_tt_rail -0.07016 -0.122048 b_tt_interaction_business 0.02197 -0.081514 b_access -0.06529 0.011317 b_cost -0.30527 -0.196966 b_cost_interaction_business 0.03771 0.001361 cost_income_elast 1.00000 0.028943 b_wifi 0.02894 1.000000 b_food -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 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) }