Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. 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 : 2023-05-10 20:20:51 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -4.440252 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) : 00:00:40.25 pre-estimation : 00:00:0.76 estimation : 00:00:19.46 initial estimation : 00:00:17.94 estimation after rescaling : 00:00:1.52 post-estimation : 00:00:20.03 Iterations : 33 initial estimation : 30 estimation after rescaling : 3 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. Rob.t.rat.(0) asc_car 0.000000 NA NA NA NA NA asc_bus 0.299228 0.445864 0.6711 -1.572 0.420741 0.7112 asc_air -0.646265 0.292126 -2.2123 -5.635 0.285270 -2.2655 asc_rail -1.563467 0.287744 -5.4335 -8.909 0.278679 -5.6103 asc_bus_shift_female 0.273643 0.105278 2.5992 -6.899 0.111521 2.4537 asc_air_shift_female 0.240311 0.076638 3.1357 -9.913 0.075900 3.1662 asc_rail_shift_female 0.178834 0.067296 2.6574 -12.202 0.067973 2.6309 b_tt_car -0.010391 7.1322e-04 -14.5689 -1416.656 7.0558e-04 -14.7267 b_tt_bus -0.016555 0.001241 -13.3373 -818.964 0.001199 -13.8090 b_tt_air -0.013074 0.001943 -6.7303 -521.504 0.001956 -6.6839 b_tt_rail -0.005460 0.001284 -4.2523 -783.034 0.001253 -4.3593 b_tt_shift_business -0.006010 5.1448e-04 -11.6817 -1955.400 4.7225e-04 -12.7263 b_access -0.017830 0.001983 -8.9923 -513.319 0.001895 -9.4116 b_cost -0.057587 0.002219 -25.9533 -476.630 0.002234 -25.7756 b_cost_shift_business 0.023262 0.002199 10.5779 -444.161 0.002050 11.3478 cost_income_elast -0.621001 0.030935 -20.0746 -52.401 0.031203 -19.9022 b_no_frills 0.000000 NA NA NA NA NA b_wifi 0.774401 0.043847 17.6614 -5.145 0.043516 17.7958 b_food 0.337788 0.038453 8.7844 -17.221 0.040823 8.2744 lambda_fastPT 0.401188 0.037274 10.7633 -16.065 0.041319 9.7096 lambda_groundPT 0.528466 0.043298 12.2053 -10.890 0.045232 11.6834 alpha_rail_fastPT_logistic -0.028385 0.214540 -0.1323 -4.793 0.206621 -0.1374 alpha_rail_groundPT_logistic 0.000000 NA NA NA NA NA Rob.t.rat.(1) asc_car NA asc_bus -1.666 asc_air -5.771 asc_rail -9.199 asc_bus_shift_female -6.513 asc_air_shift_female -10.009 asc_rail_shift_female -12.081 b_tt_car -1432.003 b_tt_bus -847.930 b_tt_air -517.911 b_tt_rail -802.741 b_tt_shift_business -2130.256 b_access -537.254 b_cost -473.367 b_cost_shift_business -476.490 cost_income_elast -51.951 b_no_frills NA b_wifi -5.184 b_food -16.221 lambda_fastPT -14.493 lambda_groundPT -10.425 alpha_rail_fastPT_logistic -4.977 alpha_rail_groundPT_logistic 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 0.198795 0.036424 0.032361 asc_air 0.036424 0.085338 0.050177 asc_rail 0.032361 0.050177 0.082797 asc_bus_shift_female -0.005656 -0.001679 -0.001772 asc_air_shift_female -0.001462 -0.002844 -0.001887 asc_rail_shift_female -0.001744 -0.001738 -0.002342 b_tt_car 1.0331e-04 1.4072e-04 1.4838e-04 b_tt_bus -4.5299e-04 3.323e-05 4.904e-05 b_tt_air -2.366e-05 -3.3537e-04 -7.030e-06 b_tt_rail 1.284e-05 3.189e-06 -2.3368e-04 b_tt_shift_business 4.004e-06 9.548e-06 1.484e-05 b_access -2.015e-05 -2.7134e-04 -1.879e-05 b_cost -3.231e-05 -2.502e-05 3.227e-05 b_cost_shift_business 4.414e-05 -3.683e-05 -9.830e-06 cost_income_elast -6.0902e-04 9.1820e-04 3.4153e-04 b_wifi 3.6886e-04 -0.001199 -0.001609 b_food -3.416e-05 -8.6763e-04 -0.001162 lambda_fastPT 1.675e-05 -6.5410e-04 -7.0749e-04 lambda_groundPT 4.7306e-04 -4.645e-05 -9.3945e-04 alpha_rail_fastPT_logistic -0.001600 -7.9369e-04 0.002128 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.005656 -0.001462 -0.001744 asc_air -0.001679 -0.002844 -0.001738 asc_rail -0.001772 -0.001887 -0.002342 asc_bus_shift_female 0.011083 0.003092 0.003366 asc_air_shift_female 0.003092 0.005873 0.003765 asc_rail_shift_female 0.003366 0.003765 0.004529 b_tt_car -1.386e-06 -1.047e-06 -5.129e-07 b_tt_bus -1.853e-06 -1.494e-06 -3.160e-07 b_tt_air -9.498e-07 -1.807e-06 -9.815e-07 b_tt_rail -1.223e-06 -1.448e-06 2.159e-07 b_tt_shift_business 4.581e-07 -7.692e-07 -3.663e-07 b_access 4.738e-07 -1.886e-06 -2.359e-06 b_cost -1.066e-05 -6.842e-06 -3.207e-06 b_cost_shift_business 1.084e-05 1.491e-06 1.018e-06 cost_income_elast -1.7149e-04 1.868e-05 7.313e-06 b_wifi 8.079e-05 1.0092e-04 3.347e-05 b_food 9.815e-06 6.104e-05 4.888e-06 lambda_fastPT 1.0202e-04 2.315e-05 2.955e-05 lambda_groundPT 1.5930e-04 6.983e-05 1.317e-05 alpha_rail_fastPT_logistic -1.0171e-04 -2.7396e-04 -1.306e-05 b_tt_car b_tt_bus b_tt_air asc_bus 1.0331e-04 -4.5299e-04 -2.366e-05 asc_air 1.4072e-04 3.323e-05 -3.3537e-04 asc_rail 1.4838e-04 4.904e-05 -7.030e-06 asc_bus_shift_female -1.386e-06 -1.853e-06 -9.498e-07 asc_air_shift_female -1.047e-06 -1.494e-06 -1.807e-06 asc_rail_shift_female -5.129e-07 -3.160e-07 -9.815e-07 b_tt_car 5.087e-07 2.034e-07 5.112e-08 b_tt_bus 2.034e-07 1.541e-06 1.485e-07 b_tt_air 5.112e-08 1.485e-07 3.774e-06 b_tt_rail 2.486e-08 3.704e-08 -4.611e-08 b_tt_shift_business -1.965e-08 -3.777e-08 -3.011e-08 b_access 6.438e-08 5.950e-08 1.288e-06 b_cost 6.136e-07 9.924e-07 1.131e-06 b_cost_shift_business -4.208e-07 -7.698e-07 -2.912e-07 cost_income_elast -5.670e-07 2.473e-06 -7.037e-06 b_wifi -8.127e-06 -1.180e-05 -1.115e-05 b_food -3.659e-06 -4.488e-06 -5.920e-06 lambda_fastPT -3.955e-06 -6.944e-06 4.377e-07 lambda_groundPT -6.392e-06 -1.338e-05 -1.165e-05 alpha_rail_fastPT_logistic 1.496e-05 1.693e-05 5.847e-05 b_tt_rail b_tt_shift_business b_access asc_bus 1.284e-05 4.004e-06 -2.015e-05 asc_air 3.189e-06 9.548e-06 -2.7134e-04 asc_rail -2.3368e-04 1.484e-05 -1.879e-05 asc_bus_shift_female -1.223e-06 4.581e-07 4.738e-07 asc_air_shift_female -1.448e-06 -7.692e-07 -1.886e-06 asc_rail_shift_female 2.159e-07 -3.663e-07 -2.359e-06 b_tt_car 2.486e-08 -1.965e-08 6.438e-08 b_tt_bus 3.704e-08 -3.777e-08 5.950e-08 b_tt_air -4.611e-08 -3.011e-08 1.288e-06 b_tt_rail 1.649e-06 -7.618e-08 -1.708e-07 b_tt_shift_business -7.618e-08 2.647e-07 6.041e-08 b_access -1.708e-07 6.041e-08 3.932e-06 b_cost 7.200e-07 -1.958e-07 1.002e-06 b_cost_shift_business -5.125e-07 7.255e-07 3.648e-08 cost_income_elast -2.594e-06 -5.059e-07 -6.611e-06 b_wifi -8.348e-06 -2.181e-06 -1.320e-05 b_food -3.363e-06 -1.226e-06 -5.812e-06 lambda_fastPT -2.617e-06 4.639e-07 1.227e-06 lambda_groundPT -3.865e-06 -1.122e-07 -1.409e-05 alpha_rail_fastPT_logistic 1.041e-05 1.632e-05 7.675e-05 b_cost b_cost_shift_business cost_income_elast asc_bus -3.231e-05 4.414e-05 -6.0902e-04 asc_air -2.502e-05 -3.683e-05 9.1820e-04 asc_rail 3.227e-05 -9.830e-06 3.4153e-04 asc_bus_shift_female -1.066e-05 1.084e-05 -1.7149e-04 asc_air_shift_female -6.842e-06 1.491e-06 1.868e-05 asc_rail_shift_female -3.207e-06 1.018e-06 7.313e-06 b_tt_car 6.136e-07 -4.208e-07 -5.670e-07 b_tt_bus 9.924e-07 -7.698e-07 2.473e-06 b_tt_air 1.131e-06 -2.912e-07 -7.037e-06 b_tt_rail 7.200e-07 -5.125e-07 -2.594e-06 b_tt_shift_business -1.958e-07 7.255e-07 -5.059e-07 b_access 1.002e-06 3.648e-08 -6.611e-06 b_cost 4.923e-06 -3.197e-06 -1.825e-05 b_cost_shift_business -3.197e-06 4.836e-06 9.915e-08 cost_income_elast -1.825e-05 9.915e-08 9.5695e-04 b_wifi -4.792e-05 1.558e-05 1.6661e-04 b_food -2.095e-05 4.659e-06 1.1555e-04 lambda_fastPT -2.786e-05 2.411e-05 2.527e-05 lambda_groundPT -4.289e-05 2.276e-05 -1.5149e-04 alpha_rail_fastPT_logistic 1.1851e-04 3.164e-05 -8.4617e-04 b_wifi b_food lambda_fastPT asc_bus 3.6886e-04 -3.416e-05 1.675e-05 asc_air -0.001199 -8.6763e-04 -6.5410e-04 asc_rail -0.001609 -0.001162 -7.0749e-04 asc_bus_shift_female 8.079e-05 9.815e-06 1.0202e-04 asc_air_shift_female 1.0092e-04 6.104e-05 2.315e-05 asc_rail_shift_female 3.347e-05 4.888e-06 2.955e-05 b_tt_car -8.127e-06 -3.659e-06 -3.955e-06 b_tt_bus -1.180e-05 -4.488e-06 -6.944e-06 b_tt_air -1.115e-05 -5.920e-06 4.377e-07 b_tt_rail -8.348e-06 -3.363e-06 -2.617e-06 b_tt_shift_business -2.181e-06 -1.226e-06 4.639e-07 b_access -1.320e-05 -5.812e-06 1.227e-06 b_cost -4.792e-05 -2.095e-05 -2.786e-05 b_cost_shift_business 1.558e-05 4.659e-06 2.411e-05 cost_income_elast 1.6661e-04 1.1555e-04 2.527e-05 b_wifi 0.001923 0.001002 2.2134e-04 b_food 0.001002 0.001479 1.606e-05 lambda_fastPT 2.2134e-04 1.606e-05 0.001389 lambda_groundPT 5.9448e-04 2.6306e-04 -2.247e-05 alpha_rail_fastPT_logistic -0.002693 -0.001406 0.003904 lambda_groundPT alpha_rail_fastPT_logistic asc_bus 4.7306e-04 -0.001600 asc_air -4.645e-05 -7.9369e-04 asc_rail -9.3945e-04 0.002128 asc_bus_shift_female 1.5930e-04 -1.0171e-04 asc_air_shift_female 6.983e-05 -2.7396e-04 asc_rail_shift_female 1.317e-05 -1.306e-05 b_tt_car -6.392e-06 1.496e-05 b_tt_bus -1.338e-05 1.693e-05 b_tt_air -1.165e-05 5.847e-05 b_tt_rail -3.865e-06 1.041e-05 b_tt_shift_business -1.122e-07 1.632e-05 b_access -1.409e-05 7.675e-05 b_cost -4.289e-05 1.1851e-04 b_cost_shift_business 2.276e-05 3.164e-05 cost_income_elast -1.5149e-04 -8.4617e-04 b_wifi 5.9448e-04 -0.002693 b_food 2.6306e-04 -0.001406 lambda_fastPT -2.247e-05 0.003904 lambda_groundPT 0.001875 -0.003714 alpha_rail_fastPT_logistic -0.003714 0.046027 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus 0.177023 0.031230 0.030636 asc_air 0.031230 0.081379 0.048658 asc_rail 0.030636 0.048658 0.077662 asc_bus_shift_female -0.004714 -9.3236e-04 -9.3274e-04 asc_air_shift_female 8.2544e-04 -0.002310 -0.002398 asc_rail_shift_female -7.9091e-04 -0.001148 -0.001598 b_tt_car 9.518e-05 1.3597e-04 1.4001e-04 b_tt_bus -4.0542e-04 4.006e-05 4.284e-05 b_tt_air -4.727e-05 -3.2725e-04 -9.992e-06 b_tt_rail 7.221e-08 -1.444e-06 -2.1601e-04 b_tt_shift_business 1.095e-05 1.855e-05 2.487e-05 b_access 5.017e-05 -2.4902e-04 -3.300e-05 b_cost -4.226e-05 -2.180e-05 1.096e-05 b_cost_shift_business 8.367e-05 -2.632e-05 2.902e-05 cost_income_elast -0.001381 9.4455e-04 8.5460e-04 b_wifi -4.7826e-04 -0.001038 -0.001152 b_food 5.8152e-04 -6.0367e-04 -9.0033e-04 lambda_fastPT -4.4843e-04 -0.001338 -7.3618e-04 lambda_groundPT 0.001666 0.001166 -4.7376e-04 alpha_rail_fastPT_logistic -0.003248 -0.004418 -7.8903e-04 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.004714 8.2544e-04 -7.9091e-04 asc_air -9.3236e-04 -0.002310 -0.001148 asc_rail -9.3274e-04 -0.002398 -0.001598 asc_bus_shift_female 0.012437 0.003264 0.003735 asc_air_shift_female 0.003264 0.005761 0.003890 asc_rail_shift_female 0.003735 0.003890 0.004620 b_tt_car 7.576e-07 -1.811e-06 1.426e-06 b_tt_bus -3.522e-06 -8.256e-06 -1.060e-06 b_tt_air 1.019e-05 -1.121e-07 4.975e-06 b_tt_rail -6.768e-07 4.141e-06 1.797e-06 b_tt_shift_business 1.043e-06 -7.021e-08 5.619e-07 b_access -1.182e-05 -4.309e-06 -2.443e-06 b_cost -1.528e-05 -1.786e-05 -8.248e-06 b_cost_shift_business 1.258e-05 1.205e-05 1.193e-05 cost_income_elast 1.1572e-04 2.5714e-04 1.9379e-04 b_wifi 8.882e-07 -4.207e-05 -8.594e-05 b_food 2.3762e-04 -1.4095e-04 -9.297e-05 lambda_fastPT 1.4581e-04 6.028e-05 2.0247e-04 lambda_groundPT 3.8628e-04 5.494e-05 -1.5078e-04 alpha_rail_fastPT_logistic -3.0748e-04 -1.1723e-04 7.9066e-04 b_tt_car b_tt_bus b_tt_air asc_bus 9.518e-05 -4.0542e-04 -4.727e-05 asc_air 1.3597e-04 4.006e-05 -3.2725e-04 asc_rail 1.4001e-04 4.284e-05 -9.992e-06 asc_bus_shift_female 7.576e-07 -3.522e-06 1.019e-05 asc_air_shift_female -1.811e-06 -8.256e-06 -1.121e-07 asc_rail_shift_female 1.426e-06 -1.060e-06 4.975e-06 b_tt_car 4.978e-07 2.138e-07 6.849e-08 b_tt_bus 2.138e-07 1.437e-06 2.169e-07 b_tt_air 6.849e-08 2.169e-07 3.826e-06 b_tt_rail 5.554e-08 1.104e-07 2.091e-08 b_tt_shift_business -2.318e-10 -4.113e-08 -5.609e-08 b_access 6.207e-08 -8.925e-08 1.208e-06 b_cost 5.979e-07 1.040e-06 9.781e-07 b_cost_shift_business -3.897e-07 -8.527e-07 -1.560e-07 cost_income_elast 5.440e-07 5.166e-06 -5.489e-06 b_wifi -7.087e-06 -9.068e-06 -1.130e-05 b_food -3.656e-06 -6.568e-06 -9.770e-06 lambda_fastPT -4.231e-06 -6.135e-06 8.458e-06 lambda_groundPT -4.478e-06 -1.616e-05 -1.534e-05 alpha_rail_fastPT_logistic 4.656e-06 1.530e-05 7.104e-05 b_tt_rail b_tt_shift_business b_access asc_bus 7.221e-08 1.095e-05 5.017e-05 asc_air -1.444e-06 1.855e-05 -2.4902e-04 asc_rail -2.1601e-04 2.487e-05 -3.300e-05 asc_bus_shift_female -6.768e-07 1.043e-06 -1.182e-05 asc_air_shift_female 4.141e-06 -7.021e-08 -4.309e-06 asc_rail_shift_female 1.797e-06 5.619e-07 -2.443e-06 b_tt_car 5.554e-08 -2.318e-10 6.207e-08 b_tt_bus 1.104e-07 -4.113e-08 -8.925e-08 b_tt_air 2.091e-08 -5.609e-08 1.208e-06 b_tt_rail 1.569e-06 -1.029e-07 -6.278e-08 b_tt_shift_business -1.029e-07 2.230e-07 5.355e-08 b_access -6.278e-08 5.355e-08 3.589e-06 b_cost 8.229e-07 -2.039e-07 1.058e-06 b_cost_shift_business -7.020e-07 5.480e-07 -1.401e-07 cost_income_elast -4.914e-06 -5.177e-07 -3.763e-06 b_wifi -9.431e-06 -2.652e-06 -8.953e-06 b_food -4.923e-06 -1.299e-06 -4.879e-06 lambda_fastPT -4.042e-06 -5.796e-07 4.276e-06 lambda_groundPT -1.422e-06 -4.992e-07 -2.056e-05 alpha_rail_fastPT_logistic 8.424e-06 1.761e-05 8.072e-05 b_cost b_cost_shift_business cost_income_elast asc_bus -4.226e-05 8.367e-05 -0.001381 asc_air -2.180e-05 -2.632e-05 9.4455e-04 asc_rail 1.096e-05 2.902e-05 8.5460e-04 asc_bus_shift_female -1.528e-05 1.258e-05 1.1572e-04 asc_air_shift_female -1.786e-05 1.205e-05 2.5714e-04 asc_rail_shift_female -8.248e-06 1.193e-05 1.9379e-04 b_tt_car 5.979e-07 -3.897e-07 5.440e-07 b_tt_bus 1.040e-06 -8.527e-07 5.166e-06 b_tt_air 9.781e-07 -1.560e-07 -5.489e-06 b_tt_rail 8.229e-07 -7.020e-07 -4.914e-06 b_tt_shift_business -2.039e-07 5.480e-07 -5.177e-07 b_access 1.058e-06 -1.401e-07 -3.763e-06 b_cost 4.992e-06 -3.298e-06 -1.718e-05 b_cost_shift_business -3.298e-06 4.202e-06 3.910e-08 cost_income_elast -1.718e-05 3.910e-08 9.7360e-04 b_wifi -4.503e-05 1.492e-05 1.3037e-04 b_food -2.039e-05 5.317e-06 3.530e-05 lambda_fastPT -3.244e-05 2.330e-05 2.1630e-04 lambda_groundPT -4.605e-05 2.312e-05 -2.1551e-04 alpha_rail_fastPT_logistic 8.632e-05 4.791e-05 -1.4086e-04 b_wifi b_food lambda_fastPT asc_bus -4.7826e-04 5.8152e-04 -4.4843e-04 asc_air -0.001038 -6.0367e-04 -0.001338 asc_rail -0.001152 -9.0033e-04 -7.3618e-04 asc_bus_shift_female 8.882e-07 2.3762e-04 1.4581e-04 asc_air_shift_female -4.207e-05 -1.4095e-04 6.028e-05 asc_rail_shift_female -8.594e-05 -9.297e-05 2.0247e-04 b_tt_car -7.087e-06 -3.656e-06 -4.231e-06 b_tt_bus -9.068e-06 -6.568e-06 -6.135e-06 b_tt_air -1.130e-05 -9.770e-06 8.458e-06 b_tt_rail -9.431e-06 -4.923e-06 -4.042e-06 b_tt_shift_business -2.652e-06 -1.299e-06 -5.796e-07 b_access -8.953e-06 -4.879e-06 4.276e-06 b_cost -4.503e-05 -2.039e-05 -3.244e-05 b_cost_shift_business 1.492e-05 5.317e-06 2.330e-05 cost_income_elast 1.3037e-04 3.530e-05 2.1630e-04 b_wifi 0.001894 0.001055 2.4137e-04 b_food 0.001055 0.001667 -5.782e-05 lambda_fastPT 2.4137e-04 -5.782e-05 0.001707 lambda_groundPT 5.4299e-04 2.8692e-04 -8.115e-05 alpha_rail_fastPT_logistic -0.002064 -0.001474 0.004341 lambda_groundPT alpha_rail_fastPT_logistic asc_bus 0.001666 -0.003248 asc_air 0.001166 -0.004418 asc_rail -4.7376e-04 -7.8903e-04 asc_bus_shift_female 3.8628e-04 -3.0748e-04 asc_air_shift_female 5.494e-05 -1.1723e-04 asc_rail_shift_female -1.5078e-04 7.9066e-04 b_tt_car -4.478e-06 4.656e-06 b_tt_bus -1.616e-05 1.530e-05 b_tt_air -1.534e-05 7.104e-05 b_tt_rail -1.422e-06 8.424e-06 b_tt_shift_business -4.992e-07 1.761e-05 b_access -2.056e-05 8.072e-05 b_cost -4.605e-05 8.632e-05 b_cost_shift_business 2.312e-05 4.791e-05 cost_income_elast -2.1551e-04 -1.4086e-04 b_wifi 5.4299e-04 -0.002064 b_food 2.8692e-04 -0.001474 lambda_fastPT -8.115e-05 0.004341 lambda_groundPT 0.002046 -0.004126 alpha_rail_fastPT_logistic -0.004126 0.042692 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus 1.000000 0.279646 0.25224 asc_air 0.279646 1.000000 0.59693 asc_rail 0.252240 0.596931 1.00000 asc_bus_shift_female -0.120489 -0.054585 -0.05850 asc_air_shift_female -0.042780 -0.127017 -0.08559 asc_rail_shift_female -0.058117 -0.088411 -0.12094 b_tt_car 0.324878 0.675411 0.72299 b_tt_bus -0.818503 0.091629 0.13730 b_tt_air -0.027318 -0.590976 -0.01258 b_tt_rail 0.022427 0.008502 -0.63247 b_tt_shift_business 0.017456 0.063530 0.10024 b_access -0.022786 -0.468445 -0.03293 b_cost -0.032656 -0.038602 0.05054 b_cost_shift_business 0.045016 -0.057336 -0.01554 cost_income_elast -0.044156 0.101606 0.03837 b_wifi 0.018868 -0.093620 -0.12755 b_food -0.001992 -0.077238 -0.10499 lambda_fastPT 0.001008 -0.060071 -0.06596 lambda_groundPT 0.024505 -0.003672 -0.07540 alpha_rail_fastPT_logistic -0.016729 -0.012664 0.03447 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.120489 -0.042780 -0.058117 asc_air -0.054585 -0.127017 -0.088411 asc_rail -0.058496 -0.085587 -0.120945 asc_bus_shift_female 1.000000 0.383262 0.475164 asc_air_shift_female 0.383262 1.000000 0.730097 asc_rail_shift_female 0.475164 0.730097 1.000000 b_tt_car -0.018464 -0.019150 -0.010686 b_tt_bus -0.014176 -0.015700 -0.003784 b_tt_air -0.004644 -0.012136 -0.007508 b_tt_rail -0.009044 -0.014716 0.002498 b_tt_shift_business 0.008458 -0.019508 -0.010581 b_access 0.002270 -0.012412 -0.017681 b_cost -0.045644 -0.040235 -0.021477 b_cost_shift_business 0.046838 0.008847 0.006878 cost_income_elast -0.052656 0.007877 0.003513 b_wifi 0.017502 0.030032 0.011343 b_food 0.002425 0.020711 0.001889 lambda_fastPT 0.025999 0.008104 0.011779 lambda_groundPT 0.034947 0.021045 0.004521 alpha_rail_fastPT_logistic -0.004503 -0.016662 -9.0428e-04 b_tt_car b_tt_bus b_tt_air asc_bus 0.32488 -0.818503 -0.027318 asc_air 0.67541 0.091629 -0.590976 asc_rail 0.72299 0.137299 -0.012576 asc_bus_shift_female -0.01846 -0.014176 -0.004644 asc_air_shift_female -0.01915 -0.015700 -0.012136 asc_rail_shift_female -0.01069 -0.003784 -0.007508 b_tt_car 1.00000 0.229757 0.036897 b_tt_bus 0.22976 1.000000 0.061579 b_tt_air 0.03690 0.061579 1.000000 b_tt_rail 0.02714 0.023242 -0.018487 b_tt_shift_business -0.05356 -0.059147 -0.030125 b_access 0.04552 0.024173 0.334502 b_cost 0.38773 0.360322 0.262322 b_cost_shift_business -0.26829 -0.282033 -0.068172 cost_income_elast -0.02570 0.064401 -0.117093 b_wifi -0.25989 -0.216774 -0.130874 b_food -0.13342 -0.094031 -0.079252 lambda_fastPT -0.14877 -0.150079 0.006045 lambda_groundPT -0.20700 -0.248929 -0.138558 alpha_rail_fastPT_logistic 0.09778 0.063571 0.140303 b_tt_rail b_tt_shift_business b_access asc_bus 0.022427 0.017456 -0.022786 asc_air 0.008502 0.063530 -0.468445 asc_rail -0.632469 0.100239 -0.032931 asc_bus_shift_female -0.009044 0.008458 0.002270 asc_air_shift_female -0.014716 -0.019508 -0.012412 asc_rail_shift_female 0.002498 -0.010581 -0.017681 b_tt_car 0.027144 -0.053563 0.045522 b_tt_bus 0.023242 -0.059147 0.024173 b_tt_air -0.018487 -0.030125 0.334502 b_tt_rail 1.000000 -0.115312 -0.067092 b_tt_shift_business -0.115312 1.000000 0.059220 b_access -0.067092 0.059220 1.000000 b_cost 0.252719 -0.171514 0.227856 b_cost_shift_business -0.181496 0.641225 0.008365 cost_income_elast -0.065297 -0.031787 -0.107784 b_wifi -0.148267 -0.096682 -0.151878 b_food -0.068115 -0.061961 -0.076223 lambda_fastPT -0.054684 0.024193 0.016601 lambda_groundPT -0.069524 -0.005035 -0.164145 alpha_rail_fastPT_logistic 0.037807 0.147866 0.180416 b_cost b_cost_shift_business cost_income_elast asc_bus -0.03266 0.045016 -0.044156 asc_air -0.03860 -0.057336 0.101606 asc_rail 0.05054 -0.015535 0.038369 asc_bus_shift_female -0.04564 0.046838 -0.052656 asc_air_shift_female -0.04024 0.008847 0.007877 asc_rail_shift_female -0.02148 0.006878 0.003513 b_tt_car 0.38773 -0.268285 -0.025699 b_tt_bus 0.36032 -0.282033 0.064401 b_tt_air 0.26232 -0.068172 -0.117093 b_tt_rail 0.25272 -0.181496 -0.065297 b_tt_shift_business -0.17151 0.641225 -0.031787 b_access 0.22786 0.008365 -0.107784 b_cost 1.00000 -0.655151 -0.265905 b_cost_shift_business -0.65515 1.000000 0.001458 cost_income_elast -0.26590 0.001458 1.000000 b_wifi -0.49254 0.161625 0.122836 b_food -0.24549 0.055093 0.097142 lambda_fastPT -0.33680 0.294184 0.021916 lambda_groundPT -0.44647 0.239057 -0.113099 alpha_rail_fastPT_logistic 0.24894 0.067067 -0.127498 b_wifi b_food lambda_fastPT asc_bus 0.01887 -0.001992 0.001008 asc_air -0.09362 -0.077238 -0.060071 asc_rail -0.12755 -0.104989 -0.065964 asc_bus_shift_female 0.01750 0.002425 0.025999 asc_air_shift_female 0.03003 0.020711 0.008104 asc_rail_shift_female 0.01134 0.001889 0.011779 b_tt_car -0.25989 -0.133425 -0.148774 b_tt_bus -0.21677 -0.094031 -0.150079 b_tt_air -0.13087 -0.079252 0.006045 b_tt_rail -0.14827 -0.068115 -0.054684 b_tt_shift_business -0.09668 -0.061961 0.024193 b_access -0.15188 -0.076223 0.016601 b_cost -0.49254 -0.245494 -0.336802 b_cost_shift_business 0.16163 0.055093 0.294184 cost_income_elast 0.12284 0.097142 0.021916 b_wifi 1.00000 0.594117 0.135430 b_food 0.59412 1.000000 0.011208 lambda_fastPT 0.13543 0.011208 1.000000 lambda_groundPT 0.31313 0.158002 -0.013926 alpha_rail_fastPT_logistic -0.28624 -0.170489 0.488200 lambda_groundPT alpha_rail_fastPT_logistic asc_bus 0.024505 -0.016729 asc_air -0.003672 -0.012664 asc_rail -0.075405 0.034474 asc_bus_shift_female 0.034947 -0.004503 asc_air_shift_female 0.021045 -0.016662 asc_rail_shift_female 0.004521 -9.0428e-04 b_tt_car -0.206999 0.097775 b_tt_bus -0.248929 0.063571 b_tt_air -0.138558 0.140303 b_tt_rail -0.069524 0.037807 b_tt_shift_business -0.005035 0.147866 b_access -0.164145 0.180416 b_cost -0.446471 0.248940 b_cost_shift_business 0.239057 0.067067 cost_income_elast -0.113099 -0.127498 b_wifi 0.313135 -0.286242 b_food 0.158002 -0.170489 lambda_fastPT -0.013926 0.488200 lambda_groundPT 1.000000 -0.399794 alpha_rail_fastPT_logistic -0.399794 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus 1.00000 0.260200 0.26128 asc_air 0.26020 1.000000 0.61206 asc_rail 0.26128 0.612056 1.00000 asc_bus_shift_female -0.10046 -0.029307 -0.03001 asc_air_shift_female 0.02585 -0.106679 -0.11339 asc_rail_shift_female -0.02766 -0.059196 -0.08434 b_tt_car 0.32061 0.675547 0.71206 b_tt_bus -0.80374 0.117135 0.12823 b_tt_air -0.05744 -0.586462 -0.01833 b_tt_rail 1.3702e-04 -0.004041 -0.61883 b_tt_shift_business 0.05509 0.137673 0.18894 b_access 0.06294 -0.460762 -0.06251 b_cost -0.04496 -0.034205 0.01761 b_cost_shift_business 0.09702 -0.045013 0.05081 cost_income_elast -0.10519 0.106115 0.09828 b_wifi -0.02612 -0.083588 -0.09500 b_food 0.03386 -0.051836 -0.07914 lambda_fastPT -0.02580 -0.113502 -0.06393 lambda_groundPT 0.08755 0.090362 -0.03758 alpha_rail_fastPT_logistic -0.03736 -0.074946 -0.01370 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.100464 0.025848 -0.02766 asc_air -0.029307 -0.106679 -0.05920 asc_rail -0.030012 -0.113386 -0.08434 asc_bus_shift_female 1.000000 0.385661 0.49266 asc_air_shift_female 0.385661 1.000000 0.75394 asc_rail_shift_female 0.492665 0.753944 1.00000 b_tt_car 0.009629 -0.033814 0.02974 b_tt_bus -0.026346 -0.090729 -0.01301 b_tt_air 0.046703 -7.5496e-04 0.03742 b_tt_rail -0.004845 0.043554 0.02110 b_tt_shift_business 0.019803 -0.001959 0.01751 b_access -0.055930 -0.029968 -0.01897 b_cost -0.061321 -0.105329 -0.05431 b_cost_shift_business 0.055012 0.077470 0.08562 cost_income_elast 0.033256 0.108575 0.09137 b_wifi 1.8302e-04 -0.012738 -0.02905 b_food 0.052195 -0.045491 -0.03350 lambda_fastPT 0.031645 0.019222 0.07209 lambda_groundPT 0.076576 0.016002 -0.04904 alpha_rail_fastPT_logistic -0.013344 -0.007475 0.05630 b_tt_car b_tt_bus b_tt_air asc_bus 0.320611 -0.80374 -0.057436 asc_air 0.675547 0.11713 -0.586462 asc_rail 0.712057 0.12823 -0.018330 asc_bus_shift_female 0.009629 -0.02635 0.046703 asc_air_shift_female -0.033814 -0.09073 -7.5496e-04 asc_rail_shift_female 0.029741 -0.01301 0.037416 b_tt_car 1.000000 0.25274 0.049627 b_tt_bus 0.252739 1.00000 0.092503 b_tt_air 0.049627 0.09250 1.000000 b_tt_rail 0.062848 0.07352 0.008536 b_tt_shift_business -6.9569e-04 -0.07264 -0.060724 b_access 0.046432 -0.03930 0.326006 b_cost 0.379291 0.38846 0.223803 b_cost_shift_business -0.269448 -0.34697 -0.038896 cost_income_elast 0.024709 0.13811 -0.089927 b_wifi -0.230821 -0.17382 -0.132765 b_food -0.126922 -0.13420 -0.122350 lambda_fastPT -0.145141 -0.12386 0.104653 lambda_groundPT -0.140299 -0.29796 -0.173416 alpha_rail_fastPT_logistic 0.031938 0.06178 0.175767 b_tt_rail b_tt_shift_business b_access asc_bus 1.3702e-04 0.055086 0.06294 asc_air -0.004041 0.137673 -0.46076 asc_rail -0.618829 0.188944 -0.06251 asc_bus_shift_female -0.004845 0.019803 -0.05593 asc_air_shift_female 0.043554 -0.001959 -0.02997 asc_rail_shift_female 0.021103 0.017505 -0.01897 b_tt_car 0.062848 -6.9569e-04 0.04643 b_tt_bus 0.073516 -0.072642 -0.03930 b_tt_air 0.008536 -0.060724 0.32601 b_tt_rail 1.000000 -0.173991 -0.02646 b_tt_shift_business -0.173991 1.000000 0.05985 b_access -0.026457 0.059854 1.00000 b_cost 0.294072 -0.193275 0.25000 b_cost_shift_business -0.273400 0.566062 -0.03607 cost_income_elast -0.125744 -0.035135 -0.06365 b_wifi -0.173038 -0.129066 -0.10860 b_food -0.096284 -0.067369 -0.06308 lambda_fastPT -0.078095 -0.029704 0.05463 lambda_groundPT -0.025098 -0.023372 -0.23989 alpha_rail_fastPT_logistic 0.032550 0.180460 0.20621 b_cost b_cost_shift_business cost_income_elast asc_bus -0.04496 0.09702 -0.10519 asc_air -0.03420 -0.04501 0.10612 asc_rail 0.01761 0.05081 0.09828 asc_bus_shift_female -0.06132 0.05501 0.03326 asc_air_shift_female -0.10533 0.07747 0.10858 asc_rail_shift_female -0.05431 0.08562 0.09137 b_tt_car 0.37929 -0.26945 0.02471 b_tt_bus 0.38846 -0.34697 0.13811 b_tt_air 0.22380 -0.03890 -0.08993 b_tt_rail 0.29407 -0.27340 -0.12574 b_tt_shift_business -0.19328 0.56606 -0.03514 b_access 0.25000 -0.03607 -0.06365 b_cost 1.00000 -0.72019 -0.24646 b_cost_shift_business -0.72019 1.00000 6.1138e-04 cost_income_elast -0.24646 6.1138e-04 1.00000 b_wifi -0.46314 0.16731 0.09601 b_food -0.22353 0.06354 0.02771 lambda_fastPT -0.35137 0.27510 0.16778 lambda_groundPT -0.45571 0.24935 -0.15269 alpha_rail_fastPT_logistic 0.18698 0.11313 -0.02185 b_wifi b_food lambda_fastPT asc_bus -0.02612 0.03386 -0.02580 asc_air -0.08359 -0.05184 -0.11350 asc_rail -0.09500 -0.07914 -0.06393 asc_bus_shift_female 1.8302e-04 0.05219 0.03164 asc_air_shift_female -0.01274 -0.04549 0.01922 asc_rail_shift_female -0.02905 -0.03350 0.07209 b_tt_car -0.23082 -0.12692 -0.14514 b_tt_bus -0.17382 -0.13420 -0.12386 b_tt_air -0.13276 -0.12235 0.10465 b_tt_rail -0.17304 -0.09628 -0.07809 b_tt_shift_business -0.12907 -0.06737 -0.02970 b_access -0.10860 -0.06308 0.05463 b_cost -0.46314 -0.22353 -0.35137 b_cost_shift_business 0.16731 0.06354 0.27510 cost_income_elast 0.09601 0.02771 0.16778 b_wifi 1.00000 0.59364 0.13424 b_food 0.59364 1.00000 -0.03428 lambda_fastPT 0.13424 -0.03428 1.00000 lambda_groundPT 0.27587 0.15538 -0.04342 alpha_rail_fastPT_logistic -0.22957 -0.17473 0.50849 lambda_groundPT alpha_rail_fastPT_logistic asc_bus 0.08755 -0.037362 asc_air 0.09036 -0.074946 asc_rail -0.03758 -0.013703 asc_bus_shift_female 0.07658 -0.013344 asc_air_shift_female 0.01600 -0.007475 asc_rail_shift_female -0.04904 0.056296 b_tt_car -0.14030 0.031938 b_tt_bus -0.29796 0.061779 b_tt_air -0.17342 0.175767 b_tt_rail -0.02510 0.032550 b_tt_shift_business -0.02337 0.180460 b_access -0.23989 0.206205 b_cost -0.45571 0.186984 b_cost_shift_business 0.24935 0.113126 cost_income_elast -0.15269 -0.021848 b_wifi 0.27587 -0.229567 b_food 0.15538 -0.174734 lambda_fastPT -0.04342 0.508489 lambda_groundPT 1.00000 -0.441516 alpha_rail_fastPT_logistic -0.44152 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2057379 464 0.2468179 181 0.2623604 146 0.2670321 317 0.2733104 276 0.2772069 370 0.2807018 447 0.2859806 367 0.2879343 161 0.2892167 59 0.2933237 434 0.2937555 379 0.2970089 307 0.2971936 293 0.2974689 73 0.2975944 186 0.2994385 259 0.2999605 441 0.3017745 467 0.3053908 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286548 0.299228 0.012680 asc_air -0.903342 -0.646265 0.257077 asc_rail -2.092649 -1.563467 0.529182 asc_bus_shift_female 0.340176 0.273643 -0.066533 asc_air_shift_female 0.268177 0.240311 -0.027866 asc_rail_shift_female 0.189615 0.178834 -0.010782 b_tt_car -0.013107 -0.010391 0.002717 b_tt_bus -0.021266 -0.016555 0.004711 b_tt_air -0.016578 -0.013074 0.003504 b_tt_rail -0.007051 -0.005460 0.001591 b_tt_shift_business -0.006234 -0.006010 2.2370e-04 b_access -0.021153 -0.017830 0.003322 b_cost -0.076190 -0.057587 0.018602 b_cost_shift_business 0.033381 0.023262 -0.010120 cost_income_elast -0.613795 -0.621001 -0.007207 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026713 0.774401 -0.252312 b_food 0.422069 0.337788 -0.084281 lambda_fastPT 1.000000 0.401188 -0.598812 lambda_groundPT 1.000000 0.528466 -0.471534 alpha_rail_fastPT_logistic 0.000000 -0.028385 -0.028385 alpha_rail_groundPT_logistic 0.000000 0.000000 0.000000 Settings and functions used in model definition: apollo_control -------------- Value modelName "CNL_logistic_transform_for_alphas" 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" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical second derivative of LL (using numDeriv) Scaling in estimation --------------------- Value asc_bus 0.299228021 asc_air 0.646265605 asc_rail 1.563465532 asc_bus_shift_female 0.273642964 asc_air_shift_female 0.240311104 asc_rail_shift_female 0.178833568 b_tt_car 0.010390878 b_tt_bus 0.016555115 b_tt_air 0.013074239 b_tt_rail 0.005460226 b_tt_shift_business 0.006009976 b_access 0.017830347 b_cost 0.057587442 b_cost_shift_business 0.023261514 cost_income_elast 0.621001334 b_wifi 0.774400525 b_food 0.337788151 lambda_fastPT 0.401187667 lambda_groundPT 0.528466365 alpha_rail_fastPT_logistic 0.028384806 Scaling used in computing Hessian --------------------------------- Value asc_bus 0.299227963 asc_air 0.646265283 asc_rail 1.563467177 asc_bus_shift_female 0.273642937 asc_air_shift_female 0.240311138 asc_rail_shift_female 0.178833552 b_tt_car 0.010390864 b_tt_bus 0.016555175 b_tt_air 0.013074228 b_tt_rail 0.005460229 b_tt_shift_business 0.006009975 b_access 0.017830336 b_cost 0.057587386 b_cost_shift_business 0.023261505 cost_income_elast 0.621001169 b_wifi 0.774400734 b_food 0.337788144 lambda_fastPT 0.401187681 lambda_groundPT 0.528466139 alpha_rail_fastPT_logistic 0.028384806 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 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) }