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_two_levels Model description : Two-level NL model with socio-demographics on mode choice SP data Model run at : 2025-09-19 11:39:15.784839 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -4.499548 reciprocal of condition number : 4.24427e-08 Number of individuals : 500 Number of rows in database : 7000 Number of modelled outcomes : 7000 Number of cores used : 2 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) : -4774.55 Rho-squared vs equal shares : 0.4175 Adj.Rho-squared vs equal shares : 0.4153 Rho-squared vs observed shares : 0.2881 Adj.Rho-squared vs observed shares : 0.2859 AIC : 9585.1 BIC : 9708.47 Estimated parameters : 18 Time taken (hh:mm:ss) : 00:00:7.5 pre-estimation : 00:00:2.48 estimation : 00:00:0.56 post-estimation : 00:00:4.46 Iterations : 7 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 0.390317 0.436666 0.8939 -1.396 0.421972 asc_air -0.703768 0.301199 -2.3366 -5.657 0.292795 asc_rail -1.666340 0.299915 -5.5560 -8.890 0.288933 asc_bus_interaction_female 0.269690 0.103710 2.6004 -7.042 0.112994 asc_air_interaction_female 0.238206 0.077606 3.0694 -9.816 0.078306 asc_rail_interaction_female 0.179808 0.067785 2.6526 -12.100 0.068429 b_tt_car -0.010496 7.2781e-04 -14.4216 -1388.411 7.2982e-04 b_tt_bus -0.016548 0.001244 -13.3006 -817.058 0.001221 b_tt_air -0.012462 0.002028 -6.1440 -499.152 0.002040 b_tt_rail -0.005176 0.001396 -3.7087 -720.292 0.001354 b_tt_interaction_business -0.006076 5.0779e-04 -11.9656 -1981.288 4.7317e-04 b_access -0.016973 0.002082 -8.1521 -488.445 0.002026 b_cost -0.058409 0.002413 -24.2104 -438.706 0.002459 b_cost_interaction_business 0.024503 0.002280 10.7485 -427.911 0.002140 cost_income_elast -0.603015 0.028930 -20.8443 -55.411 0.029927 b_no_frills 0.000000 NA NA NA NA b_wifi 0.771050 0.047051 16.3876 -4.866 0.048106 b_food 0.329407 0.040593 8.1148 -16.520 0.043123 lambda_PT 0.632436 0.028522 22.1739 -12.887 0.028225 Rob.t.rat.(0) Rob.t.rat.(1) asc_car NA NA asc_bus 0.9250 -1.445 asc_air -2.4036 -5.819 asc_rail -5.7672 -9.228 asc_bus_interaction_female 2.3868 -6.463 asc_air_interaction_female 3.0420 -9.728 asc_rail_interaction_female 2.6276 -11.986 b_tt_car -14.3818 -1384.579 b_tt_bus -13.5494 -832.342 b_tt_air -6.1089 -496.299 b_tt_rail -3.8236 -742.604 b_tt_interaction_business -12.8410 -2126.242 b_access -8.3768 -501.908 b_cost -23.7540 -430.434 b_cost_interaction_business 11.4488 -455.790 cost_income_elast -20.1496 -53.564 b_no_frills NA NA b_wifi 16.0282 -4.759 b_food 7.6387 -15.551 lambda_PT 22.4066 -13.022 Nesting structure for NL model component : Nest: root (1) |----Alternative: car '-Nest: PT (0.6324) |-Alternative: bus |-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 0.190677 0.036642 asc_air 0.036642 0.090721 asc_rail 0.034185 0.051277 asc_bus_interaction_female -0.006258 -0.001790 asc_air_interaction_female -0.001478 -0.002967 asc_rail_interaction_female -0.001619 -0.001691 b_tt_car 1.0713e-04 1.4425e-04 b_tt_bus -4.2610e-04 3.978e-05 b_tt_air -1.462e-05 -3.6995e-04 b_tt_rail 7.653e-06 7.205e-06 b_tt_interaction_business 6.164e-06 1.038e-05 b_access -1.232e-05 -3.0747e-04 b_cost -1.303e-05 -1.655e-05 b_cost_interaction_business 4.188e-05 -4.339e-05 cost_income_elast -6.3732e-04 9.7071e-04 b_wifi -1.4645e-04 -0.001630 b_food -2.0049e-04 -9.9043e-04 lambda_PT 2.869e-05 -3.0129e-04 asc_rail asc_bus_interaction_female asc_bus 0.034185 -0.006258 asc_air 0.051277 -0.001790 asc_rail 0.089949 -0.001762 asc_bus_interaction_female -0.001762 0.010756 asc_air_interaction_female -0.002029 0.003416 asc_rail_interaction_female -0.002339 0.003290 b_tt_car 1.5241e-04 -1.746e-06 b_tt_bus 5.100e-05 -5.430e-07 b_tt_air -1.465e-06 -2.674e-06 b_tt_rail -2.7407e-04 -1.809e-06 b_tt_interaction_business 1.575e-05 2.470e-07 b_access -1.508e-05 -2.010e-07 b_cost 4.130e-05 -1.483e-05 b_cost_interaction_business -1.602e-05 1.231e-05 cost_income_elast 4.1061e-04 -1.3090e-04 b_wifi -0.002053 1.4694e-04 b_food -0.001334 4.268e-05 lambda_PT -0.001069 1.6939e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.001478 -0.001619 asc_air -0.002967 -0.001691 asc_rail -0.002029 -0.002339 asc_bus_interaction_female 0.003416 0.003290 asc_air_interaction_female 0.006023 0.003677 asc_rail_interaction_female 0.003677 0.004595 b_tt_car -1.347e-06 -6.250e-07 b_tt_bus -2.508e-06 -8.712e-07 b_tt_air -1.325e-06 -1.471e-06 b_tt_rail -5.683e-07 -2.146e-07 b_tt_interaction_business -6.962e-07 -3.135e-07 b_access -3.009e-06 -2.497e-06 b_cost -8.366e-06 -3.966e-06 b_cost_interaction_business 2.519e-06 1.548e-06 cost_income_elast 6.704e-06 -4.837e-06 b_wifi 1.1241e-04 4.108e-05 b_food 4.531e-05 1.397e-05 lambda_PT 8.526e-05 3.383e-05 b_tt_car b_tt_bus asc_bus 1.0713e-04 -4.2610e-04 asc_air 1.4425e-04 3.978e-05 asc_rail 1.5241e-04 5.100e-05 asc_bus_interaction_female -1.746e-06 -5.430e-07 asc_air_interaction_female -1.347e-06 -2.508e-06 asc_rail_interaction_female -6.250e-07 -8.712e-07 b_tt_car 5.297e-07 2.408e-07 b_tt_bus 2.408e-07 1.548e-06 b_tt_air 7.979e-08 1.947e-07 b_tt_rail 3.591e-08 9.187e-08 b_tt_interaction_business -1.854e-08 -3.518e-08 b_access 8.240e-08 9.291e-08 b_cost 7.430e-07 1.266e-06 b_cost_interaction_business -4.930e-07 -9.083e-07 cost_income_elast -2.479e-07 2.365e-06 b_wifi -9.860e-06 -1.493e-05 b_food -4.350e-06 -5.834e-06 lambda_PT -7.123e-06 -1.315e-05 b_tt_air b_tt_rail asc_bus -1.462e-05 7.653e-06 asc_air -3.6995e-04 7.205e-06 asc_rail -1.465e-06 -2.7407e-04 asc_bus_interaction_female -2.674e-06 -1.809e-06 asc_air_interaction_female -1.325e-06 -5.683e-07 asc_rail_interaction_female -1.471e-06 -2.146e-07 b_tt_car 7.979e-08 3.591e-08 b_tt_bus 1.947e-07 9.187e-08 b_tt_air 4.114e-06 -6.939e-08 b_tt_rail -6.939e-08 1.947e-06 b_tt_interaction_business -4.996e-08 -8.314e-08 b_access 1.591e-06 -2.078e-07 b_cost 1.390e-06 8.687e-07 b_cost_interaction_business -4.593e-07 -5.914e-07 cost_income_elast -6.543e-06 -2.094e-06 b_wifi -1.286e-05 -9.151e-06 b_food -6.843e-06 -3.892e-06 lambda_PT -1.176e-05 -5.178e-06 b_tt_interaction_business b_access asc_bus 6.164e-06 -1.232e-05 asc_air 1.038e-05 -3.0747e-04 asc_rail 1.575e-05 -1.508e-05 asc_bus_interaction_female 2.470e-07 -2.010e-07 asc_air_interaction_female -6.962e-07 -3.009e-06 asc_rail_interaction_female -3.135e-07 -2.497e-06 b_tt_car -1.854e-08 8.240e-08 b_tt_bus -3.518e-08 9.291e-08 b_tt_air -4.996e-08 1.591e-06 b_tt_rail -8.314e-08 -2.078e-07 b_tt_interaction_business 2.578e-07 6.099e-08 b_access 6.099e-08 4.335e-06 b_cost -2.161e-07 1.181e-06 b_cost_interaction_business 7.185e-07 -9.670e-08 cost_income_elast 4.875e-07 -5.231e-06 b_wifi -2.154e-06 -1.411e-05 b_food -8.621e-07 -6.767e-06 lambda_PT -6.141e-07 -1.268e-05 b_cost b_cost_interaction_business asc_bus -1.303e-05 4.188e-05 asc_air -1.655e-05 -4.339e-05 asc_rail 4.130e-05 -1.602e-05 asc_bus_interaction_female -1.483e-05 1.231e-05 asc_air_interaction_female -8.366e-06 2.519e-06 asc_rail_interaction_female -3.966e-06 1.548e-06 b_tt_car 7.430e-07 -4.930e-07 b_tt_bus 1.266e-06 -9.083e-07 b_tt_air 1.390e-06 -4.593e-07 b_tt_rail 8.687e-07 -5.914e-07 b_tt_interaction_business -2.161e-07 7.185e-07 b_access 1.181e-06 -9.670e-08 b_cost 5.821e-06 -3.768e-06 b_cost_interaction_business -3.768e-06 5.197e-06 cost_income_elast -1.471e-05 2.926e-06 b_wifi -5.625e-05 2.039e-05 b_food -2.423e-05 7.779e-06 lambda_PT -4.982e-05 2.472e-05 cost_income_elast b_wifi asc_bus -6.3732e-04 -1.4645e-04 asc_air 9.7071e-04 -0.001630 asc_rail 4.1061e-04 -0.002053 asc_bus_interaction_female -1.3090e-04 1.4694e-04 asc_air_interaction_female 6.704e-06 1.1241e-04 asc_rail_interaction_female -4.837e-06 4.108e-05 b_tt_car -2.479e-07 -9.860e-06 b_tt_bus 2.365e-06 -1.493e-05 b_tt_air -6.543e-06 -1.286e-05 b_tt_rail -2.094e-06 -9.151e-06 b_tt_interaction_business 4.875e-07 -2.154e-06 b_access -5.231e-06 -1.411e-05 b_cost -1.471e-05 -5.625e-05 b_cost_interaction_business 2.926e-06 2.039e-05 cost_income_elast 8.3692e-04 6.764e-05 b_wifi 6.764e-05 0.002214 b_food 6.073e-05 0.001109 lambda_PT -1.623e-05 6.7986e-04 b_food lambda_PT asc_bus -2.0049e-04 2.869e-05 asc_air -9.9043e-04 -3.0129e-04 asc_rail -0.001334 -0.001069 asc_bus_interaction_female 4.268e-05 1.6939e-04 asc_air_interaction_female 4.531e-05 8.526e-05 asc_rail_interaction_female 1.397e-05 3.383e-05 b_tt_car -4.350e-06 -7.123e-06 b_tt_bus -5.834e-06 -1.315e-05 b_tt_air -6.843e-06 -1.176e-05 b_tt_rail -3.892e-06 -5.178e-06 b_tt_interaction_business -8.621e-07 -6.141e-07 b_access -6.767e-06 -1.268e-05 b_cost -2.423e-05 -4.982e-05 b_cost_interaction_business 7.779e-06 2.472e-05 cost_income_elast 6.073e-05 -1.623e-05 b_wifi 0.001109 6.7986e-04 b_food 0.001648 2.6221e-04 lambda_PT 2.6221e-04 8.1348e-04 Robust covariance matrix: asc_bus asc_air asc_bus 0.178060 0.030533 asc_air 0.030533 0.085729 asc_rail 0.032687 0.048894 asc_bus_interaction_female -0.005584 -0.001358 asc_air_interaction_female 0.001044 -0.002314 asc_rail_interaction_female -6.5232e-04 -0.001137 b_tt_car 1.0158e-04 1.3873e-04 b_tt_bus -3.9754e-04 4.926e-05 b_tt_air -1.990e-05 -3.4309e-04 b_tt_rail -1.914e-06 7.267e-06 b_tt_interaction_business 1.598e-05 2.016e-05 b_access 7.345e-05 -2.8840e-04 b_cost -2.171e-05 -9.194e-06 b_cost_interaction_business 8.995e-05 -4.250e-05 cost_income_elast -9.8379e-04 0.001283 b_wifi -0.001313 -0.001573 b_food 4.753e-05 -9.3293e-04 lambda_PT -3.1494e-04 -1.2043e-04 asc_rail asc_bus_interaction_female asc_bus 0.032687 -0.005584 asc_air 0.048894 -0.001358 asc_rail 0.083483 -8.4808e-04 asc_bus_interaction_female -8.4808e-04 0.012768 asc_air_interaction_female -0.002886 0.003309 asc_rail_interaction_female -0.001633 0.003650 b_tt_car 1.4530e-04 -1.896e-07 b_tt_bus 4.486e-05 -3.446e-06 b_tt_air 9.767e-06 1.239e-05 b_tt_rail -2.4547e-04 -3.134e-06 b_tt_interaction_business 2.793e-05 1.249e-06 b_access -2.076e-05 -9.276e-06 b_cost 3.165e-05 -2.373e-05 b_cost_interaction_business 2.487e-05 1.517e-05 cost_income_elast 8.0049e-04 2.7831e-04 b_wifi -0.001765 1.0982e-04 b_food -0.001099 2.7982e-04 lambda_PT -9.8032e-04 2.8869e-04 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.001044 -6.5232e-04 asc_air -0.002314 -0.001137 asc_rail -0.002886 -0.001633 asc_bus_interaction_female 0.003309 0.003650 asc_air_interaction_female 0.006132 0.003940 asc_rail_interaction_female 0.003940 0.004683 b_tt_car -2.158e-06 1.279e-06 b_tt_bus -9.467e-06 -1.873e-06 b_tt_air -2.154e-06 3.396e-06 b_tt_rail 7.035e-06 1.650e-06 b_tt_interaction_business 2.753e-07 4.603e-07 b_access -7.341e-06 -3.024e-06 b_cost -1.893e-05 -9.403e-06 b_cost_interaction_business 1.408e-05 1.170e-05 cost_income_elast 1.8302e-04 1.6658e-04 b_wifi -4.342e-05 -6.837e-05 b_food -1.6355e-04 -8.021e-05 lambda_PT 1.0724e-04 3.910e-05 b_tt_car b_tt_bus asc_bus 1.0158e-04 -3.9754e-04 asc_air 1.3873e-04 4.926e-05 asc_rail 1.4530e-04 4.486e-05 asc_bus_interaction_female -1.896e-07 -3.446e-06 asc_air_interaction_female -2.158e-06 -9.467e-06 asc_rail_interaction_female 1.279e-06 -1.873e-06 b_tt_car 5.326e-07 2.581e-07 b_tt_bus 2.581e-07 1.492e-06 b_tt_air 1.561e-07 2.686e-07 b_tt_rail 8.423e-08 1.819e-07 b_tt_interaction_business 3.677e-09 -4.771e-08 b_access 9.006e-08 -1.143e-07 b_cost 7.837e-07 1.347e-06 b_cost_interaction_business -4.713e-07 -1.018e-06 cost_income_elast 6.710e-07 3.191e-06 b_wifi -9.918e-06 -1.191e-05 b_food -5.035e-06 -7.813e-06 lambda_PT -7.013e-06 -1.197e-05 b_tt_air b_tt_rail asc_bus -1.990e-05 -1.914e-06 asc_air -3.4309e-04 7.267e-06 asc_rail 9.767e-06 -2.4547e-04 asc_bus_interaction_female 1.239e-05 -3.134e-06 asc_air_interaction_female -2.154e-06 7.035e-06 asc_rail_interaction_female 3.396e-06 1.650e-06 b_tt_car 1.561e-07 8.423e-08 b_tt_bus 2.686e-07 1.819e-07 b_tt_air 4.162e-06 3.516e-08 b_tt_rail 3.516e-08 1.832e-06 b_tt_interaction_business -7.142e-08 -1.184e-07 b_access 1.475e-06 -1.541e-07 b_cost 1.385e-06 1.003e-06 b_cost_interaction_business -3.466e-07 -8.363e-07 cost_income_elast -7.955e-06 -3.409e-06 b_wifi -1.661e-05 -1.158e-05 b_food -1.107e-05 -6.847e-06 lambda_PT -1.322e-05 -5.275e-06 b_tt_interaction_business b_access asc_bus 1.598e-05 7.345e-05 asc_air 2.016e-05 -2.8840e-04 asc_rail 2.793e-05 -2.076e-05 asc_bus_interaction_female 1.249e-06 -9.276e-06 asc_air_interaction_female 2.753e-07 -7.341e-06 asc_rail_interaction_female 4.603e-07 -3.024e-06 b_tt_car 3.677e-09 9.006e-08 b_tt_bus -4.771e-08 -1.143e-07 b_tt_air -7.142e-08 1.475e-06 b_tt_rail -1.184e-07 -1.541e-07 b_tt_interaction_business 2.239e-07 5.907e-08 b_access 5.907e-08 4.106e-06 b_cost -2.379e-07 1.234e-06 b_cost_interaction_business 5.569e-07 -1.431e-07 cost_income_elast 6.122e-07 -4.245e-06 b_wifi -2.555e-06 -9.183e-06 b_food -1.122e-06 -4.226e-06 lambda_PT -8.214e-07 -1.299e-05 b_cost b_cost_interaction_business asc_bus -2.171e-05 8.995e-05 asc_air -9.194e-06 -4.250e-05 asc_rail 3.165e-05 2.487e-05 asc_bus_interaction_female -2.373e-05 1.517e-05 asc_air_interaction_female -1.893e-05 1.408e-05 asc_rail_interaction_female -9.403e-06 1.170e-05 b_tt_car 7.837e-07 -4.713e-07 b_tt_bus 1.347e-06 -1.018e-06 b_tt_air 1.385e-06 -3.466e-07 b_tt_rail 1.003e-06 -8.363e-07 b_tt_interaction_business -2.379e-07 5.569e-07 b_access 1.234e-06 -1.431e-07 b_cost 6.046e-06 -3.870e-06 b_cost_interaction_business -3.870e-06 4.581e-06 cost_income_elast -1.685e-05 2.959e-06 b_wifi -5.632e-05 2.176e-05 b_food -2.751e-05 9.883e-06 lambda_PT -5.120e-05 2.445e-05 cost_income_elast b_wifi asc_bus -9.8379e-04 -0.001313 asc_air 0.001283 -0.001573 asc_rail 8.0049e-04 -0.001765 asc_bus_interaction_female 2.7831e-04 1.0982e-04 asc_air_interaction_female 1.8302e-04 -4.342e-05 asc_rail_interaction_female 1.6658e-04 -6.837e-05 b_tt_car 6.710e-07 -9.918e-06 b_tt_bus 3.191e-06 -1.191e-05 b_tt_air -7.955e-06 -1.661e-05 b_tt_rail -3.409e-06 -1.158e-05 b_tt_interaction_business 6.122e-07 -2.555e-06 b_access -4.245e-06 -9.183e-06 b_cost -1.685e-05 -5.632e-05 b_cost_interaction_business 2.959e-06 2.176e-05 cost_income_elast 8.9562e-04 8.196e-05 b_wifi 8.196e-05 0.002314 b_food 3.587e-06 0.001214 lambda_PT 6.663e-05 6.2623e-04 b_food lambda_PT asc_bus 4.753e-05 -3.1494e-04 asc_air -9.3293e-04 -1.2043e-04 asc_rail -0.001099 -9.8032e-04 asc_bus_interaction_female 2.7982e-04 2.8869e-04 asc_air_interaction_female -1.6355e-04 1.0724e-04 asc_rail_interaction_female -8.021e-05 3.910e-05 b_tt_car -5.035e-06 -7.013e-06 b_tt_bus -7.813e-06 -1.197e-05 b_tt_air -1.107e-05 -1.322e-05 b_tt_rail -6.847e-06 -5.275e-06 b_tt_interaction_business -1.122e-06 -8.214e-07 b_access -4.226e-06 -1.299e-05 b_cost -2.751e-05 -5.120e-05 b_cost_interaction_business 9.883e-06 2.445e-05 cost_income_elast 3.587e-06 6.663e-05 b_wifi 0.001214 6.2623e-04 b_food 0.001860 2.8580e-04 lambda_PT 2.8580e-04 7.9668e-04 Classical correlation matrix: asc_bus asc_air asc_bus 1.000000 0.27859 asc_air 0.278594 1.00000 asc_rail 0.261028 0.56764 asc_bus_interaction_female -0.138194 -0.05731 asc_air_interaction_female -0.043619 -0.12693 asc_rail_interaction_female -0.054694 -0.08283 b_tt_car 0.337081 0.65801 b_tt_bus -0.784302 0.10615 b_tt_air -0.016507 -0.60554 b_tt_rail 0.012559 0.01714 b_tt_interaction_business 0.027801 0.06785 b_access -0.013555 -0.49030 b_cost -0.012365 -0.02277 b_cost_interaction_business 0.042067 -0.06319 cost_income_elast -0.050450 0.11140 b_wifi -0.007128 -0.11501 b_food -0.011311 -0.08101 lambda_PT 0.002304 -0.03507 asc_rail asc_bus_interaction_female asc_bus 0.261028 -0.138194 asc_air 0.567639 -0.057306 asc_rail 1.000000 -0.056634 asc_bus_interaction_female -0.056634 1.000000 asc_air_interaction_female -0.087157 0.424482 asc_rail_interaction_female -0.115053 0.467929 b_tt_car 0.698235 -0.023134 b_tt_bus 0.136675 -0.004208 b_tt_air -0.002408 -0.012710 b_tt_rail -0.654829 -0.012501 b_tt_interaction_business 0.103416 0.004690 b_access -0.024149 -9.3077e-04 b_cost 0.057080 -0.059271 b_cost_interaction_business -0.023425 0.052081 cost_income_elast 0.047325 -0.043630 b_wifi -0.145487 0.030113 b_food -0.109541 0.010137 lambda_PT -0.124953 0.057265 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.043619 -0.054694 asc_air -0.126935 -0.082829 asc_rail -0.087157 -0.115053 asc_bus_interaction_female 0.424482 0.467929 asc_air_interaction_female 1.000000 0.698995 asc_rail_interaction_female 0.698995 1.000000 b_tt_car -0.023842 -0.012669 b_tt_bus -0.025974 -0.010330 b_tt_air -0.008419 -0.010702 b_tt_rail -0.005247 -0.002269 b_tt_interaction_business -0.017666 -0.009108 b_access -0.018622 -0.017696 b_cost -0.044684 -0.024252 b_cost_interaction_business 0.014240 0.010019 cost_income_elast 0.002986 -0.002467 b_wifi 0.030786 0.012879 b_food 0.014384 0.005077 lambda_PT 0.038519 0.017499 b_tt_car b_tt_bus asc_bus 0.33708 -0.784302 asc_air 0.65801 0.106149 asc_rail 0.69823 0.136675 asc_bus_interaction_female -0.02313 -0.004208 asc_air_interaction_female -0.02384 -0.025974 asc_rail_interaction_female -0.01267 -0.010330 b_tt_car 1.00000 0.265906 b_tt_bus 0.26591 1.000000 b_tt_air 0.05405 0.077144 b_tt_rail 0.03536 0.052914 b_tt_interaction_business -0.05016 -0.055691 b_access 0.05437 0.035866 b_cost 0.42315 0.421726 b_cost_interaction_business -0.29714 -0.320242 cost_income_elast -0.01177 0.065694 b_wifi -0.28794 -0.255007 b_food -0.14725 -0.115507 lambda_PT -0.34315 -0.370694 b_tt_air b_tt_rail asc_bus -0.016507 0.012559 asc_air -0.605538 0.017141 asc_rail -0.002408 -0.654829 asc_bus_interaction_female -0.012710 -0.012501 asc_air_interaction_female -0.008419 -0.005247 asc_rail_interaction_female -0.010702 -0.002269 b_tt_car 0.054052 0.035361 b_tt_bus 0.077144 0.052914 b_tt_air 1.000000 -0.024513 b_tt_rail -0.024513 1.000000 b_tt_interaction_business -0.048507 -0.117330 b_access 0.376822 -0.071531 b_cost 0.284000 0.258027 b_cost_interaction_business -0.099331 -0.185885 cost_income_elast -0.111502 -0.051865 b_wifi -0.134794 -0.139366 b_food -0.083103 -0.068713 lambda_PT -0.203259 -0.130105 b_tt_interaction_business b_access asc_bus 0.027801 -0.01355 asc_air 0.067848 -0.49030 asc_rail 0.103416 -0.02415 asc_bus_interaction_female 0.004690 -9.3077e-04 asc_air_interaction_female -0.017666 -0.01862 asc_rail_interaction_female -0.009108 -0.01770 b_tt_car -0.050158 0.05437 b_tt_bus -0.055691 0.03587 b_tt_air -0.048507 0.37682 b_tt_rail -0.117330 -0.07153 b_tt_interaction_business 1.000000 0.05768 b_access 0.057685 1.00000 b_cost -0.176425 0.23515 b_cost_interaction_business 0.620672 -0.02037 cost_income_elast 0.033184 -0.08684 b_wifi -0.090161 -0.14407 b_food -0.041822 -0.08007 lambda_PT -0.042401 -0.21345 b_cost b_cost_interaction_business asc_bus -0.01237 0.04207 asc_air -0.02277 -0.06319 asc_rail 0.05708 -0.02343 asc_bus_interaction_female -0.05927 0.05208 asc_air_interaction_female -0.04468 0.01424 asc_rail_interaction_female -0.02425 0.01002 b_tt_car 0.42315 -0.29714 b_tt_bus 0.42173 -0.32024 b_tt_air 0.28400 -0.09933 b_tt_rail 0.25803 -0.18588 b_tt_interaction_business -0.17642 0.62067 b_access 0.23515 -0.02037 b_cost 1.00000 -0.68511 b_cost_interaction_business -0.68511 1.00000 cost_income_elast -0.21077 0.04437 b_wifi -0.49554 0.19006 b_food -0.24738 0.08406 lambda_PT -0.72401 0.38015 cost_income_elast b_wifi asc_bus -0.050450 -0.007128 asc_air 0.111402 -0.115013 asc_rail 0.047325 -0.145487 asc_bus_interaction_female -0.043630 0.030113 asc_air_interaction_female 0.002986 0.030786 asc_rail_interaction_female -0.002467 0.012879 b_tt_car -0.011773 -0.287940 b_tt_bus 0.065694 -0.255007 b_tt_air -0.111502 -0.134794 b_tt_rail -0.051865 -0.139366 b_tt_interaction_business 0.033184 -0.090161 b_access -0.086842 -0.144068 b_cost -0.210768 -0.495536 b_cost_interaction_business 0.044371 0.190057 cost_income_elast 1.000000 0.049694 b_wifi 0.049694 1.000000 b_food 0.051715 0.580397 lambda_PT -0.019673 0.506614 b_food lambda_PT asc_bus -0.011311 0.002304 asc_air -0.081006 -0.035071 asc_rail -0.109541 -0.124953 asc_bus_interaction_female 0.010137 0.057265 asc_air_interaction_female 0.014384 0.038519 asc_rail_interaction_female 0.005077 0.017499 b_tt_car -0.147252 -0.343152 b_tt_bus -0.115507 -0.370694 b_tt_air -0.083103 -0.203259 b_tt_rail -0.068713 -0.130105 b_tt_interaction_business -0.041822 -0.042401 b_access -0.080069 -0.213450 b_cost -0.247377 -0.724012 b_cost_interaction_business 0.084058 0.380149 cost_income_elast 0.051715 -0.019673 b_wifi 0.580397 0.506614 b_food 1.000000 0.226477 lambda_PT 0.226477 1.000000 Robust correlation matrix: asc_bus asc_air asc_bus 1.000000 0.24713 asc_air 0.247127 1.00000 asc_rail 0.268099 0.57796 asc_bus_interaction_female -0.117104 -0.04104 asc_air_interaction_female 0.031589 -0.10092 asc_rail_interaction_female -0.022591 -0.05676 b_tt_car 0.329831 0.64921 b_tt_bus -0.771379 0.13775 b_tt_air -0.023122 -0.57439 b_tt_rail -0.003351 0.01834 b_tt_interaction_business 0.080012 0.14551 b_access 0.085909 -0.48611 b_cost -0.020928 -0.01277 b_cost_interaction_business 0.099600 -0.06782 cost_income_elast -0.077903 0.14644 b_wifi -0.064699 -0.11165 b_food 0.002612 -0.07389 lambda_PT -0.026443 -0.01457 asc_rail asc_bus_interaction_female asc_bus 0.26810 -0.117104 asc_air 0.57796 -0.041044 asc_rail 1.00000 -0.025977 asc_bus_interaction_female -0.02598 1.000000 asc_air_interaction_female -0.12756 0.374019 asc_rail_interaction_female -0.08259 0.472105 b_tt_car 0.68904 -0.002300 b_tt_bus 0.12712 -0.024970 b_tt_air 0.01657 0.053746 b_tt_rail -0.62764 -0.020489 b_tt_interaction_business 0.20430 0.023366 b_access -0.03546 -0.040513 b_cost 0.04454 -0.085397 b_cost_interaction_business 0.04021 0.062714 cost_income_elast 0.09258 0.082301 b_wifi -0.12698 0.020204 b_food -0.08822 0.057426 lambda_PT -0.12021 0.090519 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.031589 -0.02259 asc_air -0.100916 -0.05676 asc_rail -0.127565 -0.08259 asc_bus_interaction_female 0.374019 0.47210 asc_air_interaction_female 1.000000 0.73536 asc_rail_interaction_female 0.735358 1.00000 b_tt_car -0.037759 0.02561 b_tt_bus -0.098985 -0.02241 b_tt_air -0.013483 0.02433 b_tt_rail 0.066368 0.01781 b_tt_interaction_business 0.007431 0.01422 b_access -0.046265 -0.02181 b_cost -0.098302 -0.05588 b_cost_interaction_business 0.084043 0.07991 cost_income_elast 0.078098 0.08134 b_wifi -0.011526 -0.02077 b_food -0.048432 -0.02718 lambda_PT 0.048519 0.02024 b_tt_car b_tt_bus asc_bus 0.329831 -0.77138 asc_air 0.649210 0.13775 asc_rail 0.689043 0.12712 asc_bus_interaction_female -0.002300 -0.02497 asc_air_interaction_female -0.037759 -0.09899 asc_rail_interaction_female 0.025606 -0.02241 b_tt_car 1.000000 0.28961 b_tt_bus 0.289611 1.00000 b_tt_air 0.104861 0.10779 b_tt_rail 0.085268 0.11001 b_tt_interaction_business 0.010649 -0.08256 b_access 0.060898 -0.04617 b_cost 0.436707 0.44847 b_cost_interaction_business -0.301752 -0.38942 cost_income_elast 0.030723 0.08730 b_wifi -0.282494 -0.20266 b_food -0.159990 -0.14834 lambda_PT -0.340447 -0.34724 b_tt_air b_tt_rail asc_bus -0.02312 -0.003351 asc_air -0.57439 0.018336 asc_rail 0.01657 -0.627642 asc_bus_interaction_female 0.05375 -0.020489 asc_air_interaction_female -0.01348 0.066368 asc_rail_interaction_female 0.02433 0.017814 b_tt_car 0.10486 0.085268 b_tt_bus 0.10779 0.110014 b_tt_air 1.00000 0.012734 b_tt_rail 0.01273 1.000000 b_tt_interaction_business -0.07399 -0.184817 b_access 0.35684 -0.056183 b_cost 0.27604 0.301205 b_cost_interaction_business -0.07938 -0.288689 cost_income_elast -0.13030 -0.084158 b_wifi -0.16930 -0.177814 b_food -0.12589 -0.117307 lambda_PT -0.22956 -0.138066 b_tt_interaction_business b_access asc_bus 0.080012 0.08591 asc_air 0.145511 -0.48611 asc_rail 0.204304 -0.03546 asc_bus_interaction_female 0.023366 -0.04051 asc_air_interaction_female 0.007431 -0.04627 asc_rail_interaction_female 0.014217 -0.02181 b_tt_car 0.010649 0.06090 b_tt_bus -0.082558 -0.04617 b_tt_air -0.073988 0.35684 b_tt_rail -0.184817 -0.05618 b_tt_interaction_business 1.000000 0.06161 b_access 0.061607 1.00000 b_cost -0.204440 0.24762 b_cost_interaction_business 0.549885 -0.03301 cost_income_elast 0.043236 -0.07001 b_wifi -0.112250 -0.09422 b_food -0.054998 -0.04836 lambda_PT -0.061500 -0.22715 b_cost b_cost_interaction_business asc_bus -0.02093 0.09960 asc_air -0.01277 -0.06782 asc_rail 0.04454 0.04021 asc_bus_interaction_female -0.08540 0.06271 asc_air_interaction_female -0.09830 0.08404 asc_rail_interaction_female -0.05588 0.07991 b_tt_car 0.43671 -0.30175 b_tt_bus 0.44847 -0.38942 b_tt_air 0.27604 -0.07938 b_tt_rail 0.30120 -0.28869 b_tt_interaction_business -0.20444 0.54989 b_access 0.24762 -0.03301 b_cost 1.00000 -0.73536 b_cost_interaction_business -0.73536 1.00000 cost_income_elast -0.22896 0.04620 b_wifi -0.47613 0.21137 b_food -0.25940 0.10708 lambda_PT -0.73768 0.40473 cost_income_elast b_wifi asc_bus -0.077903 -0.06470 asc_air 0.146443 -0.11165 asc_rail 0.092575 -0.12698 asc_bus_interaction_female 0.082301 0.02020 asc_air_interaction_female 0.078098 -0.01153 asc_rail_interaction_female 0.081342 -0.02077 b_tt_car 0.030723 -0.28249 b_tt_bus 0.087305 -0.20266 b_tt_air -0.130299 -0.16930 b_tt_rail -0.084158 -0.17781 b_tt_interaction_business 0.043236 -0.11225 b_access -0.070012 -0.09422 b_cost -0.228961 -0.47613 b_cost_interaction_business 0.046203 0.21137 cost_income_elast 1.000000 0.05693 b_wifi 0.056931 1.00000 b_food 0.002779 0.58540 lambda_PT 0.078879 0.46121 b_food lambda_PT asc_bus 0.002612 -0.02644 asc_air -0.073887 -0.01457 asc_rail -0.088223 -0.12021 asc_bus_interaction_female 0.057426 0.09052 asc_air_interaction_female -0.048432 0.04852 asc_rail_interaction_female -0.027181 0.02024 b_tt_car -0.159990 -0.34045 b_tt_bus -0.148340 -0.34724 b_tt_air -0.125889 -0.22956 b_tt_rail -0.117307 -0.13807 b_tt_interaction_business -0.054998 -0.06150 b_access -0.048362 -0.22715 b_cost -0.259399 -0.73768 b_cost_interaction_business 0.107083 0.40473 cost_income_elast 0.002779 0.07888 b_wifi 0.585398 0.46121 b_food 1.000000 0.23480 lambda_PT 0.234802 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.2315081 293 0.2341924 400 0.2350224 146 0.2625511 181 0.2693510 367 0.2733214 317 0.2755096 276 0.2769893 186 0.2886280 434 0.2896035 147 0.2906669 142 0.2914471 307 0.2927484 161 0.2939947 370 0.2942649 447 0.2982663 441 0.3004613 183 0.3005768 259 0.3026343 379 0.3051645 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Two-level NL model with socio-demographics on mode choice SP data" indivID "ID" outputDirectory "output/" nCores "2" debug "FALSE" modelName "NL_two_levels" 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 0.390317033 asc_air 0.703768393 asc_rail 1.666339968 asc_bus_interaction_female 0.269690025 asc_air_interaction_female 0.238205824 asc_rail_interaction_female 0.179808059 b_tt_car 0.010496184 b_tt_bus 0.016548005 b_tt_air 0.012462248 b_tt_rail 0.005175592 b_tt_interaction_business 0.006075981 b_access 0.016973265 b_cost 0.058409411 b_cost_interaction_business 0.024503096 cost_income_elast 0.603015196 b_wifi 0.771050119 b_food 0.329407009 lambda_PT 0.632435926 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) ### Specify tree structure for NL model nlStructure= list() nlStructure[["root"]] = c("car","PT") nlStructure[["PT"]] = c("bus","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) }