Model run by stephane.hess using Apollo 0.3.4 on R 4.4.0 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 : 2024-09-27 15:32:53.360593 Estimation method : bgw Model diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -4.49955 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 : 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) : -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) : 00:00:4.45 pre-estimation : 00:00:0.41 estimation : 00:00:0.55 post-estimation : 00:00:3.49 Iterations : 7 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. Rob.t.rat.(0) Rob.t.rat.(1) asc_car 0.000000 NA NA NA NA NA NA asc_bus 0.390303 0.436666 0.8938 -1.396 0.421971 0.9250 -1.445 asc_air -0.703767 0.301199 -2.3366 -5.657 0.292795 -2.4036 -5.819 asc_rail -1.666336 0.299915 -5.5560 -8.890 0.288933 -5.7672 -9.228 asc_bus_shift_female 0.269690 0.103710 2.6004 -7.042 0.112994 2.3868 -6.463 asc_air_shift_female 0.238206 0.077606 3.0694 -9.816 0.078306 3.0420 -9.728 asc_rail_shift_female 0.179808 0.067785 2.6526 -12.100 0.068429 2.6276 -11.986 b_tt_car -0.010496 7.2781e-04 -14.4216 -1388.411 7.2982e-04 -14.3818 -1384.580 b_tt_bus -0.016548 0.001244 -13.3006 -817.059 0.001221 -13.5494 -832.344 b_tt_air -0.012462 0.002028 -6.1440 -499.152 0.002040 -6.1089 -496.299 b_tt_rail -0.005176 0.001396 -3.7088 -720.292 0.001354 -3.8236 -742.604 b_tt_shift_business -0.006076 5.0779e-04 -11.9656 -1981.288 4.7317e-04 -12.8410 -2126.243 b_access -0.016973 0.002082 -8.1521 -488.445 0.002026 -8.3768 -501.908 b_cost -0.058409 0.002413 -24.2104 -438.706 0.002459 -23.7540 -430.434 b_cost_shift_business 0.024503 0.002280 10.7485 -427.911 0.002140 11.4488 -455.791 cost_income_elast -0.603015 0.028930 -20.8443 -55.411 0.029927 -20.1496 -53.564 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.771050 0.047051 16.3876 -4.866 0.048106 16.0282 -4.759 b_food 0.329407 0.040593 8.1148 -16.520 0.043123 7.6387 -15.551 lambda_PT 0.632435 0.028522 22.1739 -12.887 0.028225 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_rail asc_bus_shift_female asc_bus 0.190677 0.036642 0.034185 -0.006258 asc_air 0.036642 0.090721 0.051277 -0.001790 asc_rail 0.034185 0.051277 0.089949 -0.001762 asc_bus_shift_female -0.006258 -0.001790 -0.001762 0.010756 asc_air_shift_female -0.001478 -0.002967 -0.002029 0.003416 asc_rail_shift_female -0.001619 -0.001691 -0.002339 0.003290 b_tt_car 1.0713e-04 1.4425e-04 1.5241e-04 -1.746e-06 b_tt_bus -4.2610e-04 3.978e-05 5.100e-05 -5.430e-07 b_tt_air -1.462e-05 -3.6995e-04 -1.465e-06 -2.674e-06 b_tt_rail 7.653e-06 7.205e-06 -2.7407e-04 -1.809e-06 b_tt_shift_business 6.164e-06 1.038e-05 1.575e-05 2.470e-07 b_access -1.232e-05 -3.0747e-04 -1.508e-05 -2.010e-07 b_cost -1.302e-05 -1.655e-05 4.130e-05 -1.483e-05 b_cost_shift_business 4.187e-05 -4.339e-05 -1.602e-05 1.231e-05 cost_income_elast -6.3731e-04 9.7071e-04 4.1061e-04 -1.3090e-04 b_wifi -1.4648e-04 -0.001630 -0.002053 1.4694e-04 b_food -2.0050e-04 -9.9043e-04 -0.001334 4.268e-05 lambda_PT 2.866e-05 -3.0129e-04 -0.001069 1.6939e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.001478 -0.001619 1.0713e-04 -4.2610e-04 asc_air -0.002967 -0.001691 1.4425e-04 3.978e-05 asc_rail -0.002029 -0.002339 1.5241e-04 5.100e-05 asc_bus_shift_female 0.003416 0.003290 -1.746e-06 -5.430e-07 asc_air_shift_female 0.006023 0.003677 -1.347e-06 -2.508e-06 asc_rail_shift_female 0.003677 0.004595 -6.250e-07 -8.712e-07 b_tt_car -1.347e-06 -6.250e-07 5.297e-07 2.408e-07 b_tt_bus -2.508e-06 -8.712e-07 2.408e-07 1.548e-06 b_tt_air -1.325e-06 -1.471e-06 7.979e-08 1.947e-07 b_tt_rail -5.683e-07 -2.146e-07 3.591e-08 9.187e-08 b_tt_shift_business -6.962e-07 -3.135e-07 -1.854e-08 -3.518e-08 b_access -3.009e-06 -2.497e-06 8.240e-08 9.291e-08 b_cost -8.366e-06 -3.966e-06 7.430e-07 1.266e-06 b_cost_shift_business 2.519e-06 1.548e-06 -4.930e-07 -9.083e-07 cost_income_elast 6.704e-06 -4.837e-06 -2.479e-07 2.365e-06 b_wifi 1.1241e-04 4.108e-05 -9.860e-06 -1.493e-05 b_food 4.531e-05 1.397e-05 -4.350e-06 -5.834e-06 lambda_PT 8.526e-05 3.383e-05 -7.123e-06 -1.315e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.462e-05 7.653e-06 6.164e-06 -1.232e-05 asc_air -3.6995e-04 7.205e-06 1.038e-05 -3.0747e-04 asc_rail -1.465e-06 -2.7407e-04 1.575e-05 -1.508e-05 asc_bus_shift_female -2.674e-06 -1.809e-06 2.470e-07 -2.010e-07 asc_air_shift_female -1.325e-06 -5.683e-07 -6.962e-07 -3.009e-06 asc_rail_shift_female -1.471e-06 -2.146e-07 -3.135e-07 -2.497e-06 b_tt_car 7.979e-08 3.591e-08 -1.854e-08 8.240e-08 b_tt_bus 1.947e-07 9.187e-08 -3.518e-08 9.291e-08 b_tt_air 4.114e-06 -6.939e-08 -4.996e-08 1.591e-06 b_tt_rail -6.939e-08 1.947e-06 -8.314e-08 -2.078e-07 b_tt_shift_business -4.996e-08 -8.314e-08 2.578e-07 6.099e-08 b_access 1.591e-06 -2.078e-07 6.099e-08 4.335e-06 b_cost 1.390e-06 8.687e-07 -2.161e-07 1.181e-06 b_cost_shift_business -4.593e-07 -5.914e-07 7.185e-07 -9.670e-08 cost_income_elast -6.543e-06 -2.094e-06 4.875e-07 -5.231e-06 b_wifi -1.286e-05 -9.151e-06 -2.154e-06 -1.411e-05 b_food -6.843e-06 -3.892e-06 -8.621e-07 -6.767e-06 lambda_PT -1.176e-05 -5.178e-06 -6.141e-07 -1.268e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -1.302e-05 4.187e-05 -6.3731e-04 -1.4648e-04 asc_air -1.655e-05 -4.339e-05 9.7071e-04 -0.001630 asc_rail 4.130e-05 -1.602e-05 4.1061e-04 -0.002053 asc_bus_shift_female -1.483e-05 1.231e-05 -1.3090e-04 1.4694e-04 asc_air_shift_female -8.366e-06 2.519e-06 6.704e-06 1.1241e-04 asc_rail_shift_female -3.966e-06 1.548e-06 -4.837e-06 4.108e-05 b_tt_car 7.430e-07 -4.930e-07 -2.479e-07 -9.860e-06 b_tt_bus 1.266e-06 -9.083e-07 2.365e-06 -1.493e-05 b_tt_air 1.390e-06 -4.593e-07 -6.543e-06 -1.286e-05 b_tt_rail 8.687e-07 -5.914e-07 -2.094e-06 -9.151e-06 b_tt_shift_business -2.161e-07 7.185e-07 4.875e-07 -2.154e-06 b_access 1.181e-06 -9.670e-08 -5.231e-06 -1.411e-05 b_cost 5.821e-06 -3.768e-06 -1.471e-05 -5.625e-05 b_cost_shift_business -3.768e-06 5.197e-06 2.926e-06 2.039e-05 cost_income_elast -1.471e-05 2.926e-06 8.3692e-04 6.764e-05 b_wifi -5.625e-05 2.039e-05 6.764e-05 0.002214 b_food -2.423e-05 7.779e-06 6.073e-05 0.001109 lambda_PT -4.982e-05 2.472e-05 -1.623e-05 6.7986e-04 b_food lambda_PT asc_bus -2.0050e-04 2.866e-05 asc_air -9.9043e-04 -3.0129e-04 asc_rail -0.001334 -0.001069 asc_bus_shift_female 4.268e-05 1.6939e-04 asc_air_shift_female 4.531e-05 8.526e-05 asc_rail_shift_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_shift_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_shift_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_rail asc_bus_shift_female asc_bus 0.178060 0.030533 0.032687 -0.005584 asc_air 0.030533 0.085729 0.048894 -0.001358 asc_rail 0.032687 0.048894 0.083482 -8.4808e-04 asc_bus_shift_female -0.005584 -0.001358 -8.4808e-04 0.012768 asc_air_shift_female 0.001044 -0.002314 -0.002886 0.003309 asc_rail_shift_female -6.5232e-04 -0.001137 -0.001633 0.003650 b_tt_car 1.0158e-04 1.3873e-04 1.4530e-04 -1.896e-07 b_tt_bus -3.9754e-04 4.926e-05 4.486e-05 -3.446e-06 b_tt_air -1.990e-05 -3.4309e-04 9.766e-06 1.239e-05 b_tt_rail -1.914e-06 7.267e-06 -2.4547e-04 -3.134e-06 b_tt_shift_business 1.598e-05 2.016e-05 2.793e-05 1.249e-06 b_access 7.345e-05 -2.8839e-04 -2.076e-05 -9.276e-06 b_cost -2.171e-05 -9.195e-06 3.165e-05 -2.373e-05 b_cost_shift_business 8.995e-05 -4.250e-05 2.487e-05 1.517e-05 cost_income_elast -9.8378e-04 0.001283 8.0049e-04 2.7831e-04 b_wifi -0.001313 -0.001573 -0.001765 1.0982e-04 b_food 4.751e-05 -9.3292e-04 -0.001099 2.7982e-04 lambda_PT -3.1498e-04 -1.2043e-04 -9.8031e-04 2.8869e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.001044 -6.5232e-04 1.0158e-04 -3.9754e-04 asc_air -0.002314 -0.001137 1.3873e-04 4.926e-05 asc_rail -0.002886 -0.001633 1.4530e-04 4.486e-05 asc_bus_shift_female 0.003309 0.003650 -1.896e-07 -3.446e-06 asc_air_shift_female 0.006132 0.003940 -2.158e-06 -9.467e-06 asc_rail_shift_female 0.003940 0.004683 1.279e-06 -1.873e-06 b_tt_car -2.158e-06 1.279e-06 5.326e-07 2.581e-07 b_tt_bus -9.467e-06 -1.873e-06 2.581e-07 1.492e-06 b_tt_air -2.154e-06 3.396e-06 1.561e-07 2.685e-07 b_tt_rail 7.035e-06 1.650e-06 8.423e-08 1.819e-07 b_tt_shift_business 2.753e-07 4.603e-07 3.677e-09 -4.771e-08 b_access -7.341e-06 -3.024e-06 9.005e-08 -1.143e-07 b_cost -1.893e-05 -9.403e-06 7.837e-07 1.347e-06 b_cost_shift_business 1.408e-05 1.170e-05 -4.713e-07 -1.018e-06 cost_income_elast 1.8302e-04 1.6658e-04 6.710e-07 3.191e-06 b_wifi -4.342e-05 -6.837e-05 -9.918e-06 -1.191e-05 b_food -1.6355e-04 -8.021e-05 -5.035e-06 -7.813e-06 lambda_PT 1.0724e-04 3.910e-05 -7.013e-06 -1.197e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.990e-05 -1.914e-06 1.598e-05 7.345e-05 asc_air -3.4309e-04 7.267e-06 2.016e-05 -2.8839e-04 asc_rail 9.766e-06 -2.4547e-04 2.793e-05 -2.076e-05 asc_bus_shift_female 1.239e-05 -3.134e-06 1.249e-06 -9.276e-06 asc_air_shift_female -2.154e-06 7.035e-06 2.753e-07 -7.341e-06 asc_rail_shift_female 3.396e-06 1.650e-06 4.603e-07 -3.024e-06 b_tt_car 1.561e-07 8.423e-08 3.677e-09 9.005e-08 b_tt_bus 2.685e-07 1.819e-07 -4.771e-08 -1.143e-07 b_tt_air 4.162e-06 3.516e-08 -7.142e-08 1.475e-06 b_tt_rail 3.516e-08 1.832e-06 -1.184e-07 -1.541e-07 b_tt_shift_business -7.142e-08 -1.184e-07 2.239e-07 5.907e-08 b_access 1.475e-06 -1.541e-07 5.907e-08 4.106e-06 b_cost 1.385e-06 1.003e-06 -2.379e-07 1.234e-06 b_cost_shift_business -3.466e-07 -8.363e-07 5.569e-07 -1.431e-07 cost_income_elast -7.955e-06 -3.409e-06 6.122e-07 -4.245e-06 b_wifi -1.661e-05 -1.158e-05 -2.555e-06 -9.183e-06 b_food -1.107e-05 -6.847e-06 -1.122e-06 -4.226e-06 lambda_PT -1.322e-05 -5.275e-06 -8.214e-07 -1.299e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -2.171e-05 8.995e-05 -9.8378e-04 -0.001313 asc_air -9.195e-06 -4.250e-05 0.001283 -0.001573 asc_rail 3.165e-05 2.487e-05 8.0049e-04 -0.001765 asc_bus_shift_female -2.373e-05 1.517e-05 2.7831e-04 1.0982e-04 asc_air_shift_female -1.893e-05 1.408e-05 1.8302e-04 -4.342e-05 asc_rail_shift_female -9.403e-06 1.170e-05 1.6658e-04 -6.837e-05 b_tt_car 7.837e-07 -4.713e-07 6.710e-07 -9.918e-06 b_tt_bus 1.347e-06 -1.018e-06 3.191e-06 -1.191e-05 b_tt_air 1.385e-06 -3.466e-07 -7.955e-06 -1.661e-05 b_tt_rail 1.003e-06 -8.363e-07 -3.409e-06 -1.158e-05 b_tt_shift_business -2.379e-07 5.569e-07 6.122e-07 -2.555e-06 b_access 1.234e-06 -1.431e-07 -4.245e-06 -9.183e-06 b_cost 6.046e-06 -3.870e-06 -1.685e-05 -5.632e-05 b_cost_shift_business -3.870e-06 4.581e-06 2.959e-06 2.176e-05 cost_income_elast -1.685e-05 2.959e-06 8.9562e-04 8.196e-05 b_wifi -5.632e-05 2.176e-05 8.196e-05 0.002314 b_food -2.751e-05 9.883e-06 3.587e-06 0.001214 lambda_PT -5.120e-05 2.445e-05 6.663e-05 6.2623e-04 b_food lambda_PT asc_bus 4.751e-05 -3.1498e-04 asc_air -9.3292e-04 -1.2043e-04 asc_rail -0.001099 -9.8031e-04 asc_bus_shift_female 2.7982e-04 2.8869e-04 asc_air_shift_female -1.6355e-04 1.0724e-04 asc_rail_shift_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_shift_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_shift_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 2.8579e-04 lambda_PT 2.8579e-04 7.9667e-04 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.27859 0.261029 -0.138194 asc_air 0.278595 1.00000 0.567639 -0.057306 asc_rail 0.261029 0.56764 1.000000 -0.056634 asc_bus_shift_female -0.138194 -0.05731 -0.056634 1.000000 asc_air_shift_female -0.043619 -0.12693 -0.087157 0.424483 asc_rail_shift_female -0.054694 -0.08283 -0.115053 0.467929 b_tt_car 0.337082 0.65801 0.698235 -0.023134 b_tt_bus -0.784302 0.10615 0.136674 -0.004208 b_tt_air -0.016506 -0.60554 -0.002408 -0.012710 b_tt_rail 0.012559 0.01714 -0.654829 -0.012501 b_tt_shift_business 0.027801 0.06785 0.103416 0.004690 b_access -0.013554 -0.49030 -0.024150 -9.3079e-04 b_cost -0.012363 -0.02277 0.057080 -0.059271 b_cost_shift_business 0.042065 -0.06319 -0.023425 0.052081 cost_income_elast -0.050450 0.11140 0.047325 -0.043630 b_wifi -0.007129 -0.11501 -0.145486 0.030113 b_food -0.011311 -0.08101 -0.109541 0.010137 lambda_PT 0.002301 -0.03507 -0.124952 0.057265 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.043619 -0.054694 0.33708 -0.784302 asc_air -0.126935 -0.082829 0.65801 0.106148 asc_rail -0.087157 -0.115053 0.69823 0.136674 asc_bus_shift_female 0.424483 0.467929 -0.02313 -0.004208 asc_air_shift_female 1.000000 0.698995 -0.02384 -0.025974 asc_rail_shift_female 0.698995 1.000000 -0.01267 -0.010330 b_tt_car -0.023842 -0.012669 1.00000 0.265905 b_tt_bus -0.025974 -0.010330 0.26591 1.000000 b_tt_air -0.008419 -0.010702 0.05405 0.077143 b_tt_rail -0.005247 -0.002269 0.03536 0.052914 b_tt_shift_business -0.017666 -0.009108 -0.05016 -0.055691 b_access -0.018622 -0.017696 0.05437 0.035866 b_cost -0.044684 -0.024252 0.42315 0.421725 b_cost_shift_business 0.014240 0.010019 -0.29713 -0.320241 cost_income_elast 0.002986 -0.002467 -0.01177 0.065694 b_wifi 0.030786 0.012879 -0.28794 -0.255006 b_food 0.014384 0.005077 -0.14725 -0.115507 lambda_PT 0.038519 0.017499 -0.34315 -0.370692 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.016506 0.012559 0.027801 -0.01355 asc_air -0.605538 0.017141 0.067848 -0.49030 asc_rail -0.002408 -0.654829 0.103416 -0.02415 asc_bus_shift_female -0.012710 -0.012501 0.004690 -9.3079e-04 asc_air_shift_female -0.008419 -0.005247 -0.017666 -0.01862 asc_rail_shift_female -0.010702 -0.002269 -0.009108 -0.01770 b_tt_car 0.054052 0.035361 -0.050158 0.05437 b_tt_bus 0.077143 0.052914 -0.055691 0.03587 b_tt_air 1.000000 -0.024513 -0.048507 0.37682 b_tt_rail -0.024513 1.000000 -0.117330 -0.07153 b_tt_shift_business -0.048507 -0.117330 1.000000 0.05768 b_access 0.376822 -0.071531 0.057685 1.00000 b_cost 0.284000 0.258028 -0.176425 0.23515 b_cost_shift_business -0.099331 -0.185885 0.620672 -0.02037 cost_income_elast -0.111502 -0.051865 0.033184 -0.08684 b_wifi -0.134794 -0.139366 -0.090161 -0.14407 b_food -0.083103 -0.068713 -0.041822 -0.08007 lambda_PT -0.203259 -0.130105 -0.042401 -0.21345 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.01236 0.04207 -0.050450 -0.007129 asc_air -0.02277 -0.06319 0.111402 -0.115013 asc_rail 0.05708 -0.02343 0.047325 -0.145486 asc_bus_shift_female -0.05927 0.05208 -0.043630 0.030113 asc_air_shift_female -0.04468 0.01424 0.002986 0.030786 asc_rail_shift_female -0.02425 0.01002 -0.002467 0.012879 b_tt_car 0.42315 -0.29713 -0.011773 -0.287940 b_tt_bus 0.42172 -0.32024 0.065694 -0.255006 b_tt_air 0.28400 -0.09933 -0.111502 -0.134794 b_tt_rail 0.25803 -0.18588 -0.051865 -0.139366 b_tt_shift_business -0.17642 0.62067 0.033184 -0.090161 b_access 0.23515 -0.02037 -0.086842 -0.144068 b_cost 1.00000 -0.68511 -0.210768 -0.495537 b_cost_shift_business -0.68511 1.00000 0.044371 0.190057 cost_income_elast -0.21077 0.04437 1.000000 0.049694 b_wifi -0.49554 0.19006 0.049694 1.000000 b_food -0.24738 0.08406 0.051715 0.580397 lambda_PT -0.72401 0.38015 -0.019673 0.506614 b_food lambda_PT asc_bus -0.011311 0.002301 asc_air -0.081006 -0.035071 asc_rail -0.109541 -0.124952 asc_bus_shift_female 0.010137 0.057265 asc_air_shift_female 0.014384 0.038519 asc_rail_shift_female 0.005077 0.017499 b_tt_car -0.147252 -0.343152 b_tt_bus -0.115507 -0.370692 b_tt_air -0.083103 -0.203259 b_tt_rail -0.068713 -0.130105 b_tt_shift_business -0.041822 -0.042401 b_access -0.080070 -0.213450 b_cost -0.247377 -0.724013 b_cost_shift_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_rail asc_bus_shift_female asc_bus 1.000000 0.24713 0.26810 -0.117104 asc_air 0.247127 1.00000 0.57796 -0.041044 asc_rail 0.268100 0.57796 1.00000 -0.025977 asc_bus_shift_female -0.117104 -0.04104 -0.02598 1.000000 asc_air_shift_female 0.031588 -0.10092 -0.12756 0.374020 asc_rail_shift_female -0.022591 -0.05676 -0.08259 0.472105 b_tt_car 0.329832 0.64921 0.68904 -0.002300 b_tt_bus -0.771379 0.13775 0.12711 -0.024970 b_tt_air -0.023122 -0.57439 0.01657 0.053746 b_tt_rail -0.003350 0.01834 -0.62764 -0.020489 b_tt_shift_business 0.080012 0.14551 0.20430 0.023366 b_access 0.085910 -0.48611 -0.03546 -0.040513 b_cost -0.020925 -0.01277 0.04454 -0.085397 b_cost_shift_business 0.099598 -0.06782 0.04021 0.062714 cost_income_elast -0.077903 0.14644 0.09258 0.082301 b_wifi -0.064702 -0.11165 -0.12698 0.020204 b_food 0.002611 -0.07389 -0.08822 0.057426 lambda_PT -0.026446 -0.01457 -0.12021 0.090519 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.031588 -0.02259 0.329832 -0.77138 asc_air -0.100916 -0.05676 0.649210 0.13775 asc_rail -0.127565 -0.08259 0.689043 0.12711 asc_bus_shift_female 0.374020 0.47211 -0.002300 -0.02497 asc_air_shift_female 1.000000 0.73536 -0.037759 -0.09898 asc_rail_shift_female 0.735358 1.00000 0.025606 -0.02241 b_tt_car -0.037759 0.02561 1.000000 0.28961 b_tt_bus -0.098985 -0.02241 0.289610 1.00000 b_tt_air -0.013483 0.02433 0.104861 0.10779 b_tt_rail 0.066368 0.01781 0.085268 0.11001 b_tt_shift_business 0.007431 0.01422 0.010649 -0.08256 b_access -0.046265 -0.02181 0.060898 -0.04617 b_cost -0.098301 -0.05588 0.436706 0.44847 b_cost_shift_business 0.084043 0.07991 -0.301751 -0.38942 cost_income_elast 0.078098 0.08134 0.030723 0.08730 b_wifi -0.011526 -0.02077 -0.282494 -0.20265 b_food -0.048432 -0.02718 -0.159990 -0.14834 lambda_PT 0.048519 0.02024 -0.340447 -0.34724 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.02312 -0.003350 0.080012 0.08591 asc_air -0.57439 0.018336 0.145511 -0.48611 asc_rail 0.01657 -0.627642 0.204304 -0.03546 asc_bus_shift_female 0.05375 -0.020489 0.023366 -0.04051 asc_air_shift_female -0.01348 0.066368 0.007431 -0.04627 asc_rail_shift_female 0.02433 0.017814 0.014217 -0.02181 b_tt_car 0.10486 0.085268 0.010649 0.06090 b_tt_bus 0.10779 0.110014 -0.082557 -0.04617 b_tt_air 1.00000 0.012734 -0.073988 0.35684 b_tt_rail 0.01273 1.000000 -0.184817 -0.05618 b_tt_shift_business -0.07399 -0.184817 1.000000 0.06161 b_access 0.35684 -0.056182 0.061607 1.00000 b_cost 0.27604 0.301205 -0.204440 0.24762 b_cost_shift_business -0.07938 -0.288690 0.549885 -0.03301 cost_income_elast -0.13030 -0.084158 0.043236 -0.07001 b_wifi -0.16930 -0.177815 -0.112251 -0.09422 b_food -0.12589 -0.117307 -0.054999 -0.04836 lambda_PT -0.22956 -0.138067 -0.061501 -0.22715 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.02092 0.09960 -0.077903 -0.06470 asc_air -0.01277 -0.06782 0.146443 -0.11165 asc_rail 0.04454 0.04021 0.092575 -0.12698 asc_bus_shift_female -0.08540 0.06271 0.082301 0.02020 asc_air_shift_female -0.09830 0.08404 0.078098 -0.01153 asc_rail_shift_female -0.05588 0.07991 0.081342 -0.02077 b_tt_car 0.43671 -0.30175 0.030723 -0.28249 b_tt_bus 0.44847 -0.38942 0.087304 -0.20265 b_tt_air 0.27604 -0.07938 -0.130299 -0.16930 b_tt_rail 0.30121 -0.28869 -0.084158 -0.17781 b_tt_shift_business -0.20444 0.54989 0.043236 -0.11225 b_access 0.24762 -0.03301 -0.070012 -0.09422 b_cost 1.00000 -0.73536 -0.228961 -0.47613 b_cost_shift_business -0.73536 1.00000 0.046203 0.21137 cost_income_elast -0.22896 0.04620 1.000000 0.05693 b_wifi -0.47613 0.21137 0.056931 1.00000 b_food -0.25940 0.10708 0.002779 0.58540 lambda_PT -0.73768 0.40473 0.078879 0.46121 b_food lambda_PT asc_bus 0.002611 -0.02645 asc_air -0.073887 -0.01457 asc_rail -0.088223 -0.12021 asc_bus_shift_female 0.057426 0.09052 asc_air_shift_female -0.048432 0.04852 asc_rail_shift_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_shift_business -0.054999 -0.06150 b_access -0.048362 -0.22715 b_cost -0.259399 -0.73768 b_cost_shift_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 0.234801 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.2315083 293 0.2341924 400 0.2350225 146 0.2625511 181 0.2693511 367 0.2733215 317 0.2755096 276 0.2769893 186 0.2886282 434 0.2896035 147 0.2906670 142 0.2914472 307 0.2927485 161 0.2939947 370 0.2942649 447 0.2982662 441 0.3004614 183 0.3005766 259 0.3026344 379 0.3051645 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286354 0.390303 0.103949 asc_air -0.903377 -0.703767 0.199610 asc_rail -2.092701 -1.666336 0.426366 asc_bus_shift_female 0.340193 0.269690 -0.070503 asc_air_shift_female 0.268174 0.238206 -0.029968 asc_rail_shift_female 0.189612 0.179808 -0.009804 b_tt_car -0.013107 -0.010496 0.002611 b_tt_bus -0.021265 -0.016548 0.004717 b_tt_air -0.016578 -0.012462 0.004116 b_tt_rail -0.007051 -0.005176 0.001875 b_tt_shift_business -0.006234 -0.006076 1.5795e-04 b_access -0.021152 -0.016973 0.004179 b_cost -0.076188 -0.058409 0.017778 b_cost_shift_business 0.033379 0.024503 -0.008876 cost_income_elast -0.613821 -0.603015 0.010806 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026711 0.771050 -0.255662 b_food 0.422072 0.329407 -0.092665 lambda_PT 1.000000 0.632435 -0.367565 Settings and functions used in model definition: apollo_control -------------- Value modelName "NL_two_levels" modelDescr "Two-level NL model with socio-demographics on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical second derivative of LL (using numDeriv) Scaling used in computing Hessian --------------------------------- Value asc_bus 0.390302623 asc_air 0.703767109 asc_rail 1.666335614 asc_bus_shift_female 0.269689981 asc_air_shift_female 0.238205721 asc_rail_shift_female 0.179808016 b_tt_car 0.010496174 b_tt_bus 0.016547950 b_tt_air 0.012462235 b_tt_rail 0.005175603 b_tt_shift_business 0.006075981 b_access 0.016973256 b_cost 0.058409365 b_cost_shift_business 0.024503064 cost_income_elast 0.603015115 b_wifi 0.771049576 b_food 0.329406793 lambda_PT 0.632435427 apollo_probabilities ---------------------- function(apollo_beta, apollo_inputs, functionality="estimate"){ ### Attach inputs and detach after function exit apollo_attach(apollo_beta, apollo_inputs) on.exit(apollo_detach(apollo_beta, apollo_inputs)) ### Create list of probabilities P P = list() ### Create alternative specific constants and coefficients using interactions with socio-demographics asc_bus_value = asc_bus + asc_bus_shift_female * female asc_air_value = asc_air + asc_air_shift_female * female asc_rail_value = asc_rail + asc_rail_shift_female * female b_tt_car_value = b_tt_car + b_tt_shift_business * business b_tt_bus_value = b_tt_bus + b_tt_shift_business * business b_tt_air_value = b_tt_air + b_tt_shift_business * business b_tt_rail_value = b_tt_rail + b_tt_shift_business * business b_cost_value = ( b_cost + b_cost_shift_business * business ) * ( income / mean_income ) ^ cost_income_elast ### List of utilities: these must use the same names as in nl_settings, order is irrelevant V = list() V[["car"]] = asc_car + b_tt_car_value * time_car + b_cost_value * cost_car V[["bus"]] = asc_bus_value + b_tt_bus_value * time_bus + b_access * access_bus + b_cost_value * cost_bus V[["air"]] = asc_air_value + b_tt_air_value * time_air + b_access * access_air + b_cost_value * cost_air + b_no_frills * ( service_air == 1 ) + b_wifi * ( service_air == 2 ) + b_food * ( service_air == 3 ) V[["rail"]] = asc_rail_value + b_tt_rail_value * time_rail + b_access * access_rail + b_cost_value * cost_rail + b_no_frills * ( service_rail == 1 ) + b_wifi * ( service_rail == 2 ) + b_food * ( service_rail == 3 ) ### Specify nests for NL model nlNests = list(root=1, PT=lambda_PT) ### 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) }