Model run by stephane.hess using Apollo 0.3.5 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 : CNL_logistic_transform_for_alphas Model description : CNL model with socio-demographics on mode choice SP data, using logistic transform to ensure alphas meet constraints Model run at : 2025-03-10 17:06:22.486831 Estimation method : bgw Model diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -4.440286 reciprocal of condition number : 4.17331e-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) : -4742.25 Rho-squared vs equal shares : 0.4214 Adj.Rho-squared vs equal shares : 0.419 Rho-squared vs observed shares : 0.2929 Adj.Rho-squared vs observed shares : 0.2904 AIC : 9524.5 BIC : 9661.57 Estimated parameters : 20 Time taken (hh:mm:ss) : 00:00:8.02 pre-estimation : 00:00:0.41 estimation : 00:00:0.9 post-estimation : 00:00:6.71 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 0.299051 0.445861 0.6707 -1.572 0.420738 0.7108 -1.666 asc_air -0.646437 0.292127 -2.2129 -5.636 0.285270 -2.2661 -5.772 asc_rail -1.563614 0.287745 -5.4340 -8.909 0.278679 -5.6108 -9.199 asc_bus_interaction_female 0.273635 0.105277 2.5992 -6.900 0.111520 2.4537 -6.513 asc_air_interaction_female 0.240318 0.076638 3.1358 -9.913 0.075900 3.1662 -10.009 asc_rail_interaction_female 0.178831 0.067296 2.6574 -12.202 0.067973 2.6309 -12.081 b_tt_car -0.010391 7.1322e-04 -14.5692 -1416.654 7.0558e-04 -14.7270 -1431.999 b_tt_bus -0.016555 0.001241 -13.3372 -818.974 0.001199 -13.8090 -847.943 b_tt_air -0.013074 0.001943 -6.7299 -521.506 0.001956 -6.6836 -517.913 b_tt_rail -0.005460 0.001284 -4.2521 -783.036 0.001253 -4.3591 -802.745 b_tt_interaction_business -0.006010 5.1448e-04 -11.6819 -1955.391 4.7225e-04 -12.7264 -2130.241 b_access -0.017829 0.001983 -8.9919 -513.322 0.001894 -9.4113 -537.260 b_cost -0.057587 0.002219 -25.9533 -476.632 0.002234 -25.7757 -473.370 b_cost_interaction_business 0.023261 0.002199 10.5776 -444.164 0.002050 11.3476 -476.495 cost_income_elast -0.620998 0.030935 -20.0746 -52.401 0.031202 -19.9023 -51.951 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.774407 0.043847 17.6615 -5.145 0.043516 17.7958 -5.184 b_food 0.337791 0.038453 8.7845 -17.221 0.040823 8.2745 -16.221 lambda_fastPT 0.401188 0.037274 10.7632 -16.065 0.041319 9.7096 -14.493 lambda_groundPT 0.528458 0.043297 12.2053 -10.891 0.045232 11.6834 -10.425 alpha_rail_fastPT_logistic -0.028384 0.214539 -0.1323 -4.793 0.206622 -0.1374 -4.977 alpha_rail_groundPT_logistic 0.000000 NA NA NA NA NA NA Structure for CNL model component : car (alpha) bus (alpha) air (alpha) rail (alpha) lambda car nest 1.000 0.000 0.000 0.0000 1.0000 groundPT nest 0.000 1.000 0.000 0.5071 0.5285 fastPT nest 0.000 0.000 1.000 0.4929 0.4012 Overview of choices for CNL 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_interaction_female asc_bus 0.198792 0.036424 0.032361 -0.005656 asc_air 0.036424 0.085338 0.050177 -0.001679 asc_rail 0.032361 0.050177 0.082797 -0.001772 asc_bus_interaction_female -0.005656 -0.001679 -0.001772 0.011083 asc_air_interaction_female -0.001462 -0.002844 -0.001887 0.003092 asc_rail_interaction_female -0.001744 -0.001738 -0.002342 0.003366 b_tt_car 1.0331e-04 1.4072e-04 1.4838e-04 -1.386e-06 b_tt_bus -4.5298e-04 3.323e-05 4.904e-05 -1.852e-06 b_tt_air -2.366e-05 -3.3537e-04 -7.030e-06 -9.494e-07 b_tt_rail 1.284e-05 3.190e-06 -2.3368e-04 -1.222e-06 b_tt_interaction_business 4.004e-06 9.549e-06 1.484e-05 4.581e-07 b_access -2.014e-05 -2.7134e-04 -1.879e-05 4.742e-07 b_cost -3.230e-05 -2.501e-05 3.228e-05 -1.066e-05 b_cost_interaction_business 4.413e-05 -3.684e-05 -9.833e-06 1.084e-05 cost_income_elast -6.0895e-04 9.1816e-04 3.4152e-04 -1.7148e-04 b_wifi 3.6874e-04 -0.001199 -0.001609 8.079e-05 b_food -3.420e-05 -8.6769e-04 -0.001162 9.814e-06 lambda_fastPT 1.669e-05 -6.5425e-04 -7.0759e-04 1.0202e-04 lambda_groundPT 4.7274e-04 -4.660e-05 -9.3957e-04 1.5929e-04 alpha_rail_fastPT_logistic -0.001600 -7.9294e-04 0.002129 -1.0171e-04 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus -0.001462 -0.001744 1.0331e-04 -4.5298e-04 asc_air -0.002844 -0.001738 1.4072e-04 3.323e-05 asc_rail -0.001887 -0.002342 1.4838e-04 4.904e-05 asc_bus_interaction_female 0.003092 0.003366 -1.386e-06 -1.852e-06 asc_air_interaction_female 0.005873 0.003765 -1.047e-06 -1.494e-06 asc_rail_interaction_female 0.003765 0.004529 -5.129e-07 -3.160e-07 b_tt_car -1.047e-06 -5.129e-07 5.087e-07 2.034e-07 b_tt_bus -1.494e-06 -3.160e-07 2.034e-07 1.541e-06 b_tt_air -1.807e-06 -9.814e-07 5.111e-08 1.485e-07 b_tt_rail -1.448e-06 2.159e-07 2.485e-08 3.703e-08 b_tt_interaction_business -7.692e-07 -3.663e-07 -1.965e-08 -3.777e-08 b_access -1.886e-06 -2.359e-06 6.436e-08 5.947e-08 b_cost -6.843e-06 -3.207e-06 6.136e-07 9.924e-07 b_cost_interaction_business 1.491e-06 1.018e-06 -4.208e-07 -7.698e-07 cost_income_elast 1.868e-05 7.311e-06 -5.670e-07 2.473e-06 b_wifi 1.0093e-04 3.347e-05 -8.128e-06 -1.180e-05 b_food 6.104e-05 4.888e-06 -3.659e-06 -4.488e-06 lambda_fastPT 2.316e-05 2.954e-05 -3.955e-06 -6.944e-06 lambda_groundPT 6.984e-05 1.317e-05 -6.392e-06 -1.338e-05 alpha_rail_fastPT_logistic -2.7400e-04 -1.305e-05 1.496e-05 1.693e-05 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -2.366e-05 1.284e-05 4.004e-06 -2.014e-05 asc_air -3.3537e-04 3.190e-06 9.549e-06 -2.7134e-04 asc_rail -7.030e-06 -2.3368e-04 1.484e-05 -1.879e-05 asc_bus_interaction_female -9.494e-07 -1.222e-06 4.581e-07 4.742e-07 asc_air_interaction_female -1.807e-06 -1.448e-06 -7.692e-07 -1.886e-06 asc_rail_interaction_female -9.814e-07 2.159e-07 -3.663e-07 -2.359e-06 b_tt_car 5.111e-08 2.485e-08 -1.965e-08 6.436e-08 b_tt_bus 1.485e-07 3.703e-08 -3.777e-08 5.947e-08 b_tt_air 3.774e-06 -4.613e-08 -3.011e-08 1.288e-06 b_tt_rail -4.613e-08 1.649e-06 -7.618e-08 -1.708e-07 b_tt_interaction_business -3.011e-08 -7.618e-08 2.647e-07 6.041e-08 b_access 1.288e-06 -1.708e-07 6.041e-08 3.932e-06 b_cost 1.131e-06 7.200e-07 -1.958e-07 1.002e-06 b_cost_interaction_business -2.912e-07 -5.125e-07 7.255e-07 3.654e-08 cost_income_elast -7.036e-06 -2.594e-06 -5.060e-07 -6.611e-06 b_wifi -1.115e-05 -8.348e-06 -2.181e-06 -1.320e-05 b_food -5.920e-06 -3.363e-06 -1.226e-06 -5.811e-06 lambda_fastPT 4.386e-07 -2.617e-06 4.638e-07 1.228e-06 lambda_groundPT -1.165e-05 -3.865e-06 -1.123e-07 -1.409e-05 alpha_rail_fastPT_logistic 5.847e-05 1.041e-05 1.632e-05 7.674e-05 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -3.230e-05 4.413e-05 -6.0895e-04 3.6874e-04 asc_air -2.501e-05 -3.684e-05 9.1816e-04 -0.001199 asc_rail 3.228e-05 -9.833e-06 3.4152e-04 -0.001609 asc_bus_interaction_female -1.066e-05 1.084e-05 -1.7148e-04 8.079e-05 asc_air_interaction_female -6.843e-06 1.491e-06 1.868e-05 1.0093e-04 asc_rail_interaction_female -3.207e-06 1.018e-06 7.311e-06 3.347e-05 b_tt_car 6.136e-07 -4.208e-07 -5.670e-07 -8.128e-06 b_tt_bus 9.924e-07 -7.698e-07 2.473e-06 -1.180e-05 b_tt_air 1.131e-06 -2.912e-07 -7.036e-06 -1.115e-05 b_tt_rail 7.200e-07 -5.125e-07 -2.594e-06 -8.348e-06 b_tt_interaction_business -1.958e-07 7.255e-07 -5.060e-07 -2.181e-06 b_access 1.002e-06 3.654e-08 -6.611e-06 -1.320e-05 b_cost 4.923e-06 -3.197e-06 -1.825e-05 -4.792e-05 b_cost_interaction_business -3.197e-06 4.836e-06 9.872e-08 1.558e-05 cost_income_elast -1.825e-05 9.872e-08 9.5695e-04 1.6662e-04 b_wifi -4.792e-05 1.558e-05 1.6662e-04 0.001923 b_food -2.095e-05 4.659e-06 1.1556e-04 0.001002 lambda_fastPT -2.786e-05 2.411e-05 2.527e-05 2.2136e-04 lambda_groundPT -4.289e-05 2.276e-05 -1.5148e-04 5.9448e-04 alpha_rail_fastPT_logistic 1.1851e-04 3.164e-05 -8.4620e-04 -0.002693 b_food lambda_fastPT lambda_groundPT alpha_rail_fastPT_logistic asc_bus -3.420e-05 1.669e-05 4.7274e-04 -0.001600 asc_air -8.6769e-04 -6.5425e-04 -4.660e-05 -7.9294e-04 asc_rail -0.001162 -7.0759e-04 -9.3957e-04 0.002129 asc_bus_interaction_female 9.814e-06 1.0202e-04 1.5929e-04 -1.0171e-04 asc_air_interaction_female 6.104e-05 2.316e-05 6.984e-05 -2.7400e-04 asc_rail_interaction_female 4.888e-06 2.954e-05 1.317e-05 -1.305e-05 b_tt_car -3.659e-06 -3.955e-06 -6.392e-06 1.496e-05 b_tt_bus -4.488e-06 -6.944e-06 -1.338e-05 1.693e-05 b_tt_air -5.920e-06 4.386e-07 -1.165e-05 5.847e-05 b_tt_rail -3.363e-06 -2.617e-06 -3.865e-06 1.041e-05 b_tt_interaction_business -1.226e-06 4.638e-07 -1.123e-07 1.632e-05 b_access -5.811e-06 1.228e-06 -1.409e-05 7.674e-05 b_cost -2.095e-05 -2.786e-05 -4.289e-05 1.1851e-04 b_cost_interaction_business 4.659e-06 2.411e-05 2.276e-05 3.164e-05 cost_income_elast 1.1556e-04 2.527e-05 -1.5148e-04 -8.4620e-04 b_wifi 0.001002 2.2136e-04 5.9448e-04 -0.002693 b_food 0.001479 1.607e-05 2.6306e-04 -0.001406 lambda_fastPT 1.607e-05 0.001389 -2.248e-05 0.003904 lambda_groundPT 2.6306e-04 -2.248e-05 0.001875 -0.003714 alpha_rail_fastPT_logistic -0.001406 0.003904 -0.003714 0.046027 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 0.177021 0.031230 0.030636 -0.004714 asc_air 0.031230 0.081379 0.048658 -9.3249e-04 asc_rail 0.030636 0.048658 0.077662 -9.3281e-04 asc_bus_interaction_female -0.004714 -9.3249e-04 -9.3281e-04 0.012437 asc_air_interaction_female 8.2537e-04 -0.002310 -0.002398 0.003264 asc_rail_interaction_female -7.9093e-04 -0.001148 -0.001598 0.003735 b_tt_car 9.518e-05 1.3598e-04 1.4001e-04 7.576e-07 b_tt_bus -4.0541e-04 4.006e-05 4.285e-05 -3.522e-06 b_tt_air -4.727e-05 -3.2725e-04 -9.990e-06 1.019e-05 b_tt_rail 7.413e-08 -1.441e-06 -2.1600e-04 -6.766e-07 b_tt_interaction_business 1.095e-05 1.855e-05 2.487e-05 1.043e-06 b_access 5.017e-05 -2.4901e-04 -3.300e-05 -1.182e-05 b_cost -4.224e-05 -2.178e-05 1.098e-05 -1.528e-05 b_cost_interaction_business 8.366e-05 -2.633e-05 2.902e-05 1.258e-05 cost_income_elast -0.001381 9.4450e-04 8.5456e-04 1.1573e-04 b_wifi -4.7849e-04 -0.001038 -0.001152 8.730e-07 b_food 5.8145e-04 -6.0373e-04 -9.0038e-04 2.3761e-04 lambda_fastPT -4.4852e-04 -0.001338 -7.3635e-04 1.4581e-04 lambda_groundPT 0.001666 0.001166 -4.7396e-04 3.8625e-04 alpha_rail_fastPT_logistic -0.003247 -0.004416 -7.8849e-04 -3.0742e-04 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 8.2537e-04 -7.9093e-04 9.518e-05 -4.0541e-04 asc_air -0.002310 -0.001148 1.3598e-04 4.006e-05 asc_rail -0.002398 -0.001598 1.4001e-04 4.285e-05 asc_bus_interaction_female 0.003264 0.003735 7.576e-07 -3.522e-06 asc_air_interaction_female 0.005761 0.003890 -1.811e-06 -8.256e-06 asc_rail_interaction_female 0.003890 0.004620 1.426e-06 -1.060e-06 b_tt_car -1.811e-06 1.426e-06 4.978e-07 2.138e-07 b_tt_bus -8.256e-06 -1.060e-06 2.138e-07 1.437e-06 b_tt_air -1.122e-07 4.975e-06 6.848e-08 2.169e-07 b_tt_rail 4.140e-06 1.797e-06 5.554e-08 1.104e-07 b_tt_interaction_business -7.040e-08 5.619e-07 -2.280e-10 -4.112e-08 b_access -4.309e-06 -2.443e-06 6.205e-08 -8.929e-08 b_cost -1.786e-05 -8.248e-06 5.979e-07 1.040e-06 b_cost_interaction_business 1.205e-05 1.193e-05 -3.897e-07 -8.526e-07 cost_income_elast 2.5715e-04 1.9379e-04 5.439e-07 5.166e-06 b_wifi -4.205e-05 -8.594e-05 -7.087e-06 -9.068e-06 b_food -1.4095e-04 -9.297e-05 -3.656e-06 -6.568e-06 lambda_fastPT 6.031e-05 2.0246e-04 -4.231e-06 -6.135e-06 lambda_groundPT 5.495e-05 -1.5078e-04 -4.478e-06 -1.616e-05 alpha_rail_fastPT_logistic -1.1726e-04 7.9068e-04 4.657e-06 1.530e-05 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -4.727e-05 7.413e-08 1.095e-05 5.017e-05 asc_air -3.2725e-04 -1.441e-06 1.855e-05 -2.4901e-04 asc_rail -9.990e-06 -2.1600e-04 2.487e-05 -3.300e-05 asc_bus_interaction_female 1.019e-05 -6.766e-07 1.043e-06 -1.182e-05 asc_air_interaction_female -1.122e-07 4.140e-06 -7.040e-08 -4.309e-06 asc_rail_interaction_female 4.975e-06 1.797e-06 5.619e-07 -2.443e-06 b_tt_car 6.848e-08 5.554e-08 -2.280e-10 6.205e-08 b_tt_bus 2.169e-07 1.104e-07 -4.112e-08 -8.929e-08 b_tt_air 3.826e-06 2.089e-08 -5.610e-08 1.208e-06 b_tt_rail 2.089e-08 1.569e-06 -1.029e-07 -6.281e-08 b_tt_interaction_business -5.610e-08 -1.029e-07 2.230e-07 5.355e-08 b_access 1.208e-06 -6.281e-08 5.355e-08 3.589e-06 b_cost 9.779e-07 8.229e-07 -2.039e-07 1.058e-06 b_cost_interaction_business -1.559e-07 -7.019e-07 5.480e-07 -1.400e-07 cost_income_elast -5.489e-06 -4.914e-06 -5.179e-07 -3.763e-06 b_wifi -1.130e-05 -9.431e-06 -2.653e-06 -8.951e-06 b_food -9.770e-06 -4.923e-06 -1.299e-06 -4.878e-06 lambda_fastPT 8.460e-06 -4.041e-06 -5.798e-07 4.278e-06 lambda_groundPT -1.534e-05 -1.421e-06 -4.995e-07 -2.055e-05 alpha_rail_fastPT_logistic 7.103e-05 8.423e-06 1.761e-05 8.071e-05 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -4.224e-05 8.366e-05 -0.001381 -4.7849e-04 asc_air -2.178e-05 -2.633e-05 9.4450e-04 -0.001038 asc_rail 1.098e-05 2.902e-05 8.5456e-04 -0.001152 asc_bus_interaction_female -1.528e-05 1.258e-05 1.1573e-04 8.730e-07 asc_air_interaction_female -1.786e-05 1.205e-05 2.5715e-04 -4.205e-05 asc_rail_interaction_female -8.248e-06 1.193e-05 1.9379e-04 -8.594e-05 b_tt_car 5.979e-07 -3.897e-07 5.439e-07 -7.087e-06 b_tt_bus 1.040e-06 -8.526e-07 5.166e-06 -9.068e-06 b_tt_air 9.779e-07 -1.559e-07 -5.489e-06 -1.130e-05 b_tt_rail 8.229e-07 -7.019e-07 -4.914e-06 -9.431e-06 b_tt_interaction_business -2.039e-07 5.480e-07 -5.179e-07 -2.653e-06 b_access 1.058e-06 -1.400e-07 -3.763e-06 -8.951e-06 b_cost 4.991e-06 -3.298e-06 -1.718e-05 -4.503e-05 b_cost_interaction_business -3.298e-06 4.202e-06 3.867e-08 1.492e-05 cost_income_elast -1.718e-05 3.867e-08 9.7359e-04 1.3038e-04 b_wifi -4.503e-05 1.492e-05 1.3038e-04 0.001894 b_food -2.039e-05 5.316e-06 3.530e-05 0.001055 lambda_fastPT -3.244e-05 2.330e-05 2.1630e-04 2.4139e-04 lambda_groundPT -4.605e-05 2.312e-05 -2.1549e-04 5.4300e-04 alpha_rail_fastPT_logistic 8.632e-05 4.792e-05 -1.4093e-04 -0.002064 b_food lambda_fastPT lambda_groundPT alpha_rail_fastPT_logistic asc_bus 5.8145e-04 -4.4852e-04 0.001666 -0.003247 asc_air -6.0373e-04 -0.001338 0.001166 -0.004416 asc_rail -9.0038e-04 -7.3635e-04 -4.7396e-04 -7.8849e-04 asc_bus_interaction_female 2.3761e-04 1.4581e-04 3.8625e-04 -3.0742e-04 asc_air_interaction_female -1.4095e-04 6.031e-05 5.495e-05 -1.1726e-04 asc_rail_interaction_female -9.297e-05 2.0246e-04 -1.5078e-04 7.9068e-04 b_tt_car -3.656e-06 -4.231e-06 -4.478e-06 4.657e-06 b_tt_bus -6.568e-06 -6.135e-06 -1.616e-05 1.530e-05 b_tt_air -9.770e-06 8.460e-06 -1.534e-05 7.103e-05 b_tt_rail -4.923e-06 -4.041e-06 -1.421e-06 8.423e-06 b_tt_interaction_business -1.299e-06 -5.798e-07 -4.995e-07 1.761e-05 b_access -4.878e-06 4.278e-06 -2.055e-05 8.071e-05 b_cost -2.039e-05 -3.244e-05 -4.605e-05 8.632e-05 b_cost_interaction_business 5.316e-06 2.330e-05 2.312e-05 4.792e-05 cost_income_elast 3.530e-05 2.1630e-04 -2.1549e-04 -1.4093e-04 b_wifi 0.001055 2.4139e-04 5.4300e-04 -0.002064 b_food 0.001667 -5.781e-05 2.8691e-04 -0.001474 lambda_fastPT -5.781e-05 0.001707 -8.116e-05 0.004341 lambda_groundPT 2.8691e-04 -8.116e-05 0.002046 -0.004126 alpha_rail_fastPT_logistic -0.001474 0.004341 -0.004126 0.042693 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.000000 0.279649 0.25224 -0.120490 asc_air 0.279649 1.000000 0.59693 -0.054587 asc_rail 0.252244 0.596933 1.00000 -0.058497 asc_bus_interaction_female -0.120490 -0.054587 -0.05850 1.000000 asc_air_interaction_female -0.042781 -0.127018 -0.08559 0.383265 asc_rail_interaction_female -0.058118 -0.088412 -0.12095 0.475169 b_tt_car 0.324885 0.675418 0.72299 -0.018463 b_tt_bus -0.818500 0.091637 0.13730 -0.014175 b_tt_air -0.027316 -0.590974 -0.01258 -0.004643 b_tt_rail 0.022429 0.008505 -0.63247 -0.009043 b_tt_interaction_business 0.017456 0.063534 0.10024 0.008457 b_access -0.022784 -0.468443 -0.03293 0.002272 b_cost -0.032647 -0.038582 0.05056 -0.045642 b_cost_interaction_business 0.045010 -0.057345 -0.01554 0.046836 cost_income_elast -0.044151 0.101603 0.03837 -0.052655 b_wifi 0.018862 -0.093634 -0.12756 0.017501 b_food -0.001995 -0.077243 -0.10499 0.002424 lambda_fastPT 0.001004 -0.060085 -0.06597 0.025998 lambda_groundPT 0.024488 -0.003685 -0.07542 0.034945 alpha_rail_fastPT_logistic -0.016725 -0.012652 0.03448 -0.004503 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus -0.042781 -0.058118 0.32489 -0.818500 asc_air -0.127018 -0.088412 0.67542 0.091637 asc_rail -0.085588 -0.120945 0.72299 0.137304 asc_bus_interaction_female 0.383265 0.475169 -0.01846 -0.014175 asc_air_interaction_female 1.000000 0.730097 -0.01915 -0.015702 asc_rail_interaction_female 0.730097 1.000000 -0.01069 -0.003783 b_tt_car -0.019153 -0.010686 1.00000 0.229757 b_tt_bus -0.015702 -0.003783 0.22976 1.000000 b_tt_air -0.012136 -0.007507 0.03689 0.061571 b_tt_rail -0.014716 0.002499 0.02714 0.023236 b_tt_interaction_business -0.019510 -0.010581 -0.05356 -0.059143 b_access -0.012412 -0.017681 0.04551 0.024162 b_cost -0.040240 -0.021476 0.38773 0.360318 b_cost_interaction_business 0.008849 0.006876 -0.26828 -0.282026 cost_income_elast 0.007879 0.003512 -0.02570 0.064394 b_wifi 0.030036 0.011342 -0.25989 -0.216774 b_food 0.020712 0.001889 -0.13343 -0.094032 lambda_fastPT 0.008109 0.011777 -0.14878 -0.150078 lambda_groundPT 0.021048 0.004521 -0.20700 -0.248914 alpha_rail_fastPT_logistic -0.016665 -9.0356e-04 0.09778 0.063569 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -0.027316 0.022429 0.017456 -0.022784 asc_air -0.590974 0.008505 0.063534 -0.468443 asc_rail -0.012576 -0.632468 0.100242 -0.032930 asc_bus_interaction_female -0.004643 -0.009043 0.008457 0.002272 asc_air_interaction_female -0.012136 -0.014716 -0.019510 -0.012412 asc_rail_interaction_female -0.007507 0.002499 -0.010581 -0.017681 b_tt_car 0.036890 0.027139 -0.053557 0.045513 b_tt_bus 0.061571 0.023236 -0.059143 0.024162 b_tt_air 1.000000 -0.018493 -0.030125 0.334494 b_tt_rail -0.018493 1.000000 -0.115311 -0.067101 b_tt_interaction_business -0.030125 -0.115311 1.000000 0.059220 b_access 0.334494 -0.067101 0.059220 1.000000 b_cost 0.262304 0.252708 -0.171505 0.227835 b_cost_interaction_business -0.068160 -0.181488 0.641229 0.008380 cost_income_elast -0.117090 -0.065297 -0.031792 -0.107782 b_wifi -0.130863 -0.148263 -0.096688 -0.151863 b_food -0.079248 -0.068114 -0.061963 -0.076218 lambda_fastPT 0.006057 -0.054677 0.024186 0.016617 lambda_groundPT -0.138547 -0.069514 -0.005040 -0.164130 alpha_rail_fastPT_logistic 0.140291 0.037803 0.147870 0.180401 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -0.03265 0.045010 -0.044151 0.01886 asc_air -0.03858 -0.057345 0.101603 -0.09363 asc_rail 0.05056 -0.015540 0.038367 -0.12756 asc_bus_interaction_female -0.04564 0.046836 -0.052655 0.01750 asc_air_interaction_female -0.04024 0.008849 0.007879 0.03004 asc_rail_interaction_female -0.02148 0.006876 0.003512 0.01134 b_tt_car 0.38773 -0.268281 -0.025699 -0.25989 b_tt_bus 0.36032 -0.282026 0.064394 -0.21677 b_tt_air 0.26230 -0.068160 -0.117090 -0.13086 b_tt_rail 0.25271 -0.181488 -0.065297 -0.14826 b_tt_interaction_business -0.17150 0.641229 -0.031792 -0.09669 b_access 0.22783 0.008380 -0.107782 -0.15186 b_cost 1.00000 -0.655138 -0.265906 -0.49254 b_cost_interaction_business -0.65514 1.000000 0.001451 0.16162 cost_income_elast -0.26591 0.001451 1.000000 0.12284 b_wifi -0.49254 0.161620 0.122837 1.00000 b_food -0.24550 0.055091 0.097144 0.59412 lambda_fastPT -0.33680 0.294172 0.021913 0.13544 lambda_groundPT -0.44647 0.239050 -0.113093 0.31314 alpha_rail_fastPT_logistic 0.24894 0.067072 -0.127504 -0.28624 b_food lambda_fastPT lambda_groundPT alpha_rail_fastPT_logistic asc_bus -0.001995 0.001004 0.024488 -0.016725 asc_air -0.077243 -0.060085 -0.003685 -0.012652 asc_rail -0.104992 -0.065973 -0.075415 0.034480 asc_bus_interaction_female 0.002424 0.025998 0.034945 -0.004503 asc_air_interaction_female 0.020712 0.008109 0.021048 -0.016665 asc_rail_interaction_female 0.001889 0.011777 0.004521 -9.0356e-04 b_tt_car -0.133427 -0.148776 -0.207001 0.097778 b_tt_bus -0.094032 -0.150078 -0.248914 0.063569 b_tt_air -0.079248 0.006057 -0.138547 0.140291 b_tt_rail -0.068114 -0.054677 -0.069514 0.037803 b_tt_interaction_business -0.061963 0.024186 -0.005040 0.147870 b_access -0.076218 0.016617 -0.164130 0.180401 b_cost -0.245498 -0.336799 -0.446472 0.248944 b_cost_interaction_business 0.055091 0.294172 0.239050 0.067072 cost_income_elast 0.097144 0.021913 -0.113093 -0.127504 b_wifi 0.594117 0.135439 0.313139 -0.286242 b_food 1.000000 0.011212 0.158005 -0.170488 lambda_fastPT 0.011212 1.000000 -0.013928 0.488198 lambda_groundPT 0.158005 -0.013928 1.000000 -0.399798 alpha_rail_fastPT_logistic -0.170488 0.488198 -0.399798 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.00000 0.260201 0.26128 -0.100464 asc_air 0.26020 1.000000 0.61206 -0.029311 asc_rail 0.26128 0.612057 1.00000 -0.030015 asc_bus_interaction_female -0.10046 -0.029311 -0.03001 1.000000 asc_air_interaction_female 0.02585 -0.106682 -0.11339 0.385664 asc_rail_interaction_female -0.02766 -0.059198 -0.08434 0.492669 b_tt_car 0.32062 0.675558 0.71206 0.009628 b_tt_bus -0.80374 0.117150 0.12824 -0.026346 b_tt_air -0.05743 -0.586459 -0.01833 0.046707 b_tt_rail 1.4067e-04 -0.004033 -0.61883 -0.004844 b_tt_interaction_business 0.05509 0.137681 0.18895 0.019802 b_access 0.06294 -0.460757 -0.06251 -0.055925 b_cost -0.04494 -0.034173 0.01763 -0.061317 b_cost_interaction_business 0.09700 -0.045027 0.05080 0.055010 cost_income_elast -0.10518 0.106110 0.09828 0.033258 b_wifi -0.02613 -0.083606 -0.09501 1.7990e-04 b_food 0.03385 -0.051842 -0.07914 0.052192 lambda_fastPT -0.02580 -0.113522 -0.06395 0.031644 lambda_groundPT 0.08753 0.090342 -0.03760 0.076572 alpha_rail_fastPT_logistic -0.03735 -0.074928 -0.01369 -0.013342 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 0.025846 -0.02766 0.320620 -0.80374 asc_air -0.106682 -0.05920 0.675558 0.11715 asc_rail -0.113389 -0.08434 0.712064 0.12824 asc_bus_interaction_female 0.385664 0.49267 0.009628 -0.02635 asc_air_interaction_female 1.000000 0.75394 -0.033819 -0.09073 asc_rail_interaction_female 0.753943 1.00000 0.029741 -0.01301 b_tt_car -0.033819 0.02974 1.000000 0.25274 b_tt_bus -0.090733 -0.01301 0.252739 1.00000 b_tt_air -7.5595e-04 0.03742 0.049618 0.09249 b_tt_rail 0.043553 0.02110 0.062841 0.07351 b_tt_interaction_business -0.001964 0.01750 -6.8419e-04 -0.07263 b_access -0.029968 -0.01897 0.046420 -0.03932 b_cost -0.105338 -0.05431 0.379296 0.38845 b_cost_interaction_business 0.077473 0.08561 -0.269441 -0.34695 cost_income_elast 0.108580 0.09137 0.024706 0.13810 b_wifi -0.012732 -0.02905 -0.230829 -0.17382 b_food -0.045490 -0.03351 -0.126925 -0.13420 lambda_fastPT 0.019230 0.07209 -0.145144 -0.12386 lambda_groundPT 0.016007 -0.04904 -0.140301 -0.29793 alpha_rail_fastPT_logistic -0.007477 0.05630 0.031944 0.06177 b_tt_air b_tt_rail b_tt_interaction_business b_access asc_bus -0.057432 1.4067e-04 0.055086 0.06294 asc_air -0.586459 -0.004033 0.137681 -0.46076 asc_rail -0.018327 -0.618827 0.188950 -0.06251 asc_bus_interaction_female 0.046707 -0.004844 0.019802 -0.05593 asc_air_interaction_female -7.5595e-04 0.043553 -0.001964 -0.02997 asc_rail_interaction_female 0.037419 0.021105 0.017504 -0.01897 b_tt_car 0.049618 0.062841 -6.8419e-04 0.04642 b_tt_bus 0.092490 0.073506 -0.072635 -0.03932 b_tt_air 1.000000 0.008525 -0.060726 0.32599 b_tt_rail 0.008525 1.000000 -0.173990 -0.02647 b_tt_interaction_business -0.060726 -0.173990 1.000000 0.05985 b_access 0.325993 -0.026472 0.059852 1.00000 b_cost 0.223778 0.294052 -0.193258 0.24997 b_cost_interaction_business -0.038877 -0.273385 0.566066 -0.03605 cost_income_elast -0.089925 -0.125745 -0.035143 -0.06365 b_wifi -0.132752 -0.173032 -0.129073 -0.10858 b_food -0.122346 -0.096283 -0.067373 -0.06308 lambda_fastPT 0.104670 -0.078082 -0.029711 0.05465 lambda_groundPT -0.173398 -0.025080 -0.023383 -0.23987 alpha_rail_fastPT_logistic 0.175750 0.032546 0.180469 0.20619 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus -0.04494 0.09700 -0.10518 -0.02613 asc_air -0.03417 -0.04503 0.10611 -0.08361 asc_rail 0.01763 0.05080 0.09828 -0.09501 asc_bus_interaction_female -0.06132 0.05501 0.03326 1.7990e-04 asc_air_interaction_female -0.10534 0.07747 0.10858 -0.01273 asc_rail_interaction_female -0.05431 0.08561 0.09137 -0.02905 b_tt_car 0.37930 -0.26944 0.02471 -0.23083 b_tt_bus 0.38845 -0.34695 0.13810 -0.17382 b_tt_air 0.22378 -0.03888 -0.08993 -0.13275 b_tt_rail 0.29405 -0.27339 -0.12574 -0.17303 b_tt_interaction_business -0.19326 0.56607 -0.03514 -0.12907 b_access 0.24997 -0.03605 -0.06365 -0.10858 b_cost 1.00000 -0.72017 -0.24647 -0.46315 b_cost_interaction_business -0.72017 1.00000 6.0465e-04 0.16730 cost_income_elast -0.24647 6.0465e-04 1.00000 0.09602 b_wifi -0.46315 0.16730 0.09602 1.00000 b_food -0.22353 0.06353 0.02772 0.59364 lambda_fastPT -0.35137 0.27509 0.16777 0.13425 lambda_groundPT -0.45571 0.24933 -0.15268 0.27587 alpha_rail_fastPT_logistic 0.18699 0.11314 -0.02186 -0.22957 b_food lambda_fastPT lambda_groundPT alpha_rail_fastPT_logistic asc_bus 0.03385 -0.02580 0.08753 -0.037353 asc_air -0.05184 -0.11352 0.09034 -0.074928 asc_rail -0.07914 -0.06395 -0.03760 -0.013694 asc_bus_interaction_female 0.05219 0.03164 0.07657 -0.013342 asc_air_interaction_female -0.04549 0.01923 0.01601 -0.007477 asc_rail_interaction_female -0.03351 0.07209 -0.04904 0.056297 b_tt_car -0.12693 -0.14514 -0.14030 0.031944 b_tt_bus -0.13420 -0.12386 -0.29793 0.061774 b_tt_air -0.12235 0.10467 -0.17340 0.175750 b_tt_rail -0.09628 -0.07808 -0.02508 0.032546 b_tt_interaction_business -0.06737 -0.02971 -0.02338 0.180469 b_access -0.06308 0.05465 -0.23987 0.206186 b_cost -0.22353 -0.35137 -0.45571 0.186989 b_cost_interaction_business 0.06353 0.27509 0.24933 0.113140 cost_income_elast 0.02772 0.16777 -0.15268 -0.021859 b_wifi 0.59364 0.13425 0.27587 -0.229568 b_food 1.00000 -0.03427 0.15538 -0.174729 lambda_fastPT -0.03427 1.00000 -0.04342 0.508488 lambda_groundPT 0.15538 -0.04342 1.00000 -0.441521 alpha_rail_fastPT_logistic -0.17473 0.50849 -0.44152 1.000000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2057397 464 0.2468188 181 0.2623606 146 0.2670324 317 0.2733118 276 0.2772067 370 0.2807018 447 0.2859800 367 0.2879348 161 0.2892149 59 0.2933235 434 0.2937537 379 0.2970110 307 0.2971935 293 0.2974699 73 0.2975948 186 0.2994404 259 0.2999602 441 0.3017748 467 0.3053896 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286354 0.299051 0.012697 asc_air -0.903377 -0.646437 0.256940 asc_rail -2.092701 -1.563614 0.529087 asc_bus_interaction_female 0.340193 0.273635 -0.066558 asc_air_interaction_female 0.268174 0.240318 -0.027855 asc_rail_interaction_female 0.189612 0.178831 -0.010781 b_tt_car -0.013107 -0.010391 0.002716 b_tt_bus -0.021265 -0.016555 0.004710 b_tt_air -0.016578 -0.013074 0.003504 b_tt_rail -0.007051 -0.005460 0.001591 b_tt_interaction_business -0.006234 -0.006010 2.2385e-04 b_access -0.021152 -0.017829 0.003323 b_cost -0.076188 -0.057587 0.018600 b_cost_interaction_business 0.033379 0.023261 -0.010119 cost_income_elast -0.613821 -0.620998 -0.007177 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026711 0.774407 -0.252304 b_food 0.422072 0.337791 -0.084280 lambda_fastPT 1.000000 0.401188 -0.598812 lambda_groundPT 1.000000 0.528458 -0.471542 alpha_rail_fastPT_logistic 0.000000 -0.028384 -0.028384 alpha_rail_groundPT_logistic 0.000000 0.000000 0.000000 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "CNL model with socio-demographics on mode choice SP data, using logistic transform to ensure alphas meet constraints" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "CNL_logistic_transform_for_alphas" 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 0.299050577 asc_air 0.646437436 asc_rail 1.563613901 asc_bus_interaction_female 0.273635337 asc_air_interaction_female 0.240318321 asc_rail_interaction_female 0.178831483 b_tt_car 0.010391109 b_tt_bus 0.016554873 b_tt_air 0.013073550 b_tt_rail 0.005459900 b_tt_interaction_business 0.006010085 b_access 0.017829486 b_cost 0.057587147 b_cost_interaction_business 0.023260691 cost_income_elast 0.620997768 b_wifi 0.774407319 b_food 0.337791291 lambda_fastPT 0.401187768 lambda_groundPT 0.528458292 alpha_rail_fastPT_logistic 0.028383569 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 cnl_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 CNL model cnlNests = list(car=1,groundPT=lambda_groundPT,fastPT=lambda_fastPT) ### Specify nest allocation parameters for alternatives included in multiple nests ### logistic transform to ensure values between 0 and 1, and summing to 1 alpha_rail_fastPT = exp(alpha_rail_fastPT_logistic)/(exp(alpha_rail_fastPT_logistic)+exp(alpha_rail_groundPT_logistic)) alpha_rail_groundPT = 1 - alpha_rail_fastPT ### Specify tree structure, showing membership in nests (one row per nest, one column per alternative) cnlStructure = matrix(0, nrow=length(cnlNests), ncol=length(V)) cnlStructure[1,] = c( 1, 0, 0, 0 ) # car cnlStructure[2,] = c( 0, 1, 0, alpha_rail_groundPT) # groundPT cnlStructure[3,] = c( 0, 0, 1, alpha_rail_fastPT ) # fastPT ### Define settings for CNL model cnl_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, cnlNests = cnlNests, cnlStructure = cnlStructure ) ### Compute probabilities using CNL model P[["model"]] = apollo_cnl(cnl_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) }