Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : NL_three_levels Model description : Three-level NL model with socio-demographics on mode choice SP data Model run at : 2023-05-10 20:04:14 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -4.25074 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) : -4830.94 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : -6706.94 LL(final) : -4770.48 Rho-squared vs equal shares : 0.418 Adj.Rho-squared vs equal shares : 0.4156 Rho-squared vs observed shares : 0.2887 Adj.Rho-squared vs observed shares : 0.2863 AIC : 9578.95 BIC : 9709.17 Estimated parameters : 19 Time taken (hh:mm:ss) : 00:00:27.65 pre-estimation : 00:00:1.09 estimation : 00:00:13.2 initial estimation : 00:00:12.17 estimation after rescaling : 00:00:1.03 post-estimation : 00:00:13.35 Iterations : 32 initial estimation : 29 estimation after rescaling : 3 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. Rob.t.rat.(0) Rob.t.rat.(1) asc_car 0.000000 NA NA NA NA NA NA asc_bus 0.414336 0.457899 0.9049 -1.279 0.434283 0.9541 -1.349 asc_air -0.715545 0.296526 -2.4131 -5.785 0.289306 -2.4733 -5.930 asc_rail -1.647888 0.296224 -5.5630 -8.939 0.286389 -5.7540 -9.246 asc_bus_shift_female 0.274687 0.107651 2.5516 -6.738 0.116094 2.3661 -6.248 asc_air_shift_female 0.237113 0.076734 3.0901 -9.942 0.077401 3.0634 -9.856 asc_rail_shift_female 0.179645 0.067700 2.6535 -12.117 0.068223 2.6332 -12.025 b_tt_car -0.010515 7.2695e-04 -14.4652 -1390.085 7.3002e-04 -14.4043 -1384.228 b_tt_bus -0.016903 0.001311 -12.8974 -775.913 0.001263 -13.3843 -805.210 b_tt_air -0.012112 0.001957 -6.1898 -517.221 0.001983 -6.1078 -510.368 b_tt_rail -0.005246 0.001357 -3.8649 -740.579 0.001324 -3.9623 -759.253 b_tt_shift_business -0.005882 5.0178e-04 -11.7231 -2004.630 4.6691e-04 -12.5986 -2154.342 b_access -0.016827 0.002032 -8.2822 -500.479 0.001983 -8.4859 -512.790 b_cost -0.058240 0.002400 -24.2658 -440.914 0.002435 -23.9175 -434.585 b_cost_shift_business 0.025466 0.002260 11.2679 -431.197 0.002137 11.9174 -456.052 cost_income_elast -0.626050 0.031247 -20.0355 -52.039 0.032313 -19.3744 -50.322 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.756579 0.045919 16.4765 -5.301 0.047168 16.0400 -5.161 b_food 0.323530 0.039245 8.2438 -17.237 0.042274 7.6531 -16.002 lambda_PT 0.695288 0.038892 17.8775 -7.835 0.038105 18.2466 -7.997 lambda_fastPT 0.586193 0.030397 19.2847 -13.613 0.029296 20.0095 -14.125 Nesting structure for model component : Nest: root (1) |-------Alternative: car '-Nest: PT (0.6953) |----Alternative: bus '-Nest: fastPT (0.5862) |-Alternative: air '-Alternative: rail Overview of choices for NL 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 0.209672 0.035790 0.033788 -0.006721 asc_air 0.035790 0.087928 0.051265 -0.001737 asc_rail 0.033788 0.051265 0.087749 -0.001708 asc_bus_shift_female -0.006721 -0.001737 -0.001708 0.011589 asc_air_shift_female -0.001466 -0.002902 -0.002050 0.003309 asc_rail_shift_female -0.001572 -0.001730 -0.002337 0.003200 b_tt_car 1.0591e-04 1.4350e-04 1.5182e-04 -1.785e-06 b_tt_bus -4.7957e-04 4.143e-05 5.126e-05 -6.854e-07 b_tt_air -1.107e-05 -3.4543e-04 -1.459e-06 -2.436e-06 b_tt_rail 7.059e-06 3.644e-06 -2.5978e-04 -1.846e-06 b_tt_shift_business 5.861e-06 1.017e-05 1.624e-05 3.382e-07 b_access -9.427e-06 -2.9316e-04 -1.866e-05 -4.071e-07 b_cost -6.079e-06 -1.806e-05 4.144e-05 -1.491e-05 b_cost_shift_business 3.768e-05 -4.367e-05 -1.502e-05 1.297e-05 cost_income_elast -8.2123e-04 0.001055 3.8827e-04 -1.5819e-04 b_wifi -2.2816e-04 -0.001441 -0.002006 1.3810e-04 b_food -2.2221e-04 -9.2646e-04 -0.001284 4.275e-05 lambda_PT 1.8174e-04 -4.2721e-04 -0.001024 2.3196e-04 lambda_fastPT -1.3418e-04 -1.7227e-04 -0.001067 1.3084e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.001466 -0.001572 1.0591e-04 -4.7957e-04 asc_air -0.002902 -0.001730 1.4350e-04 4.143e-05 asc_rail -0.002050 -0.002337 1.5182e-04 5.126e-05 asc_bus_shift_female 0.003309 0.003200 -1.785e-06 -6.854e-07 asc_air_shift_female 0.005888 0.003749 -1.319e-06 -2.331e-06 asc_rail_shift_female 0.003749 0.004583 -6.158e-07 -8.519e-07 b_tt_car -1.319e-06 -6.158e-07 5.284e-07 2.444e-07 b_tt_bus -2.331e-06 -8.519e-07 2.444e-07 1.718e-06 b_tt_air -1.361e-06 -1.431e-06 8.089e-08 1.750e-07 b_tt_rail -6.304e-07 -1.837e-07 3.664e-08 9.420e-08 b_tt_shift_business -7.166e-07 -3.278e-07 -1.670e-08 -3.770e-08 b_access -2.896e-06 -2.479e-06 8.618e-08 9.244e-08 b_cost -8.208e-06 -3.777e-06 7.319e-07 1.233e-06 b_cost_shift_business 2.440e-06 1.353e-06 -4.880e-07 -9.275e-07 cost_income_elast 1.434e-05 -4.736e-06 -2.814e-07 3.810e-06 b_wifi 1.1039e-04 4.139e-05 -9.495e-06 -1.388e-05 b_food 4.386e-05 1.463e-05 -4.206e-06 -5.476e-06 lambda_PT 7.960e-05 3.328e-05 -7.735e-06 -1.743e-05 lambda_fastPT 8.337e-05 3.217e-05 -6.416e-06 -1.021e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.107e-05 7.059e-06 5.861e-06 -9.427e-06 asc_air -3.4543e-04 3.644e-06 1.017e-05 -2.9316e-04 asc_rail -1.459e-06 -2.5978e-04 1.624e-05 -1.866e-05 asc_bus_shift_female -2.436e-06 -1.846e-06 3.382e-07 -4.071e-07 asc_air_shift_female -1.361e-06 -6.304e-07 -7.166e-07 -2.896e-06 asc_rail_shift_female -1.431e-06 -1.837e-07 -3.278e-07 -2.479e-06 b_tt_car 8.089e-08 3.664e-08 -1.670e-08 8.618e-08 b_tt_bus 1.750e-07 9.420e-08 -3.770e-08 9.244e-08 b_tt_air 3.829e-06 -5.420e-08 -3.955e-08 1.533e-06 b_tt_rail -5.420e-08 1.842e-06 -8.213e-08 -1.503e-07 b_tt_shift_business -3.955e-08 -8.213e-08 2.518e-07 6.523e-08 b_access 1.533e-06 -1.503e-07 6.523e-08 4.128e-06 b_cost 1.363e-06 8.489e-07 -1.938e-07 1.208e-06 b_cost_shift_business -4.126e-07 -5.813e-07 6.950e-07 -8.699e-08 cost_income_elast -7.790e-06 -2.186e-06 -1.155e-07 -6.596e-06 b_wifi -1.323e-05 -8.506e-06 -2.688e-06 -1.475e-05 b_food -6.578e-06 -3.668e-06 -1.107e-06 -6.854e-06 lambda_PT -9.582e-06 -5.909e-06 5.824e-07 -1.242e-05 lambda_fastPT -1.249e-05 -4.362e-06 -1.790e-06 -1.290e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -6.079e-06 3.768e-05 -8.2123e-04 -2.2816e-04 asc_air -1.806e-05 -4.367e-05 0.001055 -0.001441 asc_rail 4.144e-05 -1.502e-05 3.8827e-04 -0.002006 asc_bus_shift_female -1.491e-05 1.297e-05 -1.5819e-04 1.3810e-04 asc_air_shift_female -8.208e-06 2.440e-06 1.434e-05 1.1039e-04 asc_rail_shift_female -3.777e-06 1.353e-06 -4.736e-06 4.139e-05 b_tt_car 7.319e-07 -4.880e-07 -2.814e-07 -9.495e-06 b_tt_bus 1.233e-06 -9.275e-07 3.810e-06 -1.388e-05 b_tt_air 1.363e-06 -4.126e-07 -7.790e-06 -1.323e-05 b_tt_rail 8.489e-07 -5.813e-07 -2.186e-06 -8.506e-06 b_tt_shift_business -1.938e-07 6.950e-07 -1.155e-07 -2.688e-06 b_access 1.208e-06 -8.699e-08 -6.596e-06 -1.475e-05 b_cost 5.761e-06 -3.708e-06 -1.691e-05 -5.556e-05 b_cost_shift_business -3.708e-06 5.108e-06 9.266e-07 1.811e-05 cost_income_elast -1.691e-05 9.266e-07 9.7637e-04 1.3315e-04 b_wifi -5.556e-05 1.811e-05 1.3315e-04 0.002109 b_food -2.395e-05 6.835e-06 8.626e-05 0.001057 lambda_PT -5.115e-05 3.366e-05 -2.1705e-04 5.9746e-04 lambda_fastPT -4.663e-05 1.759e-05 1.2242e-04 6.9588e-04 b_food lambda_PT lambda_fastPT asc_bus -2.2221e-04 1.8174e-04 -1.3418e-04 asc_air -9.2646e-04 -4.2721e-04 -1.7227e-04 asc_rail -0.001284 -0.001024 -0.001067 asc_bus_shift_female 4.275e-05 2.3196e-04 1.3084e-04 asc_air_shift_female 4.386e-05 7.960e-05 8.337e-05 asc_rail_shift_female 1.463e-05 3.328e-05 3.217e-05 b_tt_car -4.206e-06 -7.735e-06 -6.416e-06 b_tt_bus -5.476e-06 -1.743e-05 -1.021e-05 b_tt_air -6.578e-06 -9.582e-06 -1.249e-05 b_tt_rail -3.668e-06 -5.909e-06 -4.362e-06 b_tt_shift_business -1.107e-06 5.824e-07 -1.790e-06 b_access -6.854e-06 -1.242e-05 -1.290e-05 b_cost -2.395e-05 -5.115e-05 -4.663e-05 b_cost_shift_business 6.835e-06 3.366e-05 1.759e-05 cost_income_elast 8.626e-05 -2.1705e-04 1.2242e-04 b_wifi 0.001057 5.9746e-04 6.9588e-04 b_food 0.001540 2.3219e-04 2.7395e-04 lambda_PT 2.3219e-04 0.001513 4.5129e-04 lambda_fastPT 2.7395e-04 4.5129e-04 9.2397e-04 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.188602 0.029813 0.032497 -0.006150 asc_air 0.029813 0.083698 0.049456 -0.001223 asc_rail 0.032497 0.049456 0.082019 -8.2682e-04 asc_bus_shift_female -0.006150 -0.001223 -8.2682e-04 0.013478 asc_air_shift_female 0.001040 -0.002360 -0.002834 0.003259 asc_rail_shift_female -6.9211e-04 -0.001137 -0.001609 0.003587 b_tt_car 1.0081e-04 1.3821e-04 1.4524e-04 -4.955e-08 b_tt_bus -4.2633e-04 5.053e-05 4.681e-05 -3.314e-06 b_tt_air -1.234e-05 -3.2418e-04 4.768e-06 1.157e-05 b_tt_rail -1.332e-06 8.362e-07 -2.3501e-04 -2.746e-06 b_tt_shift_business 1.590e-05 1.989e-05 2.692e-05 1.414e-06 b_access 7.236e-05 -2.7652e-04 -2.724e-05 -9.642e-06 b_cost -1.336e-05 -9.009e-06 3.227e-05 -2.100e-05 b_cost_shift_business 8.466e-05 -4.233e-05 1.846e-05 1.503e-05 cost_income_elast -0.001167 0.001317 8.9534e-04 1.7445e-04 b_wifi -0.001401 -0.001525 -0.001744 9.721e-05 b_food -6.798e-05 -9.3943e-04 -0.001109 3.0232e-04 lambda_PT -3.0586e-04 -1.3391e-04 -0.001247 4.2561e-04 lambda_fastPT -3.9526e-04 -1.7006e-04 -7.3631e-04 1.8638e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.001040 -6.9211e-04 1.0081e-04 -4.2633e-04 asc_air -0.002360 -0.001137 1.3821e-04 5.053e-05 asc_rail -0.002834 -0.001609 1.4524e-04 4.681e-05 asc_bus_shift_female 0.003259 0.003587 -4.955e-08 -3.314e-06 asc_air_shift_female 0.005991 0.003967 -2.160e-06 -9.260e-06 asc_rail_shift_female 0.003967 0.004654 1.262e-06 -1.657e-06 b_tt_car -2.160e-06 1.262e-06 5.329e-07 2.645e-07 b_tt_bus -9.260e-06 -1.657e-06 2.645e-07 1.595e-06 b_tt_air -1.089e-06 3.017e-06 1.589e-07 2.479e-07 b_tt_rail 6.531e-06 1.563e-06 8.408e-08 1.720e-07 b_tt_shift_business 2.886e-07 5.159e-07 2.447e-09 -5.301e-08 b_access -6.437e-06 -2.566e-06 9.320e-08 -9.958e-08 b_cost -1.982e-05 -9.732e-06 7.719e-07 1.306e-06 b_cost_shift_business 1.414e-05 1.194e-05 -4.818e-07 -1.046e-06 cost_income_elast 2.3924e-04 1.7217e-04 8.621e-07 4.991e-06 b_wifi -3.811e-05 -6.653e-05 -9.572e-06 -1.097e-05 b_food -1.6804e-04 -8.752e-05 -4.864e-06 -7.224e-06 lambda_PT 8.192e-05 3.361e-05 -8.279e-06 -1.634e-05 lambda_fastPT 1.1407e-04 3.457e-05 -5.845e-06 -9.023e-06 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.234e-05 -1.332e-06 1.590e-05 7.236e-05 asc_air -3.2418e-04 8.362e-07 1.989e-05 -2.7652e-04 asc_rail 4.768e-06 -2.3501e-04 2.692e-05 -2.724e-05 asc_bus_shift_female 1.157e-05 -2.746e-06 1.414e-06 -9.642e-06 asc_air_shift_female -1.089e-06 6.531e-06 2.886e-07 -6.437e-06 asc_rail_shift_female 3.017e-06 1.563e-06 5.159e-07 -2.566e-06 b_tt_car 1.589e-07 8.408e-08 2.447e-09 9.320e-08 b_tt_bus 2.479e-07 1.720e-07 -5.301e-08 -9.958e-08 b_tt_air 3.933e-06 8.609e-08 -6.771e-08 1.417e-06 b_tt_rail 8.609e-08 1.753e-06 -1.115e-07 -8.524e-08 b_tt_shift_business -6.771e-08 -1.115e-07 2.180e-07 5.642e-08 b_access 1.417e-06 -8.524e-08 5.642e-08 3.932e-06 b_cost 1.369e-06 9.837e-07 -2.144e-07 1.238e-06 b_cost_shift_business -3.395e-07 -7.952e-07 5.446e-07 -1.622e-07 cost_income_elast -8.890e-06 -4.118e-06 -1.487e-07 -5.103e-06 b_wifi -1.654e-05 -1.115e-05 -3.142e-06 -8.801e-06 b_food -1.028e-05 -6.406e-06 -1.449e-06 -4.190e-06 lambda_PT -1.285e-05 -4.655e-06 4.571e-07 -1.426e-05 lambda_fastPT -1.178e-05 -5.758e-06 -1.939e-06 -1.139e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -1.336e-05 8.466e-05 -0.001167 -0.001401 asc_air -9.009e-06 -4.233e-05 0.001317 -0.001525 asc_rail 3.227e-05 1.846e-05 8.9534e-04 -0.001744 asc_bus_shift_female -2.100e-05 1.503e-05 1.7445e-04 9.721e-05 asc_air_shift_female -1.982e-05 1.414e-05 2.3924e-04 -3.811e-05 asc_rail_shift_female -9.732e-06 1.194e-05 1.7217e-04 -6.653e-05 b_tt_car 7.719e-07 -4.818e-07 8.621e-07 -9.572e-06 b_tt_bus 1.306e-06 -1.046e-06 4.991e-06 -1.097e-05 b_tt_air 1.369e-06 -3.395e-07 -8.890e-06 -1.654e-05 b_tt_rail 9.837e-07 -7.952e-07 -4.118e-06 -1.115e-05 b_tt_shift_business -2.144e-07 5.446e-07 -1.487e-07 -3.142e-06 b_access 1.238e-06 -1.622e-07 -5.103e-06 -8.801e-06 b_cost 5.930e-06 -3.816e-06 -1.859e-05 -5.500e-05 b_cost_shift_business -3.816e-06 4.566e-06 3.115e-07 1.930e-05 cost_income_elast -1.859e-05 3.115e-07 0.001044 1.4407e-04 b_wifi -5.500e-05 1.930e-05 1.4407e-04 0.002225 b_food -2.651e-05 8.310e-06 2.565e-05 0.001179 lambda_PT -5.324e-05 3.417e-05 -1.4123e-04 5.5833e-04 lambda_fastPT -4.629e-05 1.707e-05 1.8869e-04 6.4068e-04 b_food lambda_PT lambda_fastPT asc_bus -6.798e-05 -3.0586e-04 -3.9526e-04 asc_air -9.3943e-04 -1.3391e-04 -1.7006e-04 asc_rail -0.001109 -0.001247 -7.3631e-04 asc_bus_shift_female 3.0232e-04 4.2561e-04 1.8638e-04 asc_air_shift_female -1.6804e-04 8.192e-05 1.1407e-04 asc_rail_shift_female -8.752e-05 3.361e-05 3.457e-05 b_tt_car -4.864e-06 -8.279e-06 -5.845e-06 b_tt_bus -7.224e-06 -1.634e-05 -9.023e-06 b_tt_air -1.028e-05 -1.285e-05 -1.178e-05 b_tt_rail -6.406e-06 -4.655e-06 -5.758e-06 b_tt_shift_business -1.449e-06 4.571e-07 -1.939e-06 b_access -4.190e-06 -1.426e-05 -1.139e-05 b_cost -2.651e-05 -5.324e-05 -4.629e-05 b_cost_shift_business 8.310e-06 3.417e-05 1.707e-05 cost_income_elast 2.565e-05 -1.4123e-04 1.8869e-04 b_wifi 0.001179 5.5833e-04 6.4068e-04 b_food 0.001787 2.6740e-04 2.9100e-04 lambda_PT 2.6740e-04 0.001452 4.4991e-04 lambda_fastPT 2.9100e-04 4.4991e-04 8.5824e-04 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.263589 0.249097 -0.136356 asc_air 0.263589 1.000000 0.583631 -0.054402 asc_rail 0.249097 0.583631 1.000000 -0.053572 asc_bus_shift_female -0.136356 -0.054402 -0.053572 1.000000 asc_air_shift_female -0.041712 -0.127560 -0.090183 0.400550 asc_rail_shift_female -0.050709 -0.086182 -0.116510 0.439094 b_tt_car 0.318184 0.665714 0.705011 -0.022805 b_tt_bus -0.799129 0.106610 0.132048 -0.004858 b_tt_air -0.012355 -0.595308 -0.002516 -0.011563 b_tt_rail 0.011357 0.009053 -0.646068 -0.012636 b_tt_shift_business 0.025508 0.068370 0.109261 0.006262 b_access -0.010133 -0.486608 -0.031006 -0.001861 b_cost -0.005532 -0.025372 0.058289 -0.057704 b_cost_shift_business 0.036411 -0.065161 -0.022440 0.053320 cost_income_elast -0.057397 0.113838 0.041948 -0.047029 b_wifi -0.010851 -0.105807 -0.147495 0.027937 b_food -0.012365 -0.079612 -0.110488 0.010118 lambda_PT 0.010205 -0.037044 -0.088873 0.055403 lambda_fastPT -0.009641 -0.019113 -0.118554 0.039985 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.041712 -0.050709 0.31818 -0.799129 asc_air -0.127560 -0.086182 0.66571 0.106610 asc_rail -0.090183 -0.116510 0.70501 0.132048 asc_bus_shift_female 0.400550 0.439094 -0.02281 -0.004858 asc_air_shift_female 1.000000 0.721589 -0.02364 -0.023180 asc_rail_shift_female 0.721589 1.000000 -0.01251 -0.009602 b_tt_car -0.023643 -0.012512 1.00000 0.256509 b_tt_bus -0.023180 -0.009602 0.25651 1.000000 b_tt_air -0.009061 -0.010800 0.05686 0.068242 b_tt_rail -0.006053 -0.001999 0.03714 0.052952 b_tt_shift_business -0.018612 -0.009651 -0.04578 -0.057323 b_access -0.018573 -0.018025 0.05835 0.034718 b_cost -0.044570 -0.023243 0.41947 0.391904 b_cost_shift_business 0.014071 0.008841 -0.29705 -0.313136 cost_income_elast 0.005979 -0.002239 -0.01239 0.093028 b_wifi 0.031330 0.013315 -0.28444 -0.230579 b_food 0.014566 0.005506 -0.14743 -0.106475 lambda_PT 0.026674 0.012639 -0.27357 -0.341975 lambda_fastPT 0.035744 0.015632 -0.29034 -0.256301 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.012355 0.011357 0.025508 -0.010133 asc_air -0.595308 0.009053 0.068370 -0.486608 asc_rail -0.002516 -0.646068 0.109261 -0.031006 asc_bus_shift_female -0.011563 -0.012636 0.006262 -0.001861 asc_air_shift_female -0.009061 -0.006053 -0.018612 -0.018573 asc_rail_shift_female -0.010800 -0.001999 -0.009651 -0.018025 b_tt_car 0.056863 0.037136 -0.045784 0.058349 b_tt_bus 0.068242 0.052952 -0.057323 0.034718 b_tt_air 1.000000 -0.020407 -0.040275 0.385692 b_tt_rail -0.020407 1.000000 -0.120582 -0.054497 b_tt_shift_business -0.040275 -0.120582 1.000000 0.063988 b_access 0.385692 -0.054497 0.063988 1.000000 b_cost 0.290255 0.260555 -0.160888 0.247684 b_cost_shift_business -0.093294 -0.189473 0.612824 -0.018945 cost_income_elast -0.127400 -0.051539 -0.007366 -0.103895 b_wifi -0.147247 -0.136465 -0.116640 -0.158106 b_food -0.085655 -0.068855 -0.056227 -0.085959 lambda_PT -0.125909 -0.111926 0.029844 -0.157206 lambda_fastPT -0.209946 -0.105714 -0.117381 -0.208815 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.005532 0.036411 -0.057397 -0.01085 asc_air -0.025372 -0.065161 0.113838 -0.10581 asc_rail 0.058289 -0.022440 0.041948 -0.14750 asc_bus_shift_female -0.057704 0.053320 -0.047029 0.02794 asc_air_shift_female -0.044570 0.014071 0.005979 0.03133 asc_rail_shift_female -0.023243 0.008841 -0.002239 0.01332 b_tt_car 0.419465 -0.297049 -0.012388 -0.28444 b_tt_bus 0.391904 -0.313136 0.093028 -0.23058 b_tt_air 0.290255 -0.093294 -0.127400 -0.14725 b_tt_rail 0.260555 -0.189473 -0.051539 -0.13647 b_tt_shift_business -0.160888 0.612824 -0.007366 -0.11664 b_access 0.247684 -0.018945 -0.103895 -0.15811 b_cost 1.000000 -0.683630 -0.225513 -0.50409 b_cost_shift_business -0.683630 1.000000 0.013120 0.17447 cost_income_elast -0.225513 0.013120 1.000000 0.09280 b_wifi -0.504092 0.174475 0.092800 1.00000 b_food -0.254231 0.077058 0.070342 0.58648 lambda_PT -0.548000 0.382889 -0.178603 0.33455 lambda_fastPT -0.639143 0.256102 0.128893 0.49856 b_food lambda_PT lambda_fastPT asc_bus -0.012365 0.01021 -0.009641 asc_air -0.079612 -0.03704 -0.019113 asc_rail -0.110488 -0.08887 -0.118554 asc_bus_shift_female 0.010118 0.05540 0.039985 asc_air_shift_female 0.014566 0.02667 0.035744 asc_rail_shift_female 0.005506 0.01264 0.015632 b_tt_car -0.147433 -0.27357 -0.290344 b_tt_bus -0.106475 -0.34198 -0.256301 b_tt_air -0.085655 -0.12591 -0.209946 b_tt_rail -0.068855 -0.11193 -0.105714 b_tt_shift_business -0.056227 0.02984 -0.117381 b_access -0.085959 -0.15721 -0.208815 b_cost -0.254231 -0.54800 -0.639143 b_cost_shift_business 0.077058 0.38289 0.256102 cost_income_elast 0.070342 -0.17860 0.128893 b_wifi 0.586478 0.33455 0.498559 b_food 1.000000 0.15213 0.229648 lambda_PT 0.152126 1.00000 0.381741 lambda_fastPT 0.229648 0.38174 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.237289 0.261286 -0.12197 asc_air 0.237289 1.000000 0.596905 -0.03642 asc_rail 0.261286 0.596905 1.000000 -0.02487 asc_bus_shift_female -0.121972 -0.036422 -0.024868 1.00000 asc_air_shift_female 0.030930 -0.105398 -0.127836 0.36271 asc_rail_shift_female -0.023360 -0.057601 -0.082349 0.45292 b_tt_car 0.317965 0.654416 0.694693 -5.8460e-04 b_tt_bus -0.777320 0.138291 0.129415 -0.02260 b_tt_air -0.014330 -0.565041 0.008395 0.05027 b_tt_rail -0.002317 0.002183 -0.619797 -0.01787 b_tt_shift_business 0.078398 0.147239 0.201338 0.02609 b_access 0.084027 -0.482010 -0.047975 -0.04188 b_cost -0.012636 -0.012789 0.046266 -0.07429 b_cost_shift_business 0.091229 -0.068466 0.030161 0.06060 cost_income_elast -0.083157 0.140926 0.096750 0.04650 b_wifi -0.068416 -0.111734 -0.129116 0.01775 b_food -0.003703 -0.076813 -0.091560 0.06160 lambda_PT -0.018483 -0.012147 -0.114224 0.09621 lambda_fastPT -0.031068 -0.020065 -0.087760 0.05480 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.030930 -0.02336 0.317965 -0.77732 asc_air -0.105398 -0.05760 0.654416 0.13829 asc_rail -0.127836 -0.08235 0.694693 0.12942 asc_bus_shift_female 0.362709 0.45292 -5.8460e-04 -0.02260 asc_air_shift_female 1.000000 0.75132 -0.038219 -0.09473 asc_rail_shift_female 0.751322 1.00000 0.025341 -0.01923 b_tt_car -0.038219 0.02534 1.000000 0.28686 b_tt_bus -0.094728 -0.01923 0.286859 1.00000 b_tt_air -0.007093 0.02230 0.109758 0.09899 b_tt_rail 0.063732 0.01730 0.086988 0.10284 b_tt_shift_business 0.007987 0.01620 0.007178 -0.08989 b_access -0.041937 -0.01897 0.064387 -0.03976 b_cost -0.105175 -0.05858 0.434216 0.42467 b_cost_shift_business 0.085499 0.08191 -0.308835 -0.38760 cost_income_elast 0.095655 0.07810 0.036547 0.12229 b_wifi -0.010438 -0.02068 -0.277988 -0.18409 b_food -0.051357 -0.03035 -0.157610 -0.13532 lambda_PT 0.027775 0.01293 -0.297603 -0.33952 lambda_fastPT 0.050305 0.01730 -0.273281 -0.24387 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.014330 -0.002317 0.078398 0.08403 asc_air -0.565041 0.002183 0.147239 -0.48201 asc_rail 0.008395 -0.619797 0.201338 -0.04798 asc_bus_shift_female 0.050272 -0.017866 0.026093 -0.04188 asc_air_shift_female -0.007093 0.063732 0.007987 -0.04194 asc_rail_shift_female 0.022297 0.017301 0.016196 -0.01897 b_tt_car 0.109758 0.086988 0.007178 0.06439 b_tt_bus 0.098992 0.102838 -0.089895 -0.03976 b_tt_air 1.000000 0.032789 -0.073129 0.36029 b_tt_rail 0.032789 1.000000 -0.180398 -0.03247 b_tt_shift_business -0.073129 -0.180398 1.000000 0.06093 b_access 0.360288 -0.032467 0.060935 1.00000 b_cost 0.283574 0.305116 -0.188581 0.25640 b_cost_shift_business -0.080122 -0.281070 0.545842 -0.03829 cost_income_elast -0.138726 -0.096256 -0.009857 -0.07964 b_wifi -0.176829 -0.178538 -0.142652 -0.09410 b_food -0.122646 -0.114447 -0.073387 -0.04999 lambda_PT -0.170030 -0.092262 0.025694 -0.18879 lambda_fastPT -0.202812 -0.148449 -0.141722 -0.19608 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.01264 0.091229 -0.083157 -0.06842 asc_air -0.01279 -0.068466 0.140926 -0.11173 asc_rail 0.04627 0.030161 0.096750 -0.12912 asc_bus_shift_female -0.07429 0.060601 0.046503 0.01775 asc_air_shift_female -0.10518 0.085499 0.095655 -0.01044 asc_rail_shift_female -0.05858 0.081911 0.078099 -0.02068 b_tt_car 0.43422 -0.308835 0.036547 -0.27799 b_tt_bus 0.42467 -0.387605 0.122291 -0.18409 b_tt_air 0.28357 -0.080122 -0.138726 -0.17683 b_tt_rail 0.30512 -0.281070 -0.096256 -0.17854 b_tt_shift_business -0.18858 0.545842 -0.009857 -0.14265 b_access 0.25640 -0.038287 -0.079636 -0.09410 b_cost 1.00000 -0.733317 -0.236237 -0.47889 b_cost_shift_business -0.73332 1.000000 0.004512 0.19151 cost_income_elast -0.23624 0.004512 1.000000 0.09452 b_wifi -0.47889 0.191515 0.094523 1.00000 b_food -0.25749 0.091991 0.018777 0.59105 lambda_PT -0.57376 0.419621 -0.114698 0.31064 lambda_fastPT -0.64895 0.272672 0.199328 0.46364 b_food lambda_PT lambda_fastPT asc_bus -0.003703 -0.01848 -0.03107 asc_air -0.076813 -0.01215 -0.02006 asc_rail -0.091560 -0.11422 -0.08776 asc_bus_shift_female 0.061599 0.09621 0.05480 asc_air_shift_female -0.051357 0.02777 0.05031 asc_rail_shift_female -0.030347 0.01293 0.01730 b_tt_car -0.157610 -0.29760 -0.27328 b_tt_bus -0.135316 -0.33952 -0.24387 b_tt_air -0.122646 -0.17003 -0.20281 b_tt_rail -0.114447 -0.09226 -0.14845 b_tt_shift_business -0.073387 0.02569 -0.14172 b_access -0.049989 -0.18879 -0.19608 b_cost -0.257491 -0.57376 -0.64895 b_cost_shift_business 0.091991 0.41962 0.27267 cost_income_elast 0.018777 -0.11470 0.19933 b_wifi 0.591051 0.31064 0.46364 b_food 1.000000 0.16600 0.23497 lambda_PT 0.165999 1.00000 0.40303 lambda_fastPT 0.234972 0.40303 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2254735 464 0.2335743 293 0.2429291 146 0.2627900 181 0.2654204 317 0.2703859 276 0.2785475 367 0.2792005 434 0.2870666 186 0.2885084 307 0.2930726 370 0.2956403 147 0.2959374 161 0.2965366 142 0.2977472 259 0.3012000 441 0.3019521 183 0.3026310 447 0.3029718 379 0.3038181 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286548 0.414336 0.127788 asc_air -0.903342 -0.715545 0.187797 asc_rail -2.092649 -1.647888 0.444761 asc_bus_shift_female 0.340176 0.274687 -0.065490 asc_air_shift_female 0.268177 0.237113 -0.031065 asc_rail_shift_female 0.189615 0.179645 -0.009971 b_tt_car -0.013107 -0.010515 0.002592 b_tt_bus -0.021266 -0.016903 0.004363 b_tt_air -0.016578 -0.012112 0.004465 b_tt_rail -0.007051 -0.005246 0.001805 b_tt_shift_business -0.006234 -0.005882 3.5125e-04 b_access -0.021153 -0.016827 0.004326 b_cost -0.076190 -0.058240 0.017949 b_cost_shift_business 0.033381 0.025466 -0.007915 cost_income_elast -0.613795 -0.626050 -0.012255 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026713 0.756579 -0.270134 b_food 0.422069 0.323530 -0.098539 lambda_PT 1.000000 0.695288 -0.304712 lambda_fastPT 1.000000 0.586193 -0.413807 Settings and functions used in model definition: apollo_control -------------- Value modelName "NL_three_levels" modelDescr "Three-level NL 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 second derivative of LL (using numDeriv) Scaling in estimation --------------------- Value asc_bus 0.414336161 asc_air 0.715545021 asc_rail 1.647889363 asc_bus_shift_female 0.274686575 asc_air_shift_female 0.237112830 asc_rail_shift_female 0.179644665 b_tt_car 0.010515412 b_tt_bus 0.016903103 b_tt_air 0.012112391 b_tt_rail 0.005246118 b_tt_shift_business 0.005882421 b_access 0.016826958 b_cost 0.058240356 b_cost_shift_business 0.025466212 cost_income_elast 0.626049593 b_wifi 0.756578950 b_food 0.323529600 lambda_PT 0.695288278 lambda_fastPT 0.586193527 Scaling used in computing Hessian --------------------------------- Value asc_bus 0.414336085 asc_air 0.715544934 asc_rail 1.647888225 asc_bus_shift_female 0.274686561 asc_air_shift_female 0.237112831 asc_rail_shift_female 0.179644671 b_tt_car 0.010515419 b_tt_bus 0.016903145 b_tt_air 0.012112388 b_tt_rail 0.005246116 b_tt_shift_business 0.005882421 b_access 0.016826956 b_cost 0.058240354 b_cost_shift_business 0.025466205 cost_income_elast 0.626049575 b_wifi 0.756578981 b_food 0.323529634 lambda_PT 0.695287761 lambda_fastPT 0.586193288 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 nl_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 ) ### Specify nests for NL model nlNests = list(root=1, PT=lambda_PT, fastPT=lambda_fastPT) ### Specify tree structure for NL model nlStructure= list() nlStructure[["root"]] = c("car","PT") nlStructure[["PT"]] = c("bus","fastPT") nlStructure[["fastPT"]] = c("air","rail") ### Define settings for NL model nl_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, nlNests = nlNests, nlStructure = nlStructure ) ### Compute probabilities using NL model P[["model"]] = apollo_nl(nl_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) }