Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : MNL_SP_covariates Model description : MNL model with socio-demographics on mode choice SP data Model run at : 2023-05-10 19:49:47 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -2.818735 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) : 00:00:8.04 pre-estimation : 00:00:1.7 estimation : 00:00:1.92 initial estimation : 00:00:1.78 estimation after rescaling : 00:00:0.14 post-estimation : 00:00:4.42 Iterations : 28 initial estimation : 27 estimation after rescaling : 1 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 0.286548 0.582954 0.4915 0.549516 0.5215 asc_air -0.903342 0.373538 -2.4183 0.361572 -2.4984 asc_rail -2.092649 0.353361 -5.9221 0.351094 -5.9604 asc_bus_shift_female 0.340176 0.132784 2.5619 0.145287 2.3414 asc_air_shift_female 0.268177 0.091507 2.9307 0.095284 2.8145 asc_rail_shift_female 0.189615 0.073759 2.5707 0.078169 2.4257 b_tt_car -0.013107 7.3441e-04 -17.8476 7.6776e-04 -17.0722 b_tt_bus -0.021266 0.001598 -13.3110 0.001518 -14.0093 b_tt_air -0.016578 0.002774 -5.9769 0.002671 -6.2073 b_tt_rail -0.007051 0.001811 -3.8930 0.001765 -3.9960 b_tt_shift_business -0.006234 6.0074e-04 -10.3767 5.9078e-04 -10.5515 b_access -0.021153 0.002865 -7.3843 0.002706 -7.8156 b_cost -0.076190 0.002097 -36.3311 0.002095 -36.3628 b_cost_shift_business 0.033381 0.002739 12.1851 0.002572 12.9790 cost_income_elast -0.613795 0.030093 -20.3966 0.030604 -20.0559 b_no_frills 0.000000 NA NA NA NA b_wifi 1.026713 0.056142 18.2877 0.057815 17.7586 b_food 0.422069 0.055027 7.6702 0.056465 7.4749 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_shift_female asc_bus 0.339835 0.035794 0.032560 -0.010456 asc_air 0.035794 0.139531 0.060929 -0.001527 asc_rail 0.032560 0.060929 0.124864 -0.001253 asc_bus_shift_female -0.010456 -0.001527 -0.001253 0.017632 asc_air_shift_female -0.001257 -0.004050 -0.001955 0.003078 asc_rail_shift_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 -7.2503e-04 -3.614e-05 -1.279e-06 b_tt_rail 1.105e-05 2.427e-05 -4.7570e-04 -1.719e-06 b_tt_shift_business 7.427e-06 1.031e-05 1.915e-05 1.057e-06 b_access -2.550e-05 -6.0647e-04 -4.581e-05 3.162e-06 b_cost 1.247e-05 -5.521e-05 -3.943e-05 -9.239e-06 b_cost_shift_business 3.794e-05 -6.534e-05 2.268e-05 1.371e-05 cost_income_elast -9.9050e-04 0.001331 5.5308e-04 -1.6237e-04 b_wifi -3.6569e-04 -0.002675 -0.001880 1.645e-05 b_food -3.2660e-04 -0.001676 -0.001756 -6.062e-06 asc_air_shift_female asc_rail_shift_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_shift_female 0.003078 0.002836 -6.434e-07 3.862e-06 asc_air_shift_female 0.008373 0.003520 -1.002e-06 -1.690e-06 asc_rail_shift_female 0.003520 0.005440 -6.108e-07 -5.673e-07 b_tt_car -1.002e-06 -6.108e-07 5.394e-07 2.066e-07 b_tt_bus -1.690e-06 -5.673e-07 2.066e-07 2.552e-06 b_tt_air -2.577e-07 -2.067e-06 -6.577e-08 -5.452e-08 b_tt_rail 1.554e-07 2.438e-08 -1.586e-08 2.637e-08 b_tt_shift_business -8.549e-07 -3.060e-07 -3.669e-08 -7.175e-08 b_access -3.012e-06 -3.484e-06 -7.030e-08 -2.594e-07 b_cost -5.142e-06 -3.640e-06 4.869e-07 6.145e-07 b_cost_shift_business 2.981e-08 1.414e-06 -4.371e-07 -7.186e-07 cost_income_elast 7.664e-06 6.540e-06 -6.249e-07 3.190e-06 b_wifi 7.076e-05 1.602e-05 -6.794e-06 -6.055e-06 b_food 4.013e-05 -4.535e-07 -3.611e-06 -2.639e-06 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.647e-05 1.105e-05 7.427e-06 -2.550e-05 asc_air -7.2503e-04 2.427e-05 1.031e-05 -6.0647e-04 asc_rail -3.614e-05 -4.7570e-04 1.915e-05 -4.581e-05 asc_bus_shift_female -1.279e-06 -1.719e-06 1.057e-06 3.162e-06 asc_air_shift_female -2.577e-07 1.554e-07 -8.549e-07 -3.012e-06 asc_rail_shift_female -2.067e-06 2.438e-08 -3.060e-07 -3.484e-06 b_tt_car -6.577e-08 -1.586e-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_shift_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_shift_business -1.221e-07 -6.923e-07 1.187e-06 5.588e-07 cost_income_elast -9.569e-06 -3.335e-06 2.741e-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_shift_business cost_income_elast b_wifi asc_bus 1.247e-05 3.794e-05 -9.9050e-04 -3.6569e-04 asc_air -5.521e-05 -6.534e-05 0.001331 -0.002675 asc_rail -3.943e-05 2.268e-05 5.5308e-04 -0.001880 asc_bus_shift_female -9.239e-06 1.371e-05 -1.6237e-04 1.645e-05 asc_air_shift_female -5.142e-06 2.981e-08 7.664e-06 7.076e-05 asc_rail_shift_female -3.640e-06 1.414e-06 6.540e-06 1.602e-05 b_tt_car 4.869e-07 -4.371e-07 -6.249e-07 -6.794e-06 b_tt_bus 6.145e-07 -7.186e-07 3.190e-06 -6.055e-06 b_tt_air 1.095e-06 -1.221e-07 -9.569e-06 -4.592e-06 b_tt_rail 8.953e-07 -6.923e-07 -3.335e-06 -1.038e-05 b_tt_shift_business -3.916e-07 1.187e-06 2.741e-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_shift_business -3.560e-06 7.505e-06 3.246e-06 -8.057e-07 cost_income_elast -2.175e-05 3.246e-06 9.0559e-04 1.1249e-04 b_wifi -2.211e-05 -8.057e-07 1.1249e-04 0.003152 b_food -1.225e-05 -5.287e-07 8.493e-05 0.001697 b_food asc_bus -3.2660e-04 asc_air -0.001676 asc_rail -0.001756 asc_bus_shift_female -6.062e-06 asc_air_shift_female 4.013e-05 asc_rail_shift_female -4.535e-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_shift_business -7.860e-07 b_access -4.785e-06 b_cost -1.225e-05 b_cost_shift_business -5.287e-07 cost_income_elast 8.493e-05 b_wifi 0.001697 b_food 0.003028 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.301968 0.032922 0.034678 -0.011775 asc_air 0.032922 0.130734 0.063502 -0.001594 asc_rail 0.034678 0.063502 0.123267 -6.4134e-04 asc_bus_shift_female -0.011775 -0.001594 -6.4134e-04 0.021108 asc_air_shift_female 0.001991 -0.003464 -0.004467 0.003662 asc_rail_shift_female -0.001726 -0.001676 -0.003047 0.004167 b_tt_car 1.0523e-04 1.7341e-04 1.7304e-04 8.860e-07 b_tt_bus -7.2894e-04 8.000e-05 5.225e-05 5.421e-06 b_tt_air -5.126e-05 -6.3103e-04 -1.928e-05 2.231e-05 b_tt_rail 2.601e-08 1.500e-05 -4.4346e-04 -4.034e-06 b_tt_shift_business 2.474e-05 3.201e-05 4.088e-05 3.043e-06 b_access 9.425e-05 -5.2316e-04 -4.849e-05 -1.149e-05 b_cost -2.841e-05 -3.853e-05 -5.651e-05 -1.634e-05 b_cost_shift_business 1.2181e-04 -4.337e-05 9.718e-05 1.524e-05 cost_income_elast -0.001429 0.001669 9.9151e-04 1.8800e-04 b_wifi -0.002178 -0.002232 -0.001700 -4.409e-05 b_food 9.604e-05 -0.001198 -0.001348 4.8059e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.001991 -0.001726 1.0523e-04 -7.2894e-04 asc_air -0.003464 -0.001676 1.7341e-04 8.000e-05 asc_rail -0.004467 -0.003047 1.7304e-04 5.225e-05 asc_bus_shift_female 0.003662 0.004167 8.860e-07 5.421e-06 asc_air_shift_female 0.009079 0.004621 -3.048e-06 -1.200e-05 asc_rail_shift_female 0.004621 0.006110 9.530e-07 4.473e-07 b_tt_car -3.048e-06 9.530e-07 5.895e-07 2.419e-07 b_tt_bus -1.200e-05 4.473e-07 2.419e-07 2.304e-06 b_tt_air -7.859e-07 7.603e-06 2.344e-08 9.275e-08 b_tt_rail 1.572e-05 6.854e-06 3.566e-08 1.314e-07 b_tt_shift_business 6.046e-07 6.700e-07 1.020e-09 -9.351e-08 b_access -1.234e-05 -4.683e-06 -3.243e-08 -5.197e-07 b_cost -2.072e-05 -1.090e-05 4.972e-07 7.365e-07 b_cost_shift_business 2.164e-05 1.750e-05 -3.570e-07 -8.567e-07 cost_income_elast 2.1861e-04 2.0129e-04 1.047e-06 5.539e-06 b_wifi -1.6432e-04 -1.1758e-04 -6.929e-06 -2.115e-06 b_food -2.7890e-04 -9.337e-05 -4.688e-06 -5.589e-06 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -5.126e-05 2.601e-08 2.474e-05 9.425e-05 asc_air -6.3103e-04 1.500e-05 3.201e-05 -5.2316e-04 asc_rail -1.928e-05 -4.4346e-04 4.088e-05 -4.849e-05 asc_bus_shift_female 2.231e-05 -4.034e-06 3.043e-06 -1.149e-05 asc_air_shift_female -7.859e-07 1.572e-05 6.046e-07 -1.234e-05 asc_rail_shift_female 7.603e-06 6.854e-06 6.700e-07 -4.683e-06 b_tt_car 2.344e-08 3.566e-08 1.020e-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_shift_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 5.360e-07 b_cost_shift_business -4.778e-10 -1.048e-06 1.010e-06 4.410e-07 cost_income_elast -9.514e-06 -3.788e-06 3.972e-07 -5.408e-06 b_wifi -1.463e-05 -1.245e-05 -2.784e-06 1.771e-06 b_food -1.692e-05 -9.011e-06 -9.262e-07 -1.814e-06 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -2.841e-05 1.2181e-04 -0.001429 -0.002178 asc_air -3.853e-05 -4.337e-05 0.001669 -0.002232 asc_rail -5.651e-05 9.718e-05 9.9151e-04 -0.001700 asc_bus_shift_female -1.634e-05 1.524e-05 1.8800e-04 -4.409e-05 asc_air_shift_female -2.072e-05 2.164e-05 2.1861e-04 -1.6432e-04 asc_rail_shift_female -1.090e-05 1.750e-05 2.0129e-04 -1.1758e-04 b_tt_car 4.972e-07 -3.570e-07 1.047e-06 -6.929e-06 b_tt_bus 7.365e-07 -8.567e-07 5.539e-06 -2.115e-06 b_tt_air 9.231e-07 -4.778e-10 -9.514e-06 -1.463e-05 b_tt_rail 1.048e-06 -1.048e-06 -3.788e-06 -1.245e-05 b_tt_shift_business -4.534e-07 1.010e-06 3.972e-07 -2.784e-06 b_access 5.360e-07 4.410e-07 -5.408e-06 1.771e-06 b_cost 4.390e-06 -3.638e-06 -1.957e-05 -2.386e-05 b_cost_shift_business -3.638e-06 6.615e-06 2.967e-06 2.032e-07 cost_income_elast -1.957e-05 2.967e-06 9.3662e-04 5.120e-05 b_wifi -2.386e-05 2.032e-07 5.120e-05 0.003343 b_food -1.647e-05 1.748e-06 -2.371e-05 0.001794 b_food asc_bus 9.604e-05 asc_air -0.001198 asc_rail -0.001348 asc_bus_shift_female 4.8059e-04 asc_air_shift_female -2.7890e-04 asc_rail_shift_female -9.337e-05 b_tt_car -4.688e-06 b_tt_bus -5.589e-06 b_tt_air -1.692e-05 b_tt_rail -9.011e-06 b_tt_shift_business -9.262e-07 b_access -1.814e-06 b_cost -1.647e-05 b_cost_shift_business 1.748e-06 cost_income_elast -2.371e-05 b_wifi 0.001794 b_food 0.003188 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.00000 0.16438 0.15806 -0.135073 asc_air 0.16438 1.00000 0.46161 -0.030796 asc_rail 0.15806 0.46161 1.00000 -0.026705 asc_bus_shift_female -0.13507 -0.03080 -0.02670 1.000000 asc_air_shift_female -0.02357 -0.11848 -0.06047 0.253328 asc_rail_shift_female -0.03315 -0.05411 -0.10585 0.289615 b_tt_car 0.24314 0.60398 0.63780 -0.006597 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_shift_business 0.02121 0.04596 0.09022 0.013250 b_access -0.01527 -0.56678 -0.04526 0.008313 b_cost 0.01020 -0.07048 -0.05321 -0.033180 b_cost_shift_business 0.02376 -0.06385 0.02343 0.037690 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 -8.2967e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.023569 -0.033152 0.243137 -0.894383 asc_air -0.118476 -0.054109 0.603979 0.113473 asc_rail -0.060472 -0.105852 0.637800 0.100299 asc_bus_shift_female 0.253328 0.289615 -0.006597 0.018204 asc_air_shift_female 1.000000 0.521489 -0.014909 -0.011563 asc_rail_shift_female 0.521489 1.000000 -0.011275 -0.004814 b_tt_car -0.014909 -0.011275 1.000000 0.176047 b_tt_bus -0.011563 -0.004814 0.176047 1.000000 b_tt_air -0.001015 -0.010101 -0.032290 -0.012303 b_tt_rail 9.3745e-04 1.8250e-04 -0.011927 0.009112 b_tt_shift_business -0.015551 -0.006905 -0.083171 -0.074758 b_access -0.011492 -0.016487 -0.033419 -0.056673 b_cost -0.026794 -0.023535 0.316139 0.183401 b_cost_shift_business 1.1891e-04 0.006996 -0.217247 -0.164197 cost_income_elast 0.002783 0.002947 -0.028276 0.066342 b_wifi 0.013773 0.003869 -0.164784 -0.067502 b_food 0.007971 -1.1173e-04 -0.089357 -0.030019 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.010189 0.010462 0.021207 -0.015270 asc_air -0.699795 0.035873 0.045959 -0.566781 asc_rail -0.036878 -0.743261 0.090216 -0.045255 asc_bus_shift_female -0.003472 -0.007148 0.013250 0.008313 asc_air_shift_female -0.001015 9.3745e-04 -0.015551 -0.011492 asc_rail_shift_female -0.010101 1.8250e-04 -0.006905 -0.016487 b_tt_car -0.032290 -0.011927 -0.083171 -0.033419 b_tt_bus -0.012303 0.009112 -0.074758 -0.056673 b_tt_air 1.000000 -0.053496 -0.041375 0.334810 b_tt_rail -0.053496 1.000000 -0.110298 -0.135702 b_tt_shift_business -0.041375 -0.110298 1.000000 0.055161 b_access 0.334810 -0.135702 0.055161 1.000000 b_cost 0.188327 0.235714 -0.310839 0.088745 b_cost_shift_business -0.016067 -0.139534 0.721313 0.071212 cost_income_elast -0.114649 -0.061185 0.015165 -0.087300 b_wifi -0.029490 -0.102069 -0.065995 -0.034912 b_food -0.041280 -0.046995 -0.023777 -0.030354 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.01020 0.023760 -0.056462 -0.011174 asc_air -0.07048 -0.063853 0.118448 -0.127563 asc_rail -0.05321 0.023434 0.052012 -0.094750 asc_bus_shift_female -0.03318 0.037690 -0.040634 0.002207 asc_air_shift_female -0.02679 1.1891e-04 0.002783 0.013773 asc_rail_shift_female -0.02354 0.006996 0.002947 0.003869 b_tt_car 0.31614 -0.217247 -0.028276 -0.164784 b_tt_bus 0.18340 -0.164197 0.066342 -0.067502 b_tt_air 0.18833 -0.016067 -0.114649 -0.029490 b_tt_rail 0.23571 -0.139534 -0.061185 -0.102069 b_tt_shift_business -0.31084 0.721313 0.015165 -0.065995 b_access 0.08875 0.071212 -0.087300 -0.034912 b_cost 1.00000 -0.619623 -0.344639 -0.187812 b_cost_shift_business -0.61962 1.000000 0.039374 -0.005238 cost_income_elast -0.34464 0.039374 1.000000 0.066584 b_wifi -0.18781 -0.005238 0.066584 1.000000 b_food -0.10618 -0.003507 0.051289 0.549323 b_food asc_bus -0.010181 asc_air -0.081558 asc_rail -0.090312 asc_bus_shift_female -8.2967e-04 asc_air_shift_female 0.007971 asc_rail_shift_female -1.1173e-04 b_tt_car -0.089357 b_tt_bus -0.030019 b_tt_air -0.041280 b_tt_rail -0.046995 b_tt_shift_business -0.023777 b_access -0.030354 b_cost -0.106178 b_cost_shift_business -0.003507 cost_income_elast 0.051289 b_wifi 0.549323 b_food 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.16569 0.17974 -0.147488 asc_air 0.165694 1.00000 0.50023 -0.030337 asc_rail 0.179743 0.50023 1.00000 -0.012573 asc_bus_shift_female -0.147488 -0.03034 -0.01257 1.000000 asc_air_shift_female 0.038032 -0.10055 -0.13352 0.264551 asc_rail_shift_female -0.040192 -0.05931 -0.11104 0.366934 b_tt_car 0.249424 0.62466 0.64195 0.007943 b_tt_bus -0.873861 0.14575 0.09803 0.024580 b_tt_air -0.034930 -0.65348 -0.02056 0.057489 b_tt_rail 2.683e-05 0.02351 -0.71581 -0.015734 b_tt_shift_business 0.076194 0.14985 0.19708 0.035451 b_access 0.063373 -0.53461 -0.05103 -0.029222 b_cost -0.024673 -0.05085 -0.07682 -0.053678 b_cost_shift_business 0.086184 -0.04663 0.10762 0.040772 cost_income_elast -0.084972 0.15079 0.09228 0.042281 b_wifi -0.068545 -0.10679 -0.08375 -0.005249 b_food 0.003095 -0.05870 -0.06801 0.058583 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.038032 -0.040192 0.249424 -0.873861 asc_air -0.100552 -0.059311 0.624662 0.145748 asc_rail -0.133517 -0.111036 0.641951 0.098035 asc_bus_shift_female 0.264551 0.366934 0.007943 0.024580 asc_air_shift_female 1.000000 0.620378 -0.041670 -0.082990 asc_rail_shift_female 0.620378 1.000000 0.015879 0.003769 b_tt_car -0.041670 0.015879 1.000000 0.207569 b_tt_bus -0.082990 0.003769 0.207569 1.000000 b_tt_air -0.003088 0.036420 0.011430 0.022878 b_tt_rail 0.093476 0.049693 0.026322 0.049070 b_tt_shift_business 0.010740 0.014509 0.002249 -0.104274 b_access -0.047857 -0.022136 -0.015608 -0.126493 b_cost -0.103761 -0.066565 0.309047 0.231571 b_cost_shift_business 0.088303 0.087026 -0.180779 -0.219426 cost_income_elast 0.074968 0.084141 0.044546 0.119223 b_wifi -0.029829 -0.026016 -0.156103 -0.024094 b_food -0.051838 -0.021154 -0.108142 -0.065202 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.034930 2.683e-05 0.076194 0.06337 asc_air -0.653477 0.02351 0.149845 -0.53461 asc_rail -0.020559 -0.71581 0.197079 -0.05103 asc_bus_shift_female 0.057489 -0.01573 0.035451 -0.02922 asc_air_shift_female -0.003088 0.09348 0.010740 -0.04786 asc_rail_shift_female 0.036420 0.04969 0.014509 -0.02214 b_tt_car 0.011430 0.02632 0.002249 -0.01561 b_tt_bus 0.022878 0.04907 -0.104274 -0.12649 b_tt_air 1.000000 -0.02771 -0.091424 0.30612 b_tt_rail -0.027715 1.00000 -0.169974 -0.11438 b_tt_shift_business -0.091424 -0.16997 1.000000 0.04759 b_access 0.306116 -0.11438 0.047587 1.00000 b_cost 0.164954 0.28349 -0.366291 0.09451 b_cost_shift_business -6.956e-05 -0.23094 0.664402 0.06335 cost_income_elast -0.116397 -0.07015 0.021966 -0.06529 b_wifi -0.094765 -0.12205 -0.081505 0.01132 b_food -0.112234 -0.09044 -0.027765 -0.01187 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.02467 0.086184 -0.08497 -0.068545 asc_air -0.05085 -0.046633 0.15079 -0.106794 asc_rail -0.07682 0.107622 0.09228 -0.083746 asc_bus_shift_female -0.05368 0.040772 0.04228 -0.005249 asc_air_shift_female -0.10376 0.088303 0.07497 -0.029829 asc_rail_shift_female -0.06656 0.087026 0.08414 -0.026016 b_tt_car 0.30905 -0.180779 0.04455 -0.156103 b_tt_bus 0.23157 -0.219426 0.11922 -0.024094 b_tt_air 0.16495 -6.956e-05 -0.11640 -0.094765 b_tt_rail 0.28349 -0.230937 -0.07015 -0.122048 b_tt_shift_business -0.36629 0.664402 0.02197 -0.081505 b_access 0.09451 0.063349 -0.06529 0.011318 b_cost 1.00000 -0.675158 -0.30523 -0.196970 b_cost_shift_business -0.67516 1.000000 0.03770 0.001366 cost_income_elast -0.30523 0.037700 1.00000 0.028935 b_wifi -0.19697 0.001366 0.02894 1.000000 b_food -0.13918 0.012034 -0.01372 0.549573 b_food asc_bus 0.003095 asc_air -0.058699 asc_rail -0.068009 asc_bus_shift_female 0.058583 asc_air_shift_female -0.051838 asc_rail_shift_female -0.021154 b_tt_car -0.108142 b_tt_bus -0.065202 b_tt_air -0.112234 b_tt_rail -0.090441 b_tt_shift_business -0.027765 b_access -0.011871 b_cost -0.139181 b_cost_shift_business 0.012034 cost_income_elast -0.013720 b_wifi 0.549573 b_food 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2353133 464 0.2378481 146 0.2461382 181 0.2489948 293 0.2527687 186 0.2576641 276 0.2616339 307 0.2693772 367 0.2717647 441 0.2744254 498 0.2809905 317 0.2816496 434 0.2857832 161 0.2870130 259 0.2980556 133 0.3012285 183 0.3032747 147 0.3048891 447 0.3085429 370 0.3092377 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.061909 0.286548 0.224639 asc_air 0.238310 -0.903342 -1.141652 asc_rail -1.481374 -2.092649 -0.611275 asc_bus_shift_female 0.000000 0.340176 0.340176 asc_air_shift_female 0.000000 0.268177 0.268177 asc_rail_shift_female 0.000000 0.189615 0.189615 b_tt_car -0.011602 -0.013107 -0.001505 b_tt_bus -0.017367 -0.021266 -0.003899 b_tt_air -0.019484 -0.016578 0.002906 b_tt_rail -0.006365 -0.007051 -6.8620e-04 b_tt_shift_business 0.000000 -0.006234 -0.006234 b_access -0.023193 -0.021153 0.002041 b_cost -0.058756 -0.076190 -0.017433 b_cost_shift_business 0.000000 0.033381 0.033381 cost_income_elast 0.000000 -0.613795 -0.613795 b_no_frills 0.000000 0.000000 0.000000 b_wifi 0.937557 1.026713 0.089155 b_food 0.409558 0.422069 0.012511 Settings and functions used in model definition: apollo_control -------------- Value modelName "MNL_SP_covariates" modelDescr "MNL model with socio-demographics on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling in estimation --------------------- Value asc_bus 0.286547989 asc_air 0.903342191 asc_rail 2.092651140 asc_bus_shift_female 0.340176141 asc_air_shift_female 0.268177409 asc_rail_shift_female 0.189615476 b_tt_car 0.013107365 b_tt_bus 0.021265942 b_tt_air 0.016577781 b_tt_rail 0.007051144 b_tt_shift_business 0.006233673 b_access 0.021152622 b_cost 0.076189994 b_cost_shift_business 0.033381019 cost_income_elast 0.613794377 b_wifi 1.026712181 b_food 0.422068919 Scaling used in computing Hessian --------------------------------- Value asc_bus 0.286547959 asc_air 0.903341947 asc_rail 2.092649139 asc_bus_shift_female 0.340176129 asc_air_shift_female 0.268177418 asc_rail_shift_female 0.189615482 b_tt_car 0.013107390 b_tt_bus 0.021265997 b_tt_air 0.016577777 b_tt_rail 0.007051141 b_tt_shift_business 0.006233676 b_access 0.021152615 b_cost 0.076189587 b_cost_shift_business 0.033381041 cost_income_elast 0.613794625 b_wifi 1.026712638 b_food 0.422068980 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_shift_female * female asc_air_value = asc_air + asc_air_shift_female * female asc_rail_value = asc_rail + asc_rail_shift_female * female b_tt_car_value = b_tt_car + b_tt_shift_business * business b_tt_bus_value = b_tt_bus + b_tt_shift_business * business b_tt_air_value = b_tt_air + b_tt_shift_business * business b_tt_rail_value = b_tt_rail + b_tt_shift_business * business b_cost_value = ( b_cost + b_cost_shift_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) }