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_constraints_on_lambdas Model description : Three-level NL model with socio-demographics on mode choice SP data, with constraints on lambdas Model run at : 2025-09-19 11:39:46.48797 Estimation method : bfgs Estimation diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -4.250729 reciprocal of condition number : 4.00758e-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) : 00:00:7.55 pre-estimation : 00:00:0.39 estimation : 00:00:1.29 post-estimation : 00:00:5.87 Iterations : 29 Constrained optimisation: lambda_PT < 1 + 1e-10 lambda_PT - lambda_fastPT > -1e-10 lambda_fastPT > 0 Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. asc_car 0.000000 NA NA NA NA asc_bus 0.414233 0.457899 0.9046 -1.279 0.434285 asc_air -0.715567 0.296527 -2.4132 -5.786 0.289306 asc_rail -1.647919 0.296225 -5.5631 -8.939 0.286390 asc_bus_interaction_female 0.274686 0.107651 2.5516 -6.738 0.116095 asc_air_interaction_female 0.237118 0.076734 3.0901 -9.942 0.077401 asc_rail_interaction_female 0.179650 0.067701 2.6536 -12.117 0.068224 b_tt_car -0.010515 7.2695e-04 -14.4653 -1390.084 7.3002e-04 b_tt_bus -0.016903 0.001311 -12.8973 -775.918 0.001263 b_tt_air -0.012112 0.001957 -6.1897 -517.221 0.001983 b_tt_rail -0.005246 0.001357 -3.8648 -740.578 0.001324 b_tt_interaction_business -0.005883 5.0178e-04 -11.7232 -2004.618 4.6691e-04 b_access -0.016827 0.002032 -8.2822 -500.477 0.001983 b_cost -0.058240 0.002400 -24.2658 -440.914 0.002435 b_cost_interaction_business 0.025466 0.002260 11.2677 -431.197 0.002137 cost_income_elast -0.626048 0.031247 -20.0356 -52.039 0.032313 b_no_frills 0.000000 NA NA NA NA b_wifi 0.756582 0.045919 16.4765 -5.301 0.047169 b_food 0.323532 0.039245 8.2439 -17.237 0.042274 lambda_PT 0.695287 0.038892 17.8775 -7.835 0.038105 lambda_fastPT 0.586194 0.030397 19.2848 -13.614 0.029296 Rob.t.rat.(0) Rob.t.rat.(1) asc_car NA NA asc_bus 0.9538 -1.349 asc_air -2.4734 -5.930 asc_rail -5.7541 -9.246 asc_bus_interaction_female 2.3661 -6.248 asc_air_interaction_female 3.0635 -9.856 asc_rail_interaction_female 2.6333 -12.024 b_tt_car -14.4043 -1384.226 b_tt_bus -13.3843 -805.216 b_tt_air -6.1077 -510.368 b_tt_rail -3.9622 -759.251 b_tt_interaction_business -12.5987 -2154.324 b_access -8.4860 -512.787 b_cost -23.9175 -434.585 b_cost_interaction_business 11.9172 -456.053 cost_income_elast -19.3744 -50.322 b_no_frills NA NA b_wifi 16.0400 -5.161 b_food 7.6531 -16.002 lambda_PT 18.2467 -7.997 lambda_fastPT 20.0096 -14.125 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 0.209672 0.035790 asc_air 0.035790 0.087928 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 -4.7957e-04 4.143e-05 b_tt_air -1.107e-05 -3.4543e-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 -6.068e-06 -1.806e-05 b_cost_interaction_business 3.767e-05 -4.367e-05 cost_income_elast -8.2117e-04 0.001055 b_wifi -2.2830e-04 -0.001441 b_food -2.2226e-04 -9.2648e-04 lambda_PT 1.8146e-04 -4.2722e-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 0.087749 -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 -6.850e-07 b_tt_air -1.459e-06 -2.436e-06 b_tt_rail -2.5978e-04 -1.846e-06 b_tt_interaction_business 1.624e-05 3.382e-07 b_access -1.866e-05 -4.070e-07 b_cost 4.144e-05 -1.491e-05 b_cost_interaction_business -1.502e-05 1.297e-05 cost_income_elast 3.8827e-04 -1.5819e-04 b_wifi -0.002006 1.3809e-04 b_food -0.001284 4.274e-05 lambda_PT -0.001024 2.3194e-04 lambda_fastPT -0.001068 1.3083e-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 -8.520e-07 b_tt_air -1.361e-06 -1.431e-06 b_tt_rail -6.304e-07 -1.837e-07 b_tt_interaction_business -7.167e-07 -3.279e-07 b_access -2.896e-06 -2.479e-06 b_cost -8.209e-06 -3.777e-06 b_cost_interaction_business 2.440e-06 1.353e-06 cost_income_elast 1.434e-05 -4.737e-06 b_wifi 1.1039e-04 4.140e-05 b_food 4.387e-05 1.463e-05 lambda_PT 7.961e-05 3.328e-05 lambda_fastPT 8.337e-05 3.217e-05 b_tt_car b_tt_bus asc_bus 1.0592e-04 -4.7957e-04 asc_air 1.4350e-04 4.143e-05 asc_rail 1.5182e-04 5.126e-05 asc_bus_interaction_female -1.785e-06 -6.850e-07 asc_air_interaction_female -1.319e-06 -2.331e-06 asc_rail_interaction_female -6.158e-07 -8.520e-07 b_tt_car 5.285e-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 -7.735e-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 -3.4543e-04 3.644e-06 asc_rail -1.459e-06 -2.5978e-04 asc_bus_interaction_female -2.436e-06 -1.846e-06 asc_air_interaction_female -1.361e-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 -4.361e-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 -4.070e-07 asc_air_interaction_female -7.167e-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 -8.698e-08 cost_income_elast -1.156e-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 -1.791e-06 -1.290e-05 b_cost b_cost_interaction_business asc_bus -6.068e-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 -8.209e-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 -8.698e-08 b_cost 5.761e-06 -3.708e-06 b_cost_interaction_business -3.708e-06 5.108e-06 cost_income_elast -1.691e-05 9.262e-07 b_wifi -5.556e-05 1.811e-05 b_food -2.395e-05 6.834e-06 lambda_PT -5.115e-05 3.365e-05 lambda_fastPT -4.663e-05 1.759e-05 cost_income_elast b_wifi asc_bus -8.2117e-04 -2.2830e-04 asc_air 0.001055 -0.001441 asc_rail 3.8827e-04 -0.002006 asc_bus_interaction_female -1.5819e-04 1.3809e-04 asc_air_interaction_female 1.434e-05 1.1039e-04 asc_rail_interaction_female -4.737e-06 4.140e-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 -1.156e-07 -2.688e-06 b_access -6.596e-06 -1.475e-05 b_cost -1.691e-05 -5.556e-05 b_cost_interaction_business 9.262e-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 5.9746e-04 lambda_fastPT 1.2242e-04 6.9588e-04 b_food lambda_PT asc_bus -2.2226e-04 1.8146e-04 asc_air -9.2648e-04 -4.2722e-04 asc_rail -0.001284 -0.001024 asc_bus_interaction_female 4.274e-05 2.3194e-04 asc_air_interaction_female 4.387e-05 7.961e-05 asc_rail_interaction_female 1.463e-05 3.328e-05 b_tt_car -4.206e-06 -7.735e-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 6.834e-06 3.365e-05 cost_income_elast 8.626e-05 -2.1704e-04 b_wifi 0.001057 5.9746e-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 -0.001068 asc_bus_interaction_female 1.3083e-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 -4.361e-06 b_tt_interaction_business -1.791e-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 6.9588e-04 b_food 2.7395e-04 lambda_PT 4.5128e-04 lambda_fastPT 9.2396e-04 Robust covariance matrix: asc_bus asc_air asc_bus 0.188603 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 -3.2418e-04 b_tt_rail -1.330e-06 8.364e-07 b_tt_interaction_business 1.590e-05 1.989e-05 b_access 7.236e-05 -2.7652e-04 b_cost -1.334e-05 -9.007e-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 -3.0622e-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 -8.2682e-04 asc_bus_interaction_female -8.2682e-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 -4.943e-08 b_tt_bus 4.681e-05 -3.314e-06 b_tt_air 4.768e-06 1.157e-05 b_tt_rail -2.3502e-04 -2.746e-06 b_tt_interaction_business 2.692e-05 1.414e-06 b_access -2.724e-05 -9.641e-06 b_cost 3.227e-05 -2.100e-05 b_cost_interaction_business 1.846e-05 1.503e-05 cost_income_elast 8.9534e-04 1.7446e-04 b_wifi -0.001744 9.720e-05 b_food -0.001109 3.0231e-04 lambda_PT -0.001247 4.2559e-04 lambda_fastPT -7.3635e-04 1.8637e-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 -9.260e-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 -9.733e-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 -1.6805e-04 -8.752e-05 lambda_PT 8.192e-05 3.362e-05 lambda_fastPT 1.1407e-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 -4.943e-08 -3.314e-06 asc_air_interaction_female -2.160e-06 -9.260e-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 8.407e-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 8.621e-07 4.990e-06 b_wifi -9.572e-06 -1.097e-05 b_food -4.864e-06 -7.224e-06 lambda_PT -8.279e-06 -1.634e-05 lambda_fastPT -5.845e-06 -9.022e-06 b_tt_air b_tt_rail asc_bus -1.234e-05 -1.330e-06 asc_air -3.2418e-04 8.364e-07 asc_rail 4.768e-06 -2.3502e-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 8.407e-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 -8.524e-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 -2.7652e-04 asc_rail 2.692e-05 -2.724e-05 asc_bus_interaction_female 1.414e-06 -9.641e-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 -8.524e-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 -8.802e-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 -9.007e-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 -9.733e-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 3.110e-07 b_wifi -5.500e-05 1.930e-05 b_food -2.651e-05 8.309e-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 8.9534e-04 -0.001744 asc_bus_interaction_female 1.7446e-04 9.720e-05 asc_air_interaction_female 2.3924e-04 -3.811e-05 asc_rail_interaction_female 1.7217e-04 -6.653e-05 b_tt_car 8.621e-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 -8.802e-06 b_cost -1.859e-05 -5.500e-05 b_cost_interaction_business 3.110e-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 -1.4122e-04 5.5833e-04 lambda_fastPT 1.8869e-04 6.4068e-04 b_food lambda_PT asc_bus -6.806e-05 -3.0622e-04 asc_air -9.3946e-04 -1.3393e-04 asc_rail -0.001109 -0.001247 asc_bus_interaction_female 3.0231e-04 4.2559e-04 asc_air_interaction_female -1.6805e-04 8.192e-05 asc_rail_interaction_female -8.752e-05 3.362e-05 b_tt_car -4.864e-06 -8.279e-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 8.309e-06 3.417e-05 cost_income_elast 2.565e-05 -1.4122e-04 b_wifi 0.001179 5.5833e-04 b_food 0.001787 2.6740e-04 lambda_PT 2.6740e-04 0.001452 lambda_fastPT 2.9101e-04 4.4990e-04 lambda_fastPT asc_bus -3.9543e-04 asc_air -1.7010e-04 asc_rail -7.3635e-04 asc_bus_interaction_female 1.8637e-04 asc_air_interaction_female 1.1407e-04 asc_rail_interaction_female 3.457e-05 b_tt_car -5.845e-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 6.4068e-04 b_food 2.9101e-04 lambda_PT 4.4990e-04 lambda_fastPT 8.5823e-04 Classical correlation matrix: asc_bus asc_air asc_bus 1.000000 0.263590 asc_air 0.263590 1.000000 asc_rail 0.249099 0.583631 asc_bus_interaction_female -0.136357 -0.054402 asc_air_interaction_female -0.041713 -0.127560 asc_rail_interaction_female -0.050709 -0.086182 b_tt_car 0.318190 0.665715 b_tt_bus -0.799127 0.106610 b_tt_air -0.012353 -0.595309 b_tt_rail 0.011359 0.009053 b_tt_interaction_business 0.025508 0.068370 b_access -0.010131 -0.486607 b_cost -0.005521 -0.025369 b_cost_interaction_business 0.036404 -0.065163 cost_income_elast -0.057393 0.113838 b_wifi -0.010858 -0.105809 b_food -0.012368 -0.079613 lambda_PT 0.010189 -0.037045 lambda_fastPT -0.009649 -0.019116 asc_rail asc_bus_interaction_female asc_bus 0.249099 -0.136357 asc_air 0.583631 -0.054402 asc_rail 1.000000 -0.053572 asc_bus_interaction_female -0.053572 1.000000 asc_air_interaction_female -0.090183 0.400551 asc_rail_interaction_female -0.116510 0.439094 b_tt_car 0.705012 -0.022804 b_tt_bus 0.132048 -0.004856 b_tt_air -0.002517 -0.011562 b_tt_rail -0.646069 -0.012635 b_tt_interaction_business 0.109263 0.006261 b_access -0.031005 -0.001861 b_cost 0.058291 -0.057702 b_cost_interaction_business -0.022439 0.053318 cost_income_elast 0.041947 -0.047028 b_wifi -0.147498 0.027936 b_food -0.110489 0.010118 lambda_PT -0.088874 0.055400 lambda_fastPT -0.118557 0.039983 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.041713 -0.050709 asc_air -0.127560 -0.086182 asc_rail -0.090183 -0.116510 asc_bus_interaction_female 0.400551 0.439094 asc_air_interaction_female 1.000000 0.721589 asc_rail_interaction_female 0.721589 1.000000 b_tt_car -0.023644 -0.012513 b_tt_bus -0.023180 -0.009602 b_tt_air -0.009061 -0.010801 b_tt_rail -0.006053 -0.001999 b_tt_interaction_business -0.018613 -0.009651 b_access -0.018574 -0.018025 b_cost -0.044571 -0.023244 b_cost_interaction_business 0.014071 0.008841 cost_income_elast 0.005979 -0.002239 b_wifi 0.031330 0.013316 b_food 0.014567 0.005507 lambda_PT 0.026675 0.012640 lambda_fastPT 0.035745 0.015633 b_tt_car b_tt_bus asc_bus 0.31819 -0.799127 asc_air 0.66571 0.106610 asc_rail 0.70501 0.132048 asc_bus_interaction_female -0.02280 -0.004856 asc_air_interaction_female -0.02364 -0.023180 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 0.052948 b_tt_interaction_business -0.04578 -0.057320 b_access 0.05835 0.034717 b_cost 0.41947 0.391896 b_cost_interaction_business -0.29704 -0.313127 cost_income_elast -0.01239 0.093023 b_wifi -0.28444 -0.230573 b_food -0.14743 -0.106473 lambda_PT -0.27357 -0.341961 lambda_fastPT -0.29034 -0.256294 b_tt_air b_tt_rail asc_bus -0.012353 0.011359 asc_air -0.595309 0.009053 asc_rail -0.002517 -0.646069 asc_bus_interaction_female -0.011562 -0.012635 asc_air_interaction_female -0.009061 -0.006053 asc_rail_interaction_female -0.010801 -0.001999 b_tt_car 0.056860 0.037133 b_tt_bus 0.068237 0.052948 b_tt_air 1.000000 -0.020409 b_tt_rail -0.020409 1.000000 b_tt_interaction_business -0.040272 -0.120581 b_access 0.385691 -0.054498 b_cost 0.290250 0.260551 b_cost_interaction_business -0.093287 -0.189469 cost_income_elast -0.127400 -0.051539 b_wifi -0.147243 -0.136461 b_food -0.085653 -0.068853 lambda_PT -0.125905 -0.111923 lambda_fastPT -0.209938 -0.105707 b_tt_interaction_business b_access asc_bus 0.025508 -0.010131 asc_air 0.068370 -0.486607 asc_rail 0.109263 -0.031005 asc_bus_interaction_female 0.006261 -0.001861 asc_air_interaction_female -0.018613 -0.018574 asc_rail_interaction_female -0.009651 -0.018025 b_tt_car -0.045780 0.058351 b_tt_bus -0.057320 0.034717 b_tt_air -0.040272 0.385691 b_tt_rail -0.120581 -0.054498 b_tt_interaction_business 1.000000 0.063992 b_access 0.063992 1.000000 b_cost -0.160880 0.247687 b_cost_interaction_business 0.612827 -0.018942 cost_income_elast -0.007370 -0.103897 b_wifi -0.116646 -0.158109 b_food -0.056230 -0.085960 lambda_PT 0.029839 -0.157208 lambda_fastPT -0.117392 -0.208820 b_cost b_cost_interaction_business asc_bus -0.005521 0.036404 asc_air -0.025369 -0.065163 asc_rail 0.058291 -0.022439 asc_bus_interaction_female -0.057702 0.053318 asc_air_interaction_female -0.044571 0.014071 asc_rail_interaction_female -0.023244 0.008841 b_tt_car 0.419465 -0.297044 b_tt_bus 0.391896 -0.313127 b_tt_air 0.290250 -0.093287 b_tt_rail 0.260551 -0.189469 b_tt_interaction_business -0.160880 0.612827 b_access 0.247687 -0.018942 b_cost 1.000000 -0.683619 b_cost_interaction_business -0.683619 1.000000 cost_income_elast -0.225514 0.013116 b_wifi -0.504092 0.174465 b_food -0.254232 0.077055 lambda_PT -0.548000 0.382882 lambda_fastPT -0.639141 0.256086 cost_income_elast b_wifi asc_bus -0.057393 -0.01086 asc_air 0.113838 -0.10581 asc_rail 0.041947 -0.14750 asc_bus_interaction_female -0.047028 0.02794 asc_air_interaction_female 0.005979 0.03133 asc_rail_interaction_female -0.002239 0.01332 b_tt_car -0.012389 -0.28444 b_tt_bus 0.093023 -0.23057 b_tt_air -0.127400 -0.14724 b_tt_rail -0.051539 -0.13646 b_tt_interaction_business -0.007370 -0.11665 b_access -0.103897 -0.15811 b_cost -0.225514 -0.50409 b_cost_interaction_business 0.013116 0.17447 cost_income_elast 1.000000 0.09280 b_wifi 0.092802 1.00000 b_food 0.070343 0.58648 lambda_PT -0.178601 0.33455 lambda_fastPT 0.128895 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 0.010118 0.05540 asc_air_interaction_female 0.014567 0.02668 asc_rail_interaction_female 0.005507 0.01264 b_tt_car -0.147434 -0.27357 b_tt_bus -0.106473 -0.34196 b_tt_air -0.085653 -0.12591 b_tt_rail -0.068853 -0.11192 b_tt_interaction_business -0.056230 0.02984 b_access -0.085960 -0.15721 b_cost -0.254232 -0.54800 b_cost_interaction_business 0.077055 0.38288 cost_income_elast 0.070343 -0.17860 b_wifi 0.586478 0.33455 b_food 1.000000 0.15213 lambda_PT 0.152127 1.00000 lambda_fastPT 0.229648 0.38174 lambda_fastPT asc_bus -0.009649 asc_air -0.019116 asc_rail -0.118557 asc_bus_interaction_female 0.039983 asc_air_interaction_female 0.035745 asc_rail_interaction_female 0.015633 b_tt_car -0.290344 b_tt_bus -0.256294 b_tt_air -0.209938 b_tt_rail -0.105707 b_tt_interaction_business -0.117392 b_access -0.208820 b_cost -0.639141 b_cost_interaction_business 0.256086 cost_income_elast 0.128895 b_wifi 0.498558 b_food 0.229648 lambda_PT 0.381740 lambda_fastPT 1.000000 Robust correlation matrix: asc_bus asc_air asc_bus 1.000000 0.237289 asc_air 0.237289 1.000000 asc_rail 0.261288 0.596905 asc_bus_interaction_female -0.121974 -0.036422 asc_air_interaction_female 0.030929 -0.105397 asc_rail_interaction_female -0.023360 -0.057601 b_tt_car 0.317973 0.654417 b_tt_bus -0.777319 0.138293 b_tt_air -0.014325 -0.565042 b_tt_rail -0.002314 0.002183 b_tt_interaction_business 0.078398 0.147240 b_access 0.084031 -0.482008 b_cost -0.012619 -0.012785 b_cost_interaction_business 0.091219 -0.068468 cost_income_elast -0.083153 0.140926 b_wifi -0.068428 -0.111737 b_food -0.003707 -0.076814 lambda_PT -0.018505 -0.012149 lambda_fastPT -0.031081 -0.020069 asc_rail asc_bus_interaction_female asc_bus 0.261288 -0.12197 asc_air 0.596905 -0.03642 asc_rail 1.000000 -0.02487 asc_bus_interaction_female -0.024868 1.00000 asc_air_interaction_female -0.127836 0.36271 asc_rail_interaction_female -0.082349 0.45292 b_tt_car 0.694693 -5.8328e-04 b_tt_bus 0.129415 -0.02260 b_tt_air 0.008396 0.05027 b_tt_rail -0.619799 -0.01787 b_tt_interaction_business 0.201342 0.02609 b_access -0.047974 -0.04188 b_cost 0.046270 -0.07429 b_cost_interaction_business 0.030163 0.06060 cost_income_elast 0.096750 0.04651 b_wifi -0.129120 0.01775 b_food -0.091562 0.06160 lambda_PT -0.114227 0.09621 lambda_fastPT -0.087765 0.05480 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.030929 -0.02336 asc_air -0.105397 -0.05760 asc_rail -0.127836 -0.08235 asc_bus_interaction_female 0.362709 0.45292 asc_air_interaction_female 1.000000 0.75132 asc_rail_interaction_female 0.751321 1.00000 b_tt_car -0.038220 0.02534 b_tt_bus -0.094729 -0.01923 b_tt_air -0.007094 0.02230 b_tt_rail 0.063733 0.01730 b_tt_interaction_business 0.007985 0.01620 b_access -0.041938 -0.01897 b_cost -0.105177 -0.05859 b_cost_interaction_business 0.085500 0.08191 cost_income_elast 0.095655 0.07810 b_wifi -0.010437 -0.02067 b_food -0.051357 -0.03035 lambda_PT 0.027777 0.01293 lambda_fastPT 0.050306 0.01730 b_tt_car b_tt_bus asc_bus 0.317973 -0.77732 asc_air 0.654417 0.13829 asc_rail 0.694693 0.12942 asc_bus_interaction_female -5.8328e-04 -0.02260 asc_air_interaction_female -0.038220 -0.09473 asc_rail_interaction_female 0.025339 -0.01923 b_tt_car 1.000000 0.28685 b_tt_bus 0.286853 1.00000 b_tt_air 0.109755 0.09899 b_tt_rail 0.086985 0.10283 b_tt_interaction_business 0.007187 -0.08989 b_access 0.064389 -0.03977 b_cost 0.434216 0.42466 b_cost_interaction_business -0.308827 -0.38759 cost_income_elast 0.036546 0.12229 b_wifi -0.277988 -0.18408 b_food -0.157610 -0.13531 lambda_PT -0.297602 -0.33950 lambda_fastPT -0.273281 -0.24386 b_tt_air b_tt_rail asc_bus -0.014325 -0.002314 asc_air -0.565042 0.002183 asc_rail 0.008396 -0.619799 asc_bus_interaction_female 0.050274 -0.017865 asc_air_interaction_female -0.007094 0.063733 asc_rail_interaction_female 0.022296 0.017300 b_tt_car 0.109755 0.086985 b_tt_bus 0.098985 0.102833 b_tt_air 1.000000 0.032784 b_tt_rail 0.032784 1.000000 b_tt_interaction_business -0.073124 -0.180396 b_access 0.360287 -0.032467 b_cost 0.283566 0.305109 b_cost_interaction_business -0.080109 -0.281063 cost_income_elast -0.138727 -0.096256 b_wifi -0.176823 -0.178532 b_food -0.122643 -0.114444 lambda_PT -0.170025 -0.092256 lambda_fastPT -0.202802 -0.148440 b_tt_interaction_business b_access asc_bus 0.078398 0.08403 asc_air 0.147240 -0.48201 asc_rail 0.201342 -0.04797 asc_bus_interaction_female 0.026092 -0.04188 asc_air_interaction_female 0.007985 -0.04194 asc_rail_interaction_female 0.016196 -0.01897 b_tt_car 0.007187 0.06439 b_tt_bus -0.089890 -0.03977 b_tt_air -0.073124 0.36029 b_tt_rail -0.180396 -0.03247 b_tt_interaction_business 1.000000 0.06094 b_access 0.060941 1.00000 b_cost -0.188568 0.25641 b_cost_interaction_business 0.545844 -0.03828 cost_income_elast -0.009864 -0.07964 b_wifi -0.142658 -0.09410 b_food -0.073392 -0.04999 lambda_PT 0.025686 -0.18879 lambda_fastPT -0.141739 -0.19608 b_cost b_cost_interaction_business asc_bus -0.01262 0.091219 asc_air -0.01279 -0.068468 asc_rail 0.04627 0.030163 asc_bus_interaction_female -0.07429 0.060599 asc_air_interaction_female -0.10518 0.085500 asc_rail_interaction_female -0.05859 0.081914 b_tt_car 0.43422 -0.308827 b_tt_bus 0.42466 -0.387591 b_tt_air 0.28357 -0.080109 b_tt_rail 0.30511 -0.281063 b_tt_interaction_business -0.18857 0.545844 b_access 0.25641 -0.038282 b_cost 1.00000 -0.733302 b_cost_interaction_business -0.73330 1.000000 cost_income_elast -0.23624 0.004505 b_wifi -0.47889 0.191504 b_food -0.25749 0.091984 lambda_PT -0.57376 0.419610 lambda_fastPT -0.64895 0.272646 cost_income_elast b_wifi asc_bus -0.083153 -0.06843 asc_air 0.140926 -0.11174 asc_rail 0.096750 -0.12912 asc_bus_interaction_female 0.046506 0.01775 asc_air_interaction_female 0.095655 -0.01044 asc_rail_interaction_female 0.078099 -0.02067 b_tt_car 0.036546 -0.27799 b_tt_bus 0.122286 -0.18408 b_tt_air -0.138727 -0.17682 b_tt_rail -0.096256 -0.17853 b_tt_interaction_business -0.009864 -0.14266 b_access -0.079639 -0.09410 b_cost -0.236239 -0.47889 b_cost_interaction_business 0.004505 0.19150 cost_income_elast 1.000000 0.09453 b_wifi 0.094525 1.00000 b_food 0.018778 0.59105 lambda_PT -0.114694 0.31064 lambda_fastPT 0.199331 0.46364 b_food lambda_PT asc_bus -0.003707 -0.01850 asc_air -0.076814 -0.01215 asc_rail -0.091562 -0.11423 asc_bus_interaction_female 0.061598 0.09621 asc_air_interaction_female -0.051357 0.02778 asc_rail_interaction_female -0.030346 0.01293 b_tt_car -0.157610 -0.29760 b_tt_bus -0.135313 -0.33950 b_tt_air -0.122643 -0.17002 b_tt_rail -0.114444 -0.09226 b_tt_interaction_business -0.073392 0.02569 b_access -0.049991 -0.18879 b_cost -0.257493 -0.57376 b_cost_interaction_business 0.091984 0.41961 cost_income_elast 0.018778 -0.11469 b_wifi 0.591051 0.31064 b_food 1.000000 0.16600 lambda_PT 0.165999 1.00000 lambda_fastPT 0.234974 0.40303 lambda_fastPT asc_bus -0.03108 asc_air -0.02007 asc_rail -0.08777 asc_bus_interaction_female 0.05480 asc_air_interaction_female 0.05031 asc_rail_interaction_female 0.01730 b_tt_car -0.27328 b_tt_bus -0.24386 b_tt_air -0.20280 b_tt_rail -0.14844 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 0.23497 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 0.2254729 464 0.2335747 293 0.2429288 146 0.2627891 181 0.2654204 317 0.2703853 276 0.2785466 367 0.2792016 434 0.2870661 186 0.2885083 307 0.2930730 370 0.2956406 147 0.2959379 161 0.2965359 142 0.2977474 259 0.3012007 441 0.3019522 183 0.3026300 447 0.3029720 379 0.3038189 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Three-level NL model with socio-demographics on mode choice SP data, with constraints on lambdas" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "NL_three_levels_constraints_on_lambdas" 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 0.414232713 asc_air 0.715567282 asc_rail 1.647919329 asc_bus_interaction_female 0.274686221 asc_air_interaction_female 0.237118383 asc_rail_interaction_female 0.179649744 b_tt_car 0.010515475 b_tt_bus 0.016902903 b_tt_air 0.012112246 b_tt_rail 0.005245994 b_tt_interaction_business 0.005882519 b_access 0.016827150 b_cost 0.058240446 b_cost_interaction_business 0.025465750 cost_income_elast 0.626047765 b_wifi 0.756581705 b_food 0.323531521 lambda_PT 0.695287076 lambda_fastPT 0.586193553 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) }