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 : NL_three_levels Model description : Three-level NL model with socio-demographics on mode choice SP data Model run at : 2025-09-19 11:39:37.063055 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -4.250769 reciprocal of condition number : 4.00761e-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) : -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) : 00:00:6.48 pre-estimation : 00:00:0.38 estimation : 00:00:0.59 post-estimation : 00:00:5.51 Iterations : 8 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. asc_car 0.000000 NA NA NA NA asc_bus 0.414211 0.457897 0.9046 -1.279 0.434282 asc_air -0.715583 0.296526 -2.4132 -5.786 0.289305 asc_rail -1.647921 0.296224 -5.5631 -8.939 0.286389 asc_bus_interaction_female 0.274688 0.107650 2.5517 -6.738 0.116094 asc_air_interaction_female 0.237109 0.076733 3.0900 -9.942 0.077401 asc_rail_interaction_female 0.179643 0.067700 2.6535 -12.117 0.068223 b_tt_car -0.010515 7.2695e-04 -14.4653 -1390.084 7.3002e-04 b_tt_bus -0.016903 0.001311 -12.8973 -775.923 0.001263 b_tt_air -0.012112 0.001957 -6.1897 -517.224 0.001983 b_tt_rail -0.005246 0.001357 -3.8649 -740.582 0.001324 b_tt_interaction_business -0.005883 5.0178e-04 -11.7233 -2004.624 4.6691e-04 b_access -0.016827 0.002032 -8.2822 -500.481 0.001983 b_cost -0.058240 0.002400 -24.2657 -440.914 0.002435 b_cost_interaction_business 0.025466 0.002260 11.2677 -431.199 0.002137 cost_income_elast -0.626049 0.031247 -20.0356 -52.039 0.032313 b_no_frills 0.000000 NA NA NA NA b_wifi 0.756577 0.045919 16.4765 -5.301 0.047168 b_food 0.323531 0.039245 8.2439 -17.237 0.042274 lambda_PT 0.695281 0.038891 17.8776 -7.835 0.038104 lambda_fastPT 0.586188 0.030396 19.2848 -13.614 0.029295 Rob.t.rat.(0) Rob.t.rat.(1) asc_car NA NA asc_bus 0.9538 -1.349 asc_air -2.4735 -5.930 asc_rail -5.7541 -9.246 asc_bus_interaction_female 2.3661 -6.248 asc_air_interaction_female 3.0634 -9.856 asc_rail_interaction_female 2.6332 -12.025 b_tt_car -14.4044 -1384.227 b_tt_bus -13.3843 -805.222 b_tt_air -6.1077 -510.371 b_tt_rail -3.9623 -759.255 b_tt_interaction_business -12.5987 -2154.329 b_access -8.4859 -512.790 b_cost -23.9174 -434.585 b_cost_interaction_business 11.9172 -456.054 cost_income_elast -19.3745 -50.322 b_no_frills NA NA b_wifi 16.0400 -5.161 b_food 7.6532 -16.002 lambda_PT 18.2468 -7.997 lambda_fastPT 20.0098 -14.126 Nesting structure for NL 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_bus 0.209669 0.035790 asc_air 0.035790 0.087927 asc_rail 0.033788 0.051265 asc_bus_interaction_female -0.006721 -0.001737 asc_air_interaction_female -0.001466 -0.002902 asc_rail_interaction_female -0.001572 -0.001730 b_tt_car 1.0592e-04 1.4350e-04 b_tt_bus -4.7956e-04 4.143e-05 b_tt_air -1.107e-05 -3.4542e-04 b_tt_rail 7.060e-06 3.644e-06 b_tt_interaction_business 5.861e-06 1.017e-05 b_access -9.425e-06 -2.9316e-04 b_cost -6.067e-06 -1.806e-05 b_cost_interaction_business 3.767e-05 -4.367e-05 cost_income_elast -8.2116e-04 0.001055 b_wifi -2.2830e-04 -0.001441 b_food -2.2226e-04 -9.2646e-04 lambda_PT 1.8144e-04 -4.2720e-04 lambda_fastPT -1.3430e-04 -1.7230e-04 asc_rail asc_bus_interaction_female asc_bus 0.033788 -0.006721 asc_air 0.051265 -0.001737 asc_rail 0.087748 -0.001708 asc_bus_interaction_female -0.001708 0.011589 asc_air_interaction_female -0.002050 0.003309 asc_rail_interaction_female -0.002337 0.003200 b_tt_car 1.5182e-04 -1.785e-06 b_tt_bus 5.126e-05 -6.854e-07 b_tt_air -1.459e-06 -2.436e-06 b_tt_rail -2.5977e-04 -1.846e-06 b_tt_interaction_business 1.624e-05 3.382e-07 b_access -1.866e-05 -4.072e-07 b_cost 4.144e-05 -1.491e-05 b_cost_interaction_business -1.502e-05 1.297e-05 cost_income_elast 3.8826e-04 -1.5819e-04 b_wifi -0.002006 1.3810e-04 b_food -0.001284 4.275e-05 lambda_PT -0.001024 2.3196e-04 lambda_fastPT -0.001067 1.3084e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.001466 -0.001572 asc_air -0.002902 -0.001730 asc_rail -0.002050 -0.002337 asc_bus_interaction_female 0.003309 0.003200 asc_air_interaction_female 0.005888 0.003749 asc_rail_interaction_female 0.003749 0.004583 b_tt_car -1.319e-06 -6.158e-07 b_tt_bus -2.331e-06 -8.519e-07 b_tt_air -1.360e-06 -1.431e-06 b_tt_rail -6.304e-07 -1.837e-07 b_tt_interaction_business -7.166e-07 -3.279e-07 b_access -2.896e-06 -2.479e-06 b_cost -8.208e-06 -3.777e-06 b_cost_interaction_business 2.440e-06 1.353e-06 cost_income_elast 1.434e-05 -4.736e-06 b_wifi 1.1039e-04 4.139e-05 b_food 4.386e-05 1.463e-05 lambda_PT 7.960e-05 3.328e-05 lambda_fastPT 8.337e-05 3.217e-05 b_tt_car b_tt_bus asc_bus 1.0592e-04 -4.7956e-04 asc_air 1.4350e-04 4.143e-05 asc_rail 1.5182e-04 5.126e-05 asc_bus_interaction_female -1.785e-06 -6.854e-07 asc_air_interaction_female -1.319e-06 -2.331e-06 asc_rail_interaction_female -6.158e-07 -8.519e-07 b_tt_car 5.284e-07 2.444e-07 b_tt_bus 2.444e-07 1.718e-06 b_tt_air 8.088e-08 1.750e-07 b_tt_rail 3.664e-08 9.419e-08 b_tt_interaction_business -1.670e-08 -3.769e-08 b_access 8.618e-08 9.244e-08 b_cost 7.319e-07 1.233e-06 b_cost_interaction_business -4.880e-07 -9.275e-07 cost_income_elast -2.814e-07 3.809e-06 b_wifi -9.495e-06 -1.388e-05 b_food -4.206e-06 -5.476e-06 lambda_PT -7.734e-06 -1.743e-05 lambda_fastPT -6.416e-06 -1.021e-05 b_tt_air b_tt_rail asc_bus -1.107e-05 7.060e-06 asc_air -3.4542e-04 3.644e-06 asc_rail -1.459e-06 -2.5977e-04 asc_bus_interaction_female -2.436e-06 -1.846e-06 asc_air_interaction_female -1.360e-06 -6.304e-07 asc_rail_interaction_female -1.431e-06 -1.837e-07 b_tt_car 8.088e-08 3.664e-08 b_tt_bus 1.750e-07 9.419e-08 b_tt_air 3.829e-06 -5.421e-08 b_tt_rail -5.421e-08 1.842e-06 b_tt_interaction_business -3.954e-08 -8.213e-08 b_access 1.533e-06 -1.503e-07 b_cost 1.363e-06 8.488e-07 b_cost_interaction_business -4.126e-07 -5.812e-07 cost_income_elast -7.790e-06 -2.186e-06 b_wifi -1.323e-05 -8.506e-06 b_food -6.578e-06 -3.668e-06 lambda_PT -9.582e-06 -5.909e-06 lambda_fastPT -1.249e-05 -4.362e-06 b_tt_interaction_business b_access asc_bus 5.861e-06 -9.425e-06 asc_air 1.017e-05 -2.9316e-04 asc_rail 1.624e-05 -1.866e-05 asc_bus_interaction_female 3.382e-07 -4.072e-07 asc_air_interaction_female -7.166e-07 -2.896e-06 asc_rail_interaction_female -3.279e-07 -2.479e-06 b_tt_car -1.670e-08 8.618e-08 b_tt_bus -3.769e-08 9.244e-08 b_tt_air -3.954e-08 1.533e-06 b_tt_rail -8.213e-08 -1.503e-07 b_tt_interaction_business 2.518e-07 6.524e-08 b_access 6.524e-08 4.128e-06 b_cost -1.938e-07 1.208e-06 b_cost_interaction_business 6.950e-07 -8.699e-08 cost_income_elast -1.155e-07 -6.596e-06 b_wifi -2.688e-06 -1.475e-05 b_food -1.107e-06 -6.854e-06 lambda_PT 5.823e-07 -1.242e-05 lambda_fastPT -1.790e-06 -1.290e-05 b_cost b_cost_interaction_business asc_bus -6.067e-06 3.767e-05 asc_air -1.806e-05 -4.367e-05 asc_rail 4.144e-05 -1.502e-05 asc_bus_interaction_female -1.491e-05 1.297e-05 asc_air_interaction_female -8.208e-06 2.440e-06 asc_rail_interaction_female -3.777e-06 1.353e-06 b_tt_car 7.319e-07 -4.880e-07 b_tt_bus 1.233e-06 -9.275e-07 b_tt_air 1.363e-06 -4.126e-07 b_tt_rail 8.488e-07 -5.812e-07 b_tt_interaction_business -1.938e-07 6.950e-07 b_access 1.208e-06 -8.699e-08 b_cost 5.760e-06 -3.708e-06 b_cost_interaction_business -3.708e-06 5.108e-06 cost_income_elast -1.691e-05 9.264e-07 b_wifi -5.556e-05 1.811e-05 b_food -2.395e-05 6.835e-06 lambda_PT -5.115e-05 3.365e-05 lambda_fastPT -4.663e-05 1.759e-05 cost_income_elast b_wifi asc_bus -8.2116e-04 -2.2830e-04 asc_air 0.001055 -0.001441 asc_rail 3.8826e-04 -0.002006 asc_bus_interaction_female -1.5819e-04 1.3810e-04 asc_air_interaction_female 1.434e-05 1.1039e-04 asc_rail_interaction_female -4.736e-06 4.139e-05 b_tt_car -2.814e-07 -9.495e-06 b_tt_bus 3.809e-06 -1.388e-05 b_tt_air -7.790e-06 -1.323e-05 b_tt_rail -2.186e-06 -8.506e-06 b_tt_interaction_business -1.155e-07 -2.688e-06 b_access -6.596e-06 -1.475e-05 b_cost -1.691e-05 -5.556e-05 b_cost_interaction_business 9.264e-07 1.811e-05 cost_income_elast 9.7636e-04 1.3315e-04 b_wifi 1.3315e-04 0.002109 b_food 8.626e-05 0.001057 lambda_PT -2.1704e-04 5.9745e-04 lambda_fastPT 1.2242e-04 6.9586e-04 b_food lambda_PT asc_bus -2.2226e-04 1.8144e-04 asc_air -9.2646e-04 -4.2720e-04 asc_rail -0.001284 -0.001024 asc_bus_interaction_female 4.275e-05 2.3196e-04 asc_air_interaction_female 4.386e-05 7.960e-05 asc_rail_interaction_female 1.463e-05 3.328e-05 b_tt_car -4.206e-06 -7.734e-06 b_tt_bus -5.476e-06 -1.743e-05 b_tt_air -6.578e-06 -9.582e-06 b_tt_rail -3.668e-06 -5.909e-06 b_tt_interaction_business -1.107e-06 5.823e-07 b_access -6.854e-06 -1.242e-05 b_cost -2.395e-05 -5.115e-05 b_cost_interaction_business 6.835e-06 3.365e-05 cost_income_elast 8.626e-05 -2.1704e-04 b_wifi 0.001057 5.9745e-04 b_food 0.001540 2.3219e-04 lambda_PT 2.3219e-04 0.001513 lambda_fastPT 2.7395e-04 4.5128e-04 lambda_fastPT asc_bus -1.3430e-04 asc_air -1.7230e-04 asc_rail -0.001067 asc_bus_interaction_female 1.3084e-04 asc_air_interaction_female 8.337e-05 asc_rail_interaction_female 3.217e-05 b_tt_car -6.416e-06 b_tt_bus -1.021e-05 b_tt_air -1.249e-05 b_tt_rail -4.362e-06 b_tt_interaction_business -1.790e-06 b_access -1.290e-05 b_cost -4.663e-05 b_cost_interaction_business 1.759e-05 cost_income_elast 1.2242e-04 b_wifi 6.9586e-04 b_food 2.7395e-04 lambda_PT 4.5128e-04 lambda_fastPT 9.2394e-04 Robust covariance matrix: asc_bus asc_air asc_bus 0.188601 0.029813 asc_air 0.029813 0.083698 asc_rail 0.032498 0.049456 asc_bus_interaction_female -0.006150 -0.001223 asc_air_interaction_female 0.001040 -0.002360 asc_rail_interaction_female -6.9213e-04 -0.001137 b_tt_car 1.0081e-04 1.3821e-04 b_tt_bus -4.2632e-04 5.053e-05 b_tt_air -1.234e-05 -3.2417e-04 b_tt_rail -1.330e-06 8.363e-07 b_tt_interaction_business 1.590e-05 1.989e-05 b_access 7.236e-05 -2.7651e-04 b_cost -1.334e-05 -9.006e-06 b_cost_interaction_business 8.465e-05 -4.233e-05 cost_income_elast -0.001167 0.001317 b_wifi -0.001402 -0.001525 b_food -6.806e-05 -9.3946e-04 lambda_PT -3.0626e-04 -1.3393e-04 lambda_fastPT -3.9543e-04 -1.7010e-04 asc_rail asc_bus_interaction_female asc_bus 0.032498 -0.006150 asc_air 0.049456 -0.001223 asc_rail 0.082019 -8.2683e-04 asc_bus_interaction_female -8.2683e-04 0.013478 asc_air_interaction_female -0.002834 0.003259 asc_rail_interaction_female -0.001609 0.003587 b_tt_car 1.4524e-04 -4.968e-08 b_tt_bus 4.681e-05 -3.314e-06 b_tt_air 4.767e-06 1.157e-05 b_tt_rail -2.3501e-04 -2.746e-06 b_tt_interaction_business 2.692e-05 1.414e-06 b_access -2.724e-05 -9.642e-06 b_cost 3.227e-05 -2.100e-05 b_cost_interaction_business 1.846e-05 1.503e-05 cost_income_elast 8.9533e-04 1.7445e-04 b_wifi -0.001744 9.722e-05 b_food -0.001109 3.0231e-04 lambda_PT -0.001247 4.2562e-04 lambda_fastPT -7.3632e-04 1.8639e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.001040 -6.9213e-04 asc_air -0.002360 -0.001137 asc_rail -0.002834 -0.001609 asc_bus_interaction_female 0.003259 0.003587 asc_air_interaction_female 0.005991 0.003967 asc_rail_interaction_female 0.003967 0.004654 b_tt_car -2.160e-06 1.262e-06 b_tt_bus -9.259e-06 -1.657e-06 b_tt_air -1.089e-06 3.017e-06 b_tt_rail 6.531e-06 1.563e-06 b_tt_interaction_business 2.886e-07 5.159e-07 b_access -6.437e-06 -2.566e-06 b_cost -1.982e-05 -9.732e-06 b_cost_interaction_business 1.414e-05 1.194e-05 cost_income_elast 2.3924e-04 1.7217e-04 b_wifi -3.811e-05 -6.653e-05 b_food -1.6804e-04 -8.753e-05 lambda_PT 8.191e-05 3.361e-05 lambda_fastPT 1.1406e-04 3.457e-05 b_tt_car b_tt_bus asc_bus 1.0081e-04 -4.2632e-04 asc_air 1.3821e-04 5.053e-05 asc_rail 1.4524e-04 4.681e-05 asc_bus_interaction_female -4.968e-08 -3.314e-06 asc_air_interaction_female -2.160e-06 -9.259e-06 asc_rail_interaction_female 1.262e-06 -1.657e-06 b_tt_car 5.329e-07 2.645e-07 b_tt_bus 2.645e-07 1.595e-06 b_tt_air 1.589e-07 2.479e-07 b_tt_rail 8.408e-08 1.719e-07 b_tt_interaction_business 2.450e-09 -5.300e-08 b_access 9.321e-08 -9.958e-08 b_cost 7.719e-07 1.306e-06 b_cost_interaction_business -4.818e-07 -1.046e-06 cost_income_elast 8.620e-07 4.990e-06 b_wifi -9.572e-06 -1.097e-05 b_food -4.864e-06 -7.224e-06 lambda_PT -8.278e-06 -1.634e-05 lambda_fastPT -5.844e-06 -9.022e-06 b_tt_air b_tt_rail asc_bus -1.234e-05 -1.330e-06 asc_air -3.2417e-04 8.363e-07 asc_rail 4.767e-06 -2.3501e-04 asc_bus_interaction_female 1.157e-05 -2.746e-06 asc_air_interaction_female -1.089e-06 6.531e-06 asc_rail_interaction_female 3.017e-06 1.563e-06 b_tt_car 1.589e-07 8.408e-08 b_tt_bus 2.479e-07 1.719e-07 b_tt_air 3.933e-06 8.608e-08 b_tt_rail 8.608e-08 1.753e-06 b_tt_interaction_business -6.771e-08 -1.115e-07 b_access 1.417e-06 -8.523e-08 b_cost 1.369e-06 9.837e-07 b_cost_interaction_business -3.395e-07 -7.952e-07 cost_income_elast -8.890e-06 -4.118e-06 b_wifi -1.654e-05 -1.115e-05 b_food -1.028e-05 -6.406e-06 lambda_PT -1.285e-05 -4.654e-06 lambda_fastPT -1.178e-05 -5.758e-06 b_tt_interaction_business b_access asc_bus 1.590e-05 7.236e-05 asc_air 1.989e-05 -2.7651e-04 asc_rail 2.692e-05 -2.724e-05 asc_bus_interaction_female 1.414e-06 -9.642e-06 asc_air_interaction_female 2.886e-07 -6.437e-06 asc_rail_interaction_female 5.159e-07 -2.566e-06 b_tt_car 2.450e-09 9.321e-08 b_tt_bus -5.300e-08 -9.958e-08 b_tt_air -6.771e-08 1.417e-06 b_tt_rail -1.115e-07 -8.523e-08 b_tt_interaction_business 2.180e-07 5.642e-08 b_access 5.642e-08 3.932e-06 b_cost -2.144e-07 1.238e-06 b_cost_interaction_business 5.446e-07 -1.622e-07 cost_income_elast -1.488e-07 -5.103e-06 b_wifi -3.142e-06 -8.801e-06 b_food -1.449e-06 -4.191e-06 lambda_PT 4.570e-07 -1.426e-05 lambda_fastPT -1.939e-06 -1.139e-05 b_cost b_cost_interaction_business asc_bus -1.334e-05 8.465e-05 asc_air -9.006e-06 -4.233e-05 asc_rail 3.227e-05 1.846e-05 asc_bus_interaction_female -2.100e-05 1.503e-05 asc_air_interaction_female -1.982e-05 1.414e-05 asc_rail_interaction_female -9.732e-06 1.194e-05 b_tt_car 7.719e-07 -4.818e-07 b_tt_bus 1.306e-06 -1.046e-06 b_tt_air 1.369e-06 -3.395e-07 b_tt_rail 9.837e-07 -7.952e-07 b_tt_interaction_business -2.144e-07 5.446e-07 b_access 1.238e-06 -1.622e-07 b_cost 5.930e-06 -3.816e-06 b_cost_interaction_business -3.816e-06 4.566e-06 cost_income_elast -1.859e-05 3.114e-07 b_wifi -5.500e-05 1.930e-05 b_food -2.651e-05 8.310e-06 lambda_PT -5.324e-05 3.417e-05 lambda_fastPT -4.629e-05 1.707e-05 cost_income_elast b_wifi asc_bus -0.001167 -0.001402 asc_air 0.001317 -0.001525 asc_rail 8.9533e-04 -0.001744 asc_bus_interaction_female 1.7445e-04 9.722e-05 asc_air_interaction_female 2.3924e-04 -3.811e-05 asc_rail_interaction_female 1.7217e-04 -6.653e-05 b_tt_car 8.620e-07 -9.572e-06 b_tt_bus 4.990e-06 -1.097e-05 b_tt_air -8.890e-06 -1.654e-05 b_tt_rail -4.118e-06 -1.115e-05 b_tt_interaction_business -1.488e-07 -3.142e-06 b_access -5.103e-06 -8.801e-06 b_cost -1.859e-05 -5.500e-05 b_cost_interaction_business 3.114e-07 1.930e-05 cost_income_elast 0.001044 1.4407e-04 b_wifi 1.4407e-04 0.002225 b_food 2.565e-05 0.001179 lambda_PT -1.4121e-04 5.5832e-04 lambda_fastPT 1.8869e-04 6.4066e-04 b_food lambda_PT asc_bus -6.806e-05 -3.0626e-04 asc_air -9.3946e-04 -1.3393e-04 asc_rail -0.001109 -0.001247 asc_bus_interaction_female 3.0231e-04 4.2562e-04 asc_air_interaction_female -1.6804e-04 8.191e-05 asc_rail_interaction_female -8.753e-05 3.361e-05 b_tt_car -4.864e-06 -8.278e-06 b_tt_bus -7.224e-06 -1.634e-05 b_tt_air -1.028e-05 -1.285e-05 b_tt_rail -6.406e-06 -4.654e-06 b_tt_interaction_business -1.449e-06 4.570e-07 b_access -4.191e-06 -1.426e-05 b_cost -2.651e-05 -5.324e-05 b_cost_interaction_business 8.310e-06 3.417e-05 cost_income_elast 2.565e-05 -1.4121e-04 b_wifi 0.001179 5.5832e-04 b_food 0.001787 2.6740e-04 lambda_PT 2.6740e-04 0.001452 lambda_fastPT 2.9100e-04 4.4989e-04 lambda_fastPT asc_bus -3.9543e-04 asc_air -1.7010e-04 asc_rail -7.3632e-04 asc_bus_interaction_female 1.8639e-04 asc_air_interaction_female 1.1406e-04 asc_rail_interaction_female 3.457e-05 b_tt_car -5.844e-06 b_tt_bus -9.022e-06 b_tt_air -1.178e-05 b_tt_rail -5.758e-06 b_tt_interaction_business -1.939e-06 b_access -1.139e-05 b_cost -4.629e-05 b_cost_interaction_business 1.707e-05 cost_income_elast 1.8869e-04 b_wifi 6.4066e-04 b_food 2.9100e-04 lambda_PT 4.4989e-04 lambda_fastPT 8.5821e-04 Classical correlation matrix: asc_bus asc_air asc_bus 1.000000 0.263592 asc_air 0.263592 1.000000 asc_rail 0.249102 0.583634 asc_bus_interaction_female -0.136357 -0.054403 asc_air_interaction_female -0.041713 -0.127560 asc_rail_interaction_female -0.050710 -0.086182 b_tt_car 0.318193 0.665716 b_tt_bus -0.799125 0.106610 b_tt_air -0.012353 -0.595307 b_tt_rail 0.011359 0.009053 b_tt_interaction_business 0.025508 0.068371 b_access -0.010131 -0.486605 b_cost -0.005521 -0.025369 b_cost_interaction_business 0.036404 -0.065162 cost_income_elast -0.057392 0.113838 b_wifi -0.010858 -0.105808 b_food -0.012368 -0.079613 lambda_PT 0.010189 -0.037044 lambda_fastPT -0.009649 -0.019116 asc_rail asc_bus_interaction_female asc_bus 0.249102 -0.136357 asc_air 0.583634 -0.054403 asc_rail 1.000000 -0.053573 asc_bus_interaction_female -0.053573 1.000000 asc_air_interaction_female -0.090183 0.400554 asc_rail_interaction_female -0.116510 0.439097 b_tt_car 0.705013 -0.022806 b_tt_bus 0.132047 -0.004858 b_tt_air -0.002517 -0.011563 b_tt_rail -0.646066 -0.012636 b_tt_interaction_business 0.109263 0.006262 b_access -0.031005 -0.001862 b_cost 0.058291 -0.057705 b_cost_interaction_business -0.022439 0.053321 cost_income_elast 0.041947 -0.047029 b_wifi -0.147497 0.027938 b_food -0.110489 0.010119 lambda_PT -0.088874 0.055405 lambda_fastPT -0.118556 0.039986 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.041713 -0.050710 asc_air -0.127560 -0.086182 asc_rail -0.090183 -0.116510 asc_bus_interaction_female 0.400554 0.439097 asc_air_interaction_female 1.000000 0.721592 asc_rail_interaction_female 0.721592 1.000000 b_tt_car -0.023642 -0.012513 b_tt_bus -0.023179 -0.009602 b_tt_air -0.009061 -0.010800 b_tt_rail -0.006052 -0.001999 b_tt_interaction_business -0.018612 -0.009651 b_access -0.018573 -0.018025 b_cost -0.044568 -0.023243 b_cost_interaction_business 0.014070 0.008841 cost_income_elast 0.005979 -0.002239 b_wifi 0.031328 0.013315 b_food 0.014566 0.005507 lambda_PT 0.026673 0.012639 lambda_fastPT 0.035742 0.015633 b_tt_car b_tt_bus asc_bus 0.31819 -0.799125 asc_air 0.66572 0.106610 asc_rail 0.70501 0.132047 asc_bus_interaction_female -0.02281 -0.004858 asc_air_interaction_female -0.02364 -0.023179 asc_rail_interaction_female -0.01251 -0.009602 b_tt_car 1.00000 0.256506 b_tt_bus 0.25651 1.000000 b_tt_air 0.05686 0.068237 b_tt_rail 0.03713 0.052950 b_tt_interaction_business -0.04578 -0.057320 b_access 0.05835 0.034717 b_cost 0.41947 0.391898 b_cost_interaction_business -0.29705 -0.313130 cost_income_elast -0.01239 0.093022 b_wifi -0.28444 -0.230574 b_food -0.14743 -0.106475 lambda_PT -0.27358 -0.341962 lambda_fastPT -0.29034 -0.256296 b_tt_air b_tt_rail asc_bus -0.012353 0.011359 asc_air -0.595307 0.009053 asc_rail -0.002517 -0.646066 asc_bus_interaction_female -0.011563 -0.012636 asc_air_interaction_female -0.009061 -0.006052 asc_rail_interaction_female -0.010800 -0.001999 b_tt_car 0.056859 0.037135 b_tt_bus 0.068237 0.052950 b_tt_air 1.000000 -0.020408 b_tt_rail -0.020408 1.000000 b_tt_interaction_business -0.040273 -0.120581 b_access 0.385691 -0.054496 b_cost 0.290249 0.260554 b_cost_interaction_business -0.093289 -0.189471 cost_income_elast -0.127400 -0.051540 b_wifi -0.147242 -0.136464 b_food -0.085653 -0.068854 lambda_PT -0.125905 -0.111926 lambda_fastPT -0.209936 -0.105711 b_tt_interaction_business b_access asc_bus 0.025508 -0.010131 asc_air 0.068371 -0.486605 asc_rail 0.109263 -0.031005 asc_bus_interaction_female 0.006262 -0.001862 asc_air_interaction_female -0.018612 -0.018573 asc_rail_interaction_female -0.009651 -0.018025 b_tt_car -0.045779 0.058351 b_tt_bus -0.057320 0.034717 b_tt_air -0.040273 0.385691 b_tt_rail -0.120581 -0.054496 b_tt_interaction_business 1.000000 0.063991 b_access 0.063991 1.000000 b_cost -0.160880 0.247688 b_cost_interaction_business 0.612825 -0.018944 cost_income_elast -0.007369 -0.103897 b_wifi -0.116646 -0.158109 b_food -0.056230 -0.085960 lambda_PT 0.029840 -0.157209 lambda_fastPT -0.117391 -0.208819 b_cost b_cost_interaction_business asc_bus -0.005521 0.036404 asc_air -0.025369 -0.065162 asc_rail 0.058291 -0.022439 asc_bus_interaction_female -0.057705 0.053321 asc_air_interaction_female -0.044568 0.014070 asc_rail_interaction_female -0.023243 0.008841 b_tt_car 0.419465 -0.297046 b_tt_bus 0.391898 -0.313130 b_tt_air 0.290249 -0.093289 b_tt_rail 0.260554 -0.189471 b_tt_interaction_business -0.160880 0.612825 b_access 0.247688 -0.018944 b_cost 1.000000 -0.683623 b_cost_interaction_business -0.683623 1.000000 cost_income_elast -0.225516 0.013119 b_wifi -0.504093 0.174469 b_food -0.254234 0.077057 lambda_PT -0.548002 0.382886 lambda_fastPT -0.639143 0.256092 cost_income_elast b_wifi asc_bus -0.057392 -0.01086 asc_air 0.113838 -0.10581 asc_rail 0.041947 -0.14750 asc_bus_interaction_female -0.047029 0.02794 asc_air_interaction_female 0.005979 0.03133 asc_rail_interaction_female -0.002239 0.01332 b_tt_car -0.012390 -0.28444 b_tt_bus 0.093022 -0.23057 b_tt_air -0.127400 -0.14724 b_tt_rail -0.051540 -0.13646 b_tt_interaction_business -0.007369 -0.11665 b_access -0.103897 -0.15811 b_cost -0.225516 -0.50409 b_cost_interaction_business 0.013119 0.17447 cost_income_elast 1.000000 0.09280 b_wifi 0.092803 1.00000 b_food 0.070344 0.58648 lambda_PT -0.178599 0.33455 lambda_fastPT 0.128896 0.49856 b_food lambda_PT asc_bus -0.012368 0.01019 asc_air -0.079613 -0.03704 asc_rail -0.110489 -0.08887 asc_bus_interaction_female 0.010119 0.05541 asc_air_interaction_female 0.014566 0.02667 asc_rail_interaction_female 0.005507 0.01264 b_tt_car -0.147435 -0.27358 b_tt_bus -0.106475 -0.34196 b_tt_air -0.085653 -0.12591 b_tt_rail -0.068854 -0.11193 b_tt_interaction_business -0.056230 0.02984 b_access -0.085960 -0.15721 b_cost -0.254234 -0.54800 b_cost_interaction_business 0.077057 0.38289 cost_income_elast 0.070344 -0.17860 b_wifi 0.586480 0.33455 b_food 1.000000 0.15213 lambda_PT 0.152129 1.00000 lambda_fastPT 0.229651 0.38174 lambda_fastPT asc_bus -0.009649 asc_air -0.019116 asc_rail -0.118556 asc_bus_interaction_female 0.039986 asc_air_interaction_female 0.035742 asc_rail_interaction_female 0.015633 b_tt_car -0.290344 b_tt_bus -0.256296 b_tt_air -0.209936 b_tt_rail -0.105711 b_tt_interaction_business -0.117391 b_access -0.208819 b_cost -0.639143 b_cost_interaction_business 0.256092 cost_income_elast 0.128896 b_wifi 0.498557 b_food 0.229651 lambda_PT 0.381742 lambda_fastPT 1.000000 Robust correlation matrix: asc_bus asc_air asc_bus 1.000000 0.237292 asc_air 0.237292 1.000000 asc_rail 0.261291 0.596907 asc_bus_interaction_female -0.121974 -0.036423 asc_air_interaction_female 0.030929 -0.105398 asc_rail_interaction_female -0.023360 -0.057601 b_tt_car 0.317976 0.654419 b_tt_bus -0.777316 0.138294 b_tt_air -0.014325 -0.565041 b_tt_rail -0.002313 0.002183 b_tt_interaction_business 0.078398 0.147241 b_access 0.084032 -0.482007 b_cost -0.012617 -0.012784 b_cost_interaction_business 0.091217 -0.068468 cost_income_elast -0.083150 0.140926 b_wifi -0.068428 -0.111738 b_food -0.003707 -0.076815 lambda_PT -0.018507 -0.012149 lambda_fastPT -0.031082 -0.020070 asc_rail asc_bus_interaction_female asc_bus 0.261291 -0.12197 asc_air 0.596907 -0.03642 asc_rail 1.000000 -0.02487 asc_bus_interaction_female -0.024869 1.00000 asc_air_interaction_female -0.127835 0.36271 asc_rail_interaction_female -0.082348 0.45292 b_tt_car 0.694694 -5.8617e-04 b_tt_bus 0.129415 -0.02260 b_tt_air 0.008394 0.05027 b_tt_rail -0.619796 -0.01787 b_tt_interaction_business 0.201342 0.02609 b_access -0.047974 -0.04188 b_cost 0.046270 -0.07430 b_cost_interaction_business 0.030162 0.06060 cost_income_elast 0.096750 0.04650 b_wifi -0.129119 0.01775 b_food -0.091562 0.06160 lambda_PT -0.114226 0.09621 lambda_fastPT -0.087764 0.05480 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.030929 -0.02336 asc_air -0.105398 -0.05760 asc_rail -0.127835 -0.08235 asc_bus_interaction_female 0.362712 0.45292 asc_air_interaction_female 1.000000 0.75132 asc_rail_interaction_female 0.751323 1.00000 b_tt_car -0.038218 0.02534 b_tt_bus -0.094728 -0.01923 b_tt_air -0.007092 0.02230 b_tt_rail 0.063732 0.01730 b_tt_interaction_business 0.007987 0.01620 b_access -0.041937 -0.01897 b_cost -0.105173 -0.05858 b_cost_interaction_business 0.085498 0.08191 cost_income_elast 0.095655 0.07810 b_wifi -0.010439 -0.02068 b_food -0.051357 -0.03035 lambda_PT 0.027774 0.01293 lambda_fastPT 0.050303 0.01730 b_tt_car b_tt_bus asc_bus 0.317976 -0.77732 asc_air 0.654419 0.13829 asc_rail 0.694694 0.12942 asc_bus_interaction_female -5.8617e-04 -0.02260 asc_air_interaction_female -0.038218 -0.09473 asc_rail_interaction_female 0.025341 -0.01923 b_tt_car 1.000000 0.28685 b_tt_bus 0.286854 1.00000 b_tt_air 0.109754 0.09898 b_tt_rail 0.086987 0.10283 b_tt_interaction_business 0.007187 -0.08989 b_access 0.064389 -0.03977 b_cost 0.434217 0.42466 b_cost_interaction_business -0.308830 -0.38759 cost_income_elast 0.036544 0.12228 b_wifi -0.277989 -0.18409 b_food -0.157611 -0.13531 lambda_PT -0.297603 -0.33950 lambda_fastPT -0.273282 -0.24386 b_tt_air b_tt_rail asc_bus -0.014325 -0.002313 asc_air -0.565041 0.002183 asc_rail 0.008394 -0.619796 asc_bus_interaction_female 0.050273 -0.017867 asc_air_interaction_female -0.007092 0.063732 asc_rail_interaction_female 0.022297 0.017300 b_tt_car 0.109754 0.086987 b_tt_bus 0.098984 0.102834 b_tt_air 1.000000 0.032786 b_tt_rail 0.032786 1.000000 b_tt_interaction_business -0.073125 -0.180396 b_access 0.360286 -0.032466 b_cost 0.283563 0.305113 b_cost_interaction_business -0.080110 -0.281066 cost_income_elast -0.138727 -0.096258 b_wifi -0.176820 -0.178535 b_food -0.122642 -0.114446 lambda_PT -0.170023 -0.092259 lambda_fastPT -0.202796 -0.148446 b_tt_interaction_business b_access asc_bus 0.078398 0.08403 asc_air 0.147241 -0.48201 asc_rail 0.201342 -0.04797 asc_bus_interaction_female 0.026093 -0.04188 asc_air_interaction_female 0.007987 -0.04194 asc_rail_interaction_female 0.016196 -0.01897 b_tt_car 0.007187 0.06439 b_tt_bus -0.089889 -0.03977 b_tt_air -0.073125 0.36029 b_tt_rail -0.180396 -0.03247 b_tt_interaction_business 1.000000 0.06094 b_access 0.060939 1.00000 b_cost -0.188569 0.25641 b_cost_interaction_business 0.545842 -0.03829 cost_income_elast -0.009862 -0.07964 b_wifi -0.142657 -0.09410 b_food -0.073393 -0.04999 lambda_PT 0.025687 -0.18879 lambda_fastPT -0.141738 -0.19608 b_cost b_cost_interaction_business asc_bus -0.01262 0.091217 asc_air -0.01278 -0.068468 asc_rail 0.04627 0.030162 asc_bus_interaction_female -0.07430 0.060603 asc_air_interaction_female -0.10517 0.085498 asc_rail_interaction_female -0.05858 0.081912 b_tt_car 0.43422 -0.308830 b_tt_bus 0.42466 -0.387593 b_tt_air 0.28356 -0.080110 b_tt_rail 0.30511 -0.281066 b_tt_interaction_business -0.18857 0.545842 b_access 0.25641 -0.038285 b_cost 1.00000 -0.733307 b_cost_interaction_business -0.73331 1.000000 cost_income_elast -0.23624 0.004510 b_wifi -0.47889 0.191508 b_food -0.25749 0.091987 lambda_PT -0.57376 0.419613 lambda_fastPT -0.64895 0.272654 cost_income_elast b_wifi asc_bus -0.083150 -0.06843 asc_air 0.140926 -0.11174 asc_rail 0.096750 -0.12912 asc_bus_interaction_female 0.046503 0.01775 asc_air_interaction_female 0.095655 -0.01044 asc_rail_interaction_female 0.078100 -0.02068 b_tt_car 0.036544 -0.27799 b_tt_bus 0.122282 -0.18409 b_tt_air -0.138727 -0.17682 b_tt_rail -0.096258 -0.17854 b_tt_interaction_business -0.009862 -0.14266 b_access -0.079639 -0.09410 b_cost -0.236243 -0.47889 b_cost_interaction_business 0.004510 0.19151 cost_income_elast 1.000000 0.09453 b_wifi 0.094528 1.00000 b_food 0.018780 0.59105 lambda_PT -0.114691 0.31064 lambda_fastPT 0.199335 0.46364 b_food lambda_PT asc_bus -0.003707 -0.01851 asc_air -0.076815 -0.01215 asc_rail -0.091562 -0.11423 asc_bus_interaction_female 0.061599 0.09621 asc_air_interaction_female -0.051357 0.02777 asc_rail_interaction_female -0.030348 0.01293 b_tt_car -0.157611 -0.29760 b_tt_bus -0.135315 -0.33950 b_tt_air -0.122642 -0.17002 b_tt_rail -0.114446 -0.09226 b_tt_interaction_business -0.073393 0.02569 b_access -0.049991 -0.18879 b_cost -0.257494 -0.57376 b_cost_interaction_business 0.091987 0.41961 cost_income_elast 0.018780 -0.11469 b_wifi 0.591052 0.31064 b_food 1.000000 0.16600 lambda_PT 0.166001 1.00000 lambda_fastPT 0.234976 0.40303 lambda_fastPT asc_bus -0.03108 asc_air -0.02007 asc_rail -0.08776 asc_bus_interaction_female 0.05480 asc_air_interaction_female 0.05030 asc_rail_interaction_female 0.01730 b_tt_car -0.27328 b_tt_bus -0.24386 b_tt_air -0.20280 b_tt_rail -0.14845 b_tt_interaction_business -0.14174 b_access -0.19608 b_cost -0.64895 b_cost_interaction_business 0.27265 cost_income_elast 0.19933 b_wifi 0.46364 b_food 0.23498 lambda_PT 0.40303 lambda_fastPT 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2254728 464 0.2335753 293 0.2429284 146 0.2627897 181 0.2654200 317 0.2703856 276 0.2785474 367 0.2792006 434 0.2870652 186 0.2885091 307 0.2930729 370 0.2956401 147 0.2959372 161 0.2965362 142 0.2977471 259 0.3012005 441 0.3019523 183 0.3026299 447 0.3029711 379 0.3038191 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Three-level NL model with socio-demographics on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "NL_three_levels" 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 0.414211414 asc_air 0.715582554 asc_rail 1.647920945 asc_bus_interaction_female 0.274687595 asc_air_interaction_female 0.237109408 asc_rail_interaction_female 0.179643271 b_tt_car 0.010515495 b_tt_bus 0.016902822 b_tt_air 0.012112085 b_tt_rail 0.005246045 b_tt_interaction_business 0.005882509 b_access 0.016827036 b_cost 0.058240266 b_cost_interaction_business 0.025465755 cost_income_elast 0.626048621 b_wifi 0.756576984 b_food 0.323531198 lambda_PT 0.695280753 lambda_fastPT 0.586188475 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 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) }