Model run using Apollo for R, version 0.2.3 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : Apollo_example_6 Model description : CNL model with socio-demographics on mode choice SP data Model run at : 2021-02-04 16:54:47 Estimation method : bfgs Model diagnosis : successful convergence 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) : -4819.799 LL(0) : -8196.021 LL(final) : -4742.248 Rho-square (0) : 0.4214 Adj.Rho-square (0) : 0.419 AIC : 9524.5 BIC : 9661.57 Estimated parameters : 20 Time taken (hh:mm:ss) : 00:01:0.49 pre-estimation : 00:00:1.21 estimation : 00:00:29.41 post-estimation : 00:00:29.86 Iterations : 29 Min abs eigenvalue of Hessian : 4.44004 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 0.298995 0.445878 0.6706 -1.572 0.420776 0.7106 -1.666 asc_air -0.646329 0.292128 -2.2125 -5.636 0.285273 -2.2657 -5.771 asc_rail -1.563474 0.287746 -5.4335 -8.909 0.278681 -5.6103 -9.199 asc_bus_shift_female 0.273662 0.105281 2.5993 -6.899 0.111530 2.4537 -6.512 asc_air_shift_female 0.240314 0.076639 3.1357 -9.913 0.075901 3.1662 -10.009 asc_rail_shift_female 0.178820 0.067296 2.6572 -12.203 0.067973 2.6308 -12.081 b_tt_car -0.010391 7.1323e-04 -14.5688 -1416.649 7.0558e-04 -14.7266 -1431.995 b_tt_bus -0.016555 0.001241 -13.3366 -818.940 0.001199 -13.8076 -847.860 b_tt_air -0.013074 0.001943 -6.7303 -521.498 0.001956 -6.6839 -517.901 b_tt_rail -0.005460 0.001284 -4.2520 -783.026 0.001253 -4.3591 -802.732 b_tt_shift_business -0.006010 5.1448e-04 -11.6814 -1955.404 4.7225e-04 -12.7260 -2130.267 b_access -0.017830 0.001983 -8.9920 -513.311 0.001895 -9.4112 -537.239 b_cost -0.057587 0.002219 -25.9530 -476.625 0.002234 -25.7753 -473.361 b_cost_shift_business 0.023263 0.002199 10.5782 -444.151 0.002050 11.3480 -476.473 cost_income_elast -0.620989 0.030935 -20.0740 -52.400 0.031203 -19.9013 -51.949 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.774403 0.043848 17.6611 -5.145 0.043517 17.7954 -5.184 b_food 0.337786 0.038454 8.7842 -17.221 0.040824 8.2742 -16.221 lambda_fastPT 0.401203 0.037278 10.7624 -16.063 0.041327 9.7081 -14.489 lambda_groundPT 0.528465 0.043300 12.2047 -10.890 0.045239 11.6816 -10.423 alpha0_rail_fastPT -0.028439 0.214589 -0.1325 -4.793 0.206706 -0.1376 -4.975 alpha0_rail_groundPT 0.000000 NA NA NA NA NA NA Structure for CNL model component : car (alpha) bus (alpha) air (alpha) rail (alpha) lambda fastPT nest 0.000 0.000 1.000 0.4929 0.4012 groundPT nest 0.000 1.000 0.000 0.5071 0.5285 car nest 1.000 0.000 0.000 0.0000 1.0000 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_shift_female asc_bus 0.198807 0.036424 0.032362 -0.005656 asc_air 0.036424 0.085339 0.050177 -0.001679 asc_rail 0.032362 0.050177 0.082798 -0.001772 asc_bus_shift_female -0.005656 -0.001679 -0.001772 0.011084 asc_air_shift_female -0.001462 -0.002844 -0.001887 0.003092 asc_rail_shift_female -0.001744 -0.001738 -0.002342 0.003366 b_tt_car 1.0331e-04 1.4072e-04 1.4838e-04 -1.387e-06 b_tt_bus -4.5302e-04 3.323e-05 4.904e-05 -1.853e-06 b_tt_air -2.366e-05 -3.3537e-04 -7.028e-06 -9.505e-07 b_tt_rail 1.284e-05 3.190e-06 -2.3369e-04 -1.223e-06 b_tt_shift_business 4.004e-06 9.549e-06 1.484e-05 4.582e-07 b_access -2.014e-05 -2.7135e-04 -1.879e-05 4.732e-07 b_cost -3.229e-05 -2.501e-05 3.227e-05 -1.067e-05 b_cost_shift_business 4.412e-05 -3.684e-05 -9.833e-06 1.085e-05 cost_income_elast -6.0906e-04 9.1814e-04 3.4153e-04 -1.7151e-04 b_wifi 3.6865e-04 -0.001199 -0.001609 8.083e-05 b_food -3.425e-05 -8.6772e-04 -0.001162 9.828e-06 lambda_fastPT 1.649e-05 -6.5432e-04 -7.0758e-04 1.0204e-04 lambda_groundPT 4.7261e-04 -4.654e-05 -9.3943e-04 1.5936e-04 alpha0_rail_fastPT -0.001601 -7.9412e-04 0.002129 -1.0186e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.001462 -0.001744 1.0331e-04 -4.5302e-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_shift_female 0.003092 0.003366 -1.387e-06 -1.853e-06 asc_air_shift_female 0.005873 0.003765 -1.047e-06 -1.494e-06 asc_rail_shift_female 0.003765 0.004529 -5.127e-07 -3.158e-07 b_tt_car -1.047e-06 -5.127e-07 5.087e-07 2.034e-07 b_tt_bus -1.494e-06 -3.158e-07 2.034e-07 1.541e-06 b_tt_air -1.807e-06 -9.813e-07 5.113e-08 1.485e-07 b_tt_rail -1.448e-06 2.160e-07 2.486e-08 3.704e-08 b_tt_shift_business -7.692e-07 -3.663e-07 -1.966e-08 -3.777e-08 b_access -1.886e-06 -2.359e-06 6.438e-08 5.949e-08 b_cost -6.843e-06 -3.206e-06 6.136e-07 9.924e-07 b_cost_shift_business 1.491e-06 1.017e-06 -4.208e-07 -7.699e-07 cost_income_elast 1.868e-05 7.311e-06 -5.666e-07 2.474e-06 b_wifi 1.0094e-04 3.345e-05 -8.128e-06 -1.180e-05 b_food 6.104e-05 4.882e-06 -3.659e-06 -4.488e-06 lambda_fastPT 2.316e-05 2.954e-05 -3.955e-06 -6.943e-06 lambda_groundPT 6.985e-05 1.315e-05 -6.393e-06 -1.338e-05 alpha0_rail_fastPT -2.7411e-04 -1.296e-05 1.497e-05 1.694e-05 b_tt_air b_tt_rail b_tt_shift_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 -2.7135e-04 asc_rail -7.028e-06 -2.3369e-04 1.484e-05 -1.879e-05 asc_bus_shift_female -9.505e-07 -1.223e-06 4.582e-07 4.732e-07 asc_air_shift_female -1.807e-06 -1.448e-06 -7.692e-07 -1.886e-06 asc_rail_shift_female -9.813e-07 2.160e-07 -3.663e-07 -2.359e-06 b_tt_car 5.113e-08 2.486e-08 -1.966e-08 6.438e-08 b_tt_bus 1.485e-07 3.704e-08 -3.777e-08 5.949e-08 b_tt_air 3.774e-06 -4.612e-08 -3.011e-08 1.289e-06 b_tt_rail -4.612e-08 1.649e-06 -7.618e-08 -1.708e-07 b_tt_shift_business -3.011e-08 -7.618e-08 2.647e-07 6.042e-08 b_access 1.289e-06 -1.708e-07 6.042e-08 3.932e-06 b_cost 1.131e-06 7.200e-07 -1.958e-07 1.002e-06 b_cost_shift_business -2.912e-07 -5.125e-07 7.255e-07 3.653e-08 cost_income_elast -7.036e-06 -2.593e-06 -5.058e-07 -6.610e-06 b_wifi -1.115e-05 -8.347e-06 -2.181e-06 -1.321e-05 b_food -5.920e-06 -3.363e-06 -1.226e-06 -5.812e-06 lambda_fastPT 4.399e-07 -2.617e-06 4.641e-07 1.230e-06 lambda_groundPT -1.166e-05 -3.866e-06 -1.123e-07 -1.409e-05 alpha0_rail_fastPT 5.851e-05 1.042e-05 1.632e-05 7.678e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -3.229e-05 4.412e-05 -6.0906e-04 3.6865e-04 asc_air -2.501e-05 -3.684e-05 9.1814e-04 -0.001199 asc_rail 3.227e-05 -9.833e-06 3.4153e-04 -0.001609 asc_bus_shift_female -1.067e-05 1.085e-05 -1.7151e-04 8.083e-05 asc_air_shift_female -6.843e-06 1.491e-06 1.868e-05 1.0094e-04 asc_rail_shift_female -3.206e-06 1.017e-06 7.311e-06 3.345e-05 b_tt_car 6.136e-07 -4.208e-07 -5.666e-07 -8.128e-06 b_tt_bus 9.924e-07 -7.699e-07 2.474e-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 -2.593e-06 -8.347e-06 b_tt_shift_business -1.958e-07 7.255e-07 -5.058e-07 -2.181e-06 b_access 1.002e-06 3.653e-08 -6.610e-06 -1.321e-05 b_cost 4.924e-06 -3.197e-06 -1.825e-05 -4.792e-05 b_cost_shift_business -3.197e-06 4.836e-06 9.890e-08 1.559e-05 cost_income_elast -1.825e-05 9.890e-08 9.5698e-04 1.6658e-04 b_wifi -4.792e-05 1.559e-05 1.6658e-04 0.001923 b_food -2.095e-05 4.659e-06 1.1553e-04 0.001002 lambda_fastPT -2.786e-05 2.412e-05 2.529e-05 2.2132e-04 lambda_groundPT -4.290e-05 2.276e-05 -1.5153e-04 5.9458e-04 alpha0_rail_fastPT 1.1854e-04 3.165e-05 -8.4589e-04 -0.002694 b_food lambda_fastPT lambda_groundPT alpha0_rail_fastPT asc_bus -3.425e-05 1.649e-05 4.7261e-04 -0.001601 asc_air -8.6772e-04 -6.5432e-04 -4.654e-05 -7.9412e-04 asc_rail -0.001162 -7.0758e-04 -9.3943e-04 0.002129 asc_bus_shift_female 9.828e-06 1.0204e-04 1.5936e-04 -1.0186e-04 asc_air_shift_female 6.104e-05 2.316e-05 6.985e-05 -2.7411e-04 asc_rail_shift_female 4.882e-06 2.954e-05 1.315e-05 -1.296e-05 b_tt_car -3.659e-06 -3.955e-06 -6.393e-06 1.497e-05 b_tt_bus -4.488e-06 -6.943e-06 -1.338e-05 1.694e-05 b_tt_air -5.920e-06 4.399e-07 -1.166e-05 5.851e-05 b_tt_rail -3.363e-06 -2.617e-06 -3.866e-06 1.042e-05 b_tt_shift_business -1.226e-06 4.641e-07 -1.123e-07 1.632e-05 b_access -5.812e-06 1.230e-06 -1.409e-05 7.678e-05 b_cost -2.095e-05 -2.786e-05 -4.290e-05 1.1854e-04 b_cost_shift_business 4.659e-06 2.412e-05 2.276e-05 3.165e-05 cost_income_elast 1.1553e-04 2.529e-05 -1.5153e-04 -8.4589e-04 b_wifi 0.001002 2.2132e-04 5.9458e-04 -0.002694 b_food 0.001479 1.603e-05 2.6311e-04 -0.001407 lambda_fastPT 1.603e-05 0.001390 -2.270e-05 0.003906 lambda_groundPT 2.6311e-04 -2.270e-05 0.001875 -0.003716 alpha0_rail_fastPT -0.001407 0.003906 -0.003716 0.046048 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.177053 0.031229 0.030637 -0.004716 asc_air 0.031229 0.081380 0.048658 -9.3223e-04 asc_rail 0.030637 0.048658 0.077663 -9.3269e-04 asc_bus_shift_female -0.004716 -9.3223e-04 -9.3269e-04 0.012439 asc_air_shift_female 8.2546e-04 -0.002310 -0.002398 0.003264 asc_rail_shift_female -7.9109e-04 -0.001148 -0.001598 0.003735 b_tt_car 9.518e-05 1.3598e-04 1.4001e-04 7.578e-07 b_tt_bus -4.0549e-04 4.007e-05 4.284e-05 -3.521e-06 b_tt_air -4.726e-05 -3.2726e-04 -9.991e-06 1.019e-05 b_tt_rail 6.683e-08 -1.444e-06 -2.1601e-04 -6.762e-07 b_tt_shift_business 1.095e-05 1.855e-05 2.487e-05 1.043e-06 b_access 5.019e-05 -2.4903e-04 -3.301e-05 -1.182e-05 b_cost -4.223e-05 -2.179e-05 1.096e-05 -1.528e-05 b_cost_shift_business 8.366e-05 -2.634e-05 2.902e-05 1.258e-05 cost_income_elast -0.001381 9.4447e-04 8.5458e-04 1.1575e-04 b_wifi -4.7874e-04 -0.001038 -0.001152 8.729e-07 b_food 5.8146e-04 -6.0367e-04 -9.0045e-04 2.3762e-04 lambda_fastPT -4.4902e-04 -0.001339 -7.3642e-04 1.4577e-04 lambda_groundPT 0.001666 0.001166 -4.7360e-04 3.8639e-04 alpha0_rail_fastPT -0.003251 -0.004422 -7.8965e-04 -3.0795e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 8.2546e-04 -7.9109e-04 9.518e-05 -4.0549e-04 asc_air -0.002310 -0.001148 1.3598e-04 4.007e-05 asc_rail -0.002398 -0.001598 1.4001e-04 4.284e-05 asc_bus_shift_female 0.003264 0.003735 7.578e-07 -3.521e-06 asc_air_shift_female 0.005761 0.003890 -1.811e-06 -8.256e-06 asc_rail_shift_female 0.003890 0.004620 1.427e-06 -1.060e-06 b_tt_car -1.811e-06 1.427e-06 4.978e-07 2.138e-07 b_tt_bus -8.256e-06 -1.060e-06 2.138e-07 1.438e-06 b_tt_air -1.132e-07 4.975e-06 6.851e-08 2.169e-07 b_tt_rail 4.141e-06 1.796e-06 5.554e-08 1.104e-07 b_tt_shift_business -7.016e-08 5.622e-07 -2.338e-10 -4.113e-08 b_access -4.309e-06 -2.443e-06 6.206e-08 -8.929e-08 b_cost -1.786e-05 -8.247e-06 5.979e-07 1.041e-06 b_cost_shift_business 1.205e-05 1.193e-05 -3.897e-07 -8.527e-07 cost_income_elast 2.5712e-04 1.9378e-04 5.447e-07 5.169e-06 b_wifi -4.213e-05 -8.594e-05 -7.088e-06 -9.069e-06 b_food -1.4101e-04 -9.295e-05 -3.656e-06 -6.568e-06 lambda_fastPT 6.029e-05 2.0253e-04 -4.232e-06 -6.134e-06 lambda_groundPT 5.491e-05 -1.5085e-04 -4.478e-06 -1.616e-05 alpha0_rail_fastPT -1.1725e-04 7.9134e-04 4.661e-06 1.532e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -4.726e-05 6.683e-08 1.095e-05 5.019e-05 asc_air -3.2726e-04 -1.444e-06 1.855e-05 -2.4903e-04 asc_rail -9.991e-06 -2.1601e-04 2.487e-05 -3.301e-05 asc_bus_shift_female 1.019e-05 -6.762e-07 1.043e-06 -1.182e-05 asc_air_shift_female -1.132e-07 4.141e-06 -7.016e-08 -4.309e-06 asc_rail_shift_female 4.975e-06 1.796e-06 5.622e-07 -2.443e-06 b_tt_car 6.851e-08 5.554e-08 -2.338e-10 6.206e-08 b_tt_bus 2.169e-07 1.104e-07 -4.113e-08 -8.929e-08 b_tt_air 3.826e-06 2.091e-08 -5.609e-08 1.208e-06 b_tt_rail 2.091e-08 1.569e-06 -1.029e-07 -6.276e-08 b_tt_shift_business -5.609e-08 -1.029e-07 2.230e-07 5.356e-08 b_access 1.208e-06 -6.276e-08 5.356e-08 3.589e-06 b_cost 9.782e-07 8.229e-07 -2.039e-07 1.058e-06 b_cost_shift_business -1.559e-07 -7.020e-07 5.480e-07 -1.400e-07 cost_income_elast -5.487e-06 -4.913e-06 -5.175e-07 -3.761e-06 b_wifi -1.130e-05 -9.431e-06 -2.653e-06 -8.955e-06 b_food -9.772e-06 -4.923e-06 -1.299e-06 -4.880e-06 lambda_fastPT 8.465e-06 -4.041e-06 -5.792e-07 4.283e-06 lambda_groundPT -1.535e-05 -1.423e-06 -4.995e-07 -2.056e-05 alpha0_rail_fastPT 7.111e-05 8.426e-06 1.761e-05 8.079e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -4.223e-05 8.366e-05 -0.001381 -4.7874e-04 asc_air -2.179e-05 -2.634e-05 9.4447e-04 -0.001038 asc_rail 1.096e-05 2.902e-05 8.5458e-04 -0.001152 asc_bus_shift_female -1.528e-05 1.258e-05 1.1575e-04 8.729e-07 asc_air_shift_female -1.786e-05 1.205e-05 2.5712e-04 -4.213e-05 asc_rail_shift_female -8.247e-06 1.193e-05 1.9378e-04 -8.594e-05 b_tt_car 5.979e-07 -3.897e-07 5.447e-07 -7.088e-06 b_tt_bus 1.041e-06 -8.527e-07 5.169e-06 -9.069e-06 b_tt_air 9.782e-07 -1.559e-07 -5.487e-06 -1.130e-05 b_tt_rail 8.229e-07 -7.020e-07 -4.913e-06 -9.431e-06 b_tt_shift_business -2.039e-07 5.480e-07 -5.175e-07 -2.653e-06 b_access 1.058e-06 -1.400e-07 -3.761e-06 -8.955e-06 b_cost 4.992e-06 -3.299e-06 -1.718e-05 -4.503e-05 b_cost_shift_business -3.299e-06 4.202e-06 3.758e-08 1.493e-05 cost_income_elast -1.718e-05 3.758e-08 9.7366e-04 1.3028e-04 b_wifi -4.503e-05 1.493e-05 1.3028e-04 0.001894 b_food -2.039e-05 5.317e-06 3.525e-05 0.001055 lambda_fastPT -3.244e-05 2.331e-05 2.1638e-04 2.4130e-04 lambda_groundPT -4.606e-05 2.312e-05 -2.1564e-04 5.4323e-04 alpha0_rail_fastPT 8.637e-05 4.793e-05 -1.3997e-04 -0.002066 b_food lambda_fastPT lambda_groundPT alpha0_rail_fastPT asc_bus 5.8146e-04 -4.4902e-04 0.001666 -0.003251 asc_air -6.0367e-04 -0.001339 0.001166 -0.004422 asc_rail -9.0045e-04 -7.3642e-04 -4.7360e-04 -7.8965e-04 asc_bus_shift_female 2.3762e-04 1.4577e-04 3.8639e-04 -3.0795e-04 asc_air_shift_female -1.4101e-04 6.029e-05 5.491e-05 -1.1725e-04 asc_rail_shift_female -9.295e-05 2.0253e-04 -1.5085e-04 7.9134e-04 b_tt_car -3.656e-06 -4.232e-06 -4.478e-06 4.661e-06 b_tt_bus -6.568e-06 -6.134e-06 -1.616e-05 1.532e-05 b_tt_air -9.772e-06 8.465e-06 -1.535e-05 7.111e-05 b_tt_rail -4.923e-06 -4.041e-06 -1.423e-06 8.426e-06 b_tt_shift_business -1.299e-06 -5.792e-07 -4.995e-07 1.761e-05 b_access -4.880e-06 4.283e-06 -2.056e-05 8.079e-05 b_cost -2.039e-05 -3.244e-05 -4.606e-05 8.637e-05 b_cost_shift_business 5.317e-06 2.331e-05 2.312e-05 4.793e-05 cost_income_elast 3.525e-05 2.1638e-04 -2.1564e-04 -1.3997e-04 b_wifi 0.001055 2.4130e-04 5.4323e-04 -0.002066 b_food 0.001667 -5.792e-05 2.8707e-04 -0.001475 lambda_fastPT -5.792e-05 0.001708 -8.165e-05 0.004345 lambda_groundPT 2.8707e-04 -8.165e-05 0.002047 -0.004131 alpha0_rail_fastPT -0.001475 0.004345 -0.004131 0.042727 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.279638 0.25224 -0.120493 asc_air 0.279638 1.000000 0.59693 -0.054584 asc_rail 0.252236 0.596930 1.00000 -0.058495 asc_bus_shift_female -0.120493 -0.054584 -0.05849 1.000000 asc_air_shift_female -0.042779 -0.127018 -0.08559 0.383252 asc_rail_shift_female -0.058115 -0.088411 -0.12094 0.475150 b_tt_car 0.324877 0.675412 0.72299 -0.018468 b_tt_bus -0.818504 0.091632 0.13729 -0.014178 b_tt_air -0.027313 -0.590972 -0.01257 -0.004648 b_tt_rail 0.022428 0.008503 -0.63247 -0.009046 b_tt_shift_business 0.017455 0.063533 0.10024 0.008459 b_access -0.022782 -0.468447 -0.03293 0.002267 b_cost -0.032637 -0.038583 0.05054 -0.045654 b_cost_shift_business 0.045000 -0.057350 -0.01554 0.046844 cost_income_elast -0.044157 0.101598 0.03837 -0.052662 b_wifi 0.018856 -0.093631 -0.12756 0.017509 b_food -0.001997 -0.077245 -0.10499 0.002428 lambda_fastPT 9.9215e-04 -0.060084 -0.06596 0.025998 lambda_groundPT 0.024479 -0.003680 -0.07540 0.034958 alpha0_rail_fastPT -0.016736 -0.012668 0.03448 -0.004509 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.042779 -0.058115 0.32488 -0.818504 asc_air -0.127018 -0.088411 0.67541 0.091632 asc_rail -0.085587 -0.120942 0.72299 0.137293 asc_bus_shift_female 0.383252 0.475150 -0.01847 -0.014178 asc_air_shift_female 1.000000 0.730094 -0.01915 -0.015701 asc_rail_shift_female 0.730094 1.000000 -0.01068 -0.003781 b_tt_car -0.019152 -0.010682 1.00000 0.229752 b_tt_bus -0.015701 -0.003781 0.22975 1.000000 b_tt_air -0.012137 -0.007506 0.03690 0.061579 b_tt_rail -0.014715 0.002499 0.02714 0.023240 b_tt_shift_business -0.019510 -0.010580 -0.05357 -0.059149 b_access -0.012414 -0.017678 0.04552 0.024169 b_cost -0.040239 -0.021469 0.38774 0.360313 b_cost_shift_business 0.008848 0.006874 -0.26829 -0.282027 cost_income_elast 0.007878 0.003512 -0.02568 0.064421 b_wifi 0.030036 0.011337 -0.25990 -0.216771 b_food 0.020713 0.001886 -0.13343 -0.094029 lambda_fastPT 0.008105 0.011776 -0.14876 -0.150052 lambda_groundPT 0.021048 0.004514 -0.20700 -0.248913 alpha0_rail_fastPT -0.016668 -8.9750e-04 0.09779 0.063590 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.027313 0.022428 0.017455 -0.022782 asc_air -0.590972 0.008503 0.063533 -0.468447 asc_rail -0.012573 -0.632475 0.100240 -0.032935 asc_bus_shift_female -0.004648 -0.009046 0.008459 0.002267 asc_air_shift_female -0.012137 -0.014715 -0.019510 -0.012414 asc_rail_shift_female -0.007506 0.002499 -0.010580 -0.017678 b_tt_car 0.036904 0.027141 -0.053566 0.045520 b_tt_bus 0.061579 0.023240 -0.059149 0.024169 b_tt_air 1.000000 -0.018490 -0.030124 0.334516 b_tt_rail -0.018490 1.000000 -0.115317 -0.067092 b_tt_shift_business -0.030124 -0.115317 1.000000 0.059223 b_access 0.334516 -0.067092 0.059223 1.000000 b_cost 0.262327 0.252711 -0.171523 0.227850 b_cost_shift_business -0.068167 -0.181494 0.641217 0.008377 cost_income_elast -0.117078 -0.065280 -0.031779 -0.107766 b_wifi -0.130888 -0.148255 -0.096685 -0.151883 b_food -0.079256 -0.068110 -0.061961 -0.076230 lambda_fastPT 0.006075 -0.054669 0.024198 0.016634 lambda_groundPT -0.138582 -0.069525 -0.005039 -0.164157 alpha0_rail_fastPT 0.140345 0.037802 0.147848 0.180449 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.03264 0.045000 -0.044157 0.01886 asc_air -0.03858 -0.057350 0.101598 -0.09363 asc_rail 0.05054 -0.015539 0.038368 -0.12756 asc_bus_shift_female -0.04565 0.046844 -0.052662 0.01751 asc_air_shift_female -0.04024 0.008848 0.007878 0.03004 asc_rail_shift_female -0.02147 0.006874 0.003512 0.01134 b_tt_car 0.38774 -0.268293 -0.025681 -0.25990 b_tt_bus 0.36031 -0.282027 0.064421 -0.21677 b_tt_air 0.26233 -0.068167 -0.117078 -0.13089 b_tt_rail 0.25271 -0.181494 -0.065280 -0.14826 b_tt_shift_business -0.17152 0.641217 -0.031779 -0.09668 b_access 0.22785 0.008377 -0.107766 -0.15188 b_cost 1.00000 -0.655163 -0.265859 -0.49255 b_cost_shift_business -0.65516 1.000000 0.001454 0.16163 cost_income_elast -0.26586 0.001454 1.000000 0.12281 b_wifi -0.49255 0.161626 0.122805 1.00000 b_food -0.24550 0.055091 0.097123 0.59412 lambda_fastPT -0.33676 0.294188 0.021932 0.13540 lambda_groundPT -0.44647 0.239034 -0.113126 0.31317 alpha0_rail_fastPT 0.24895 0.067064 -0.127425 -0.28627 b_food lambda_fastPT lambda_groundPT alpha0_rail_fastPT asc_bus -0.001997 9.9215e-04 0.024479 -0.016736 asc_air -0.077245 -0.060084 -0.003680 -0.012668 asc_rail -0.104992 -0.065965 -0.075399 0.034475 asc_bus_shift_female 0.002428 0.025998 0.034958 -0.004509 asc_air_shift_female 0.020713 0.008105 0.021048 -0.016668 asc_rail_shift_female 0.001886 0.011776 0.004514 -8.9750e-04 b_tt_car -0.133430 -0.148760 -0.207004 0.097786 b_tt_bus -0.094029 -0.150052 -0.248913 0.063590 b_tt_air -0.079256 0.006075 -0.138582 0.140345 b_tt_rail -0.068110 -0.054669 -0.069525 0.037802 b_tt_shift_business -0.061961 0.024198 -0.005039 0.147848 b_access -0.076230 0.016634 -0.164157 0.180449 b_cost -0.245495 -0.336764 -0.446473 0.248947 b_cost_shift_business 0.055091 0.294188 0.239034 0.067064 cost_income_elast 0.097123 0.021932 -0.113126 -0.127425 b_wifi 0.594119 0.135397 0.313166 -0.286274 b_food 1.000000 0.011182 0.158023 -0.170516 lambda_fastPT 0.011182 1.000000 -0.014064 0.488300 lambda_groundPT 0.158023 -0.014064 1.000000 -0.399948 alpha0_rail_fastPT -0.170516 0.488300 -0.399948 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.00000 0.260167 0.26127 -0.100483 asc_air 0.26017 1.000000 0.61206 -0.029300 asc_rail 0.26127 0.612056 1.00000 -0.030008 asc_bus_shift_female -0.10048 -0.029300 -0.03001 1.000000 asc_air_shift_female 0.02585 -0.106673 -0.11338 0.385632 asc_rail_shift_female -0.02766 -0.059194 -0.08433 0.492631 b_tt_car 0.32059 0.675547 0.71205 0.009629 b_tt_bus -0.80376 0.117143 0.12821 -0.026332 b_tt_air -0.05742 -0.586459 -0.01833 0.046700 b_tt_rail 1.2680e-04 -0.004042 -0.61884 -0.004840 b_tt_shift_business 0.05508 0.137674 0.18894 0.019802 b_access 0.06295 -0.460773 -0.06252 -0.055940 b_cost -0.04493 -0.034184 0.01760 -0.061319 b_cost_shift_business 0.09700 -0.045046 0.05080 0.055007 cost_income_elast -0.10522 0.106102 0.09828 0.033260 b_wifi -0.02615 -0.083591 -0.09501 1.7984e-04 b_food 0.03385 -0.051835 -0.07915 0.052188 lambda_fastPT -0.02582 -0.113536 -0.06394 0.031625 lambda_groundPT 0.08751 0.090368 -0.03757 0.076581 alpha0_rail_fastPT -0.03738 -0.074984 -0.01371 -0.013358 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.025846 -0.02766 0.320591 -0.80376 asc_air -0.106673 -0.05919 0.675547 0.11714 asc_rail -0.113382 -0.08433 0.712051 0.12821 asc_bus_shift_female 0.385632 0.49263 0.009629 -0.02633 asc_air_shift_female 1.000000 0.75394 -0.033809 -0.09072 asc_rail_shift_female 0.753941 1.00000 0.029744 -0.01300 b_tt_car -0.033809 0.02974 1.000000 0.25273 b_tt_bus -0.090720 -0.01300 0.252727 1.00000 b_tt_air -7.6229e-04 0.03741 0.049636 0.09250 b_tt_rail 0.043559 0.02110 0.062847 0.07352 b_tt_shift_business -0.001957 0.01751 -7.0152e-04 -0.07265 b_access -0.029967 -0.01897 0.046427 -0.03931 b_cost -0.105322 -0.05430 0.379298 0.38844 b_cost_shift_business 0.077466 0.08561 -0.269460 -0.34695 cost_income_elast 0.108565 0.09136 0.024740 0.13817 b_wifi -0.012754 -0.02905 -0.230835 -0.17381 b_food -0.045507 -0.03350 -0.126928 -0.13420 lambda_fastPT 0.019221 0.07210 -0.145121 -0.12380 lambda_groundPT 0.015992 -0.04906 -0.140301 -0.29792 alpha0_rail_fastPT -0.007473 0.05632 0.031955 0.06182 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.057423 1.2680e-04 0.055085 0.06295 asc_air -0.586459 -0.004042 0.137674 -0.46077 asc_rail -0.018328 -0.618835 0.188945 -0.06252 asc_bus_shift_female 0.046700 -0.004840 0.019802 -0.05594 asc_air_shift_female -7.6229e-04 0.043559 -0.001957 -0.02997 asc_rail_shift_female 0.037415 0.021099 0.017515 -0.01897 b_tt_car 0.049636 0.062847 -7.0152e-04 0.04643 b_tt_bus 0.092498 0.073524 -0.072647 -0.03931 b_tt_air 1.000000 0.008536 -0.060722 0.32603 b_tt_rail 0.008536 1.000000 -0.174002 -0.02645 b_tt_shift_business -0.060722 -0.174002 1.000000 0.05986 b_access 0.326034 -0.026447 0.059862 1.00000 b_cost 0.223815 0.294065 -0.193287 0.25000 b_cost_shift_business -0.038876 -0.273401 0.566047 -0.03604 cost_income_elast -0.089897 -0.125706 -0.035121 -0.06361 b_wifi -0.132794 -0.173019 -0.129080 -0.10862 b_food -0.122365 -0.096273 -0.067372 -0.06310 lambda_fastPT 0.104709 -0.078067 -0.029679 0.05470 lambda_groundPT -0.173474 -0.025110 -0.023381 -0.23993 alpha0_rail_fastPT 0.175864 0.032542 0.180413 0.20629 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.04493 0.09700 -0.10522 -0.02615 asc_air -0.03418 -0.04505 0.10610 -0.08359 asc_rail 0.01760 0.05080 0.09828 -0.09501 asc_bus_shift_female -0.06132 0.05501 0.03326 1.7984e-04 asc_air_shift_female -0.10532 0.07747 0.10856 -0.01275 asc_rail_shift_female -0.05430 0.08561 0.09136 -0.02905 b_tt_car 0.37930 -0.26946 0.02474 -0.23083 b_tt_bus 0.38844 -0.34695 0.13817 -0.17381 b_tt_air 0.22382 -0.03888 -0.08990 -0.13279 b_tt_rail 0.29407 -0.27340 -0.12571 -0.17302 b_tt_shift_business -0.19329 0.56605 -0.03512 -0.12908 b_access 0.25000 -0.03604 -0.06361 -0.10862 b_cost 1.00000 -0.72020 -0.24636 -0.46316 b_cost_shift_business -0.72020 1.00000 5.8758e-04 0.16731 cost_income_elast -0.24636 5.8758e-04 1.00000 0.09595 b_wifi -0.46316 0.16731 0.09595 1.00000 b_food -0.22354 0.06353 0.02767 0.59365 lambda_fastPT -0.35129 0.27511 0.16779 0.13417 lambda_groundPT -0.45571 0.24930 -0.15276 0.27594 alpha0_rail_fastPT 0.18701 0.11311 -0.02170 -0.22964 b_food lambda_fastPT lambda_groundPT alpha0_rail_fastPT asc_bus 0.03385 -0.02582 0.08751 -0.037378 asc_air -0.05184 -0.11354 0.09037 -0.074984 asc_rail -0.07915 -0.06394 -0.03757 -0.013708 asc_bus_shift_female 0.05219 0.03162 0.07658 -0.013358 asc_air_shift_female -0.04551 0.01922 0.01599 -0.007473 asc_rail_shift_female -0.03350 0.07210 -0.04906 0.056322 b_tt_car -0.12693 -0.14512 -0.14030 0.031955 b_tt_bus -0.13420 -0.12380 -0.29792 0.061825 b_tt_air -0.12236 0.10471 -0.17347 0.175864 b_tt_rail -0.09627 -0.07807 -0.02511 0.032542 b_tt_shift_business -0.06737 -0.02968 -0.02338 0.180413 b_access -0.06310 0.05470 -0.23993 0.206291 b_cost -0.22354 -0.35129 -0.45571 0.187013 b_cost_shift_business 0.06353 0.27511 0.24930 0.113108 cost_income_elast 0.02767 0.16779 -0.15276 -0.021700 b_wifi 0.59365 0.13417 0.27594 -0.229636 b_food 1.00000 -0.03433 0.15544 -0.174800 lambda_fastPT -0.03433 1.00000 -0.04367 0.508676 lambda_groundPT 0.15544 -0.04367 1.00000 -0.441785 alpha0_rail_fastPT -0.17480 0.50868 -0.44179 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2057379 464 0.2468096 181 0.2623671 146 0.2670278 317 0.2733033 276 0.2771946 370 0.2806995 447 0.2859780 367 0.2879382 161 0.2892123 59 0.2933163 434 0.2937621 379 0.2970010 307 0.2971992 293 0.2974658 73 0.2975863 186 0.2994303 259 0.2999600 441 0.3017761 467 0.3053909 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286717 0.298995 0.012278 asc_air -0.903270 -0.646329 0.256941 asc_rail -2.092578 -1.563474 0.529105 asc_bus_shift_female 0.340222 0.273662 -0.066559 asc_air_shift_female 0.268170 0.240314 -0.027857 asc_rail_shift_female 0.189612 0.178820 -0.010792 b_tt_car -0.013107 -0.010391 0.002716 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 2.2422e-04 b_access -0.021152 -0.017830 0.003322 b_cost -0.076187 -0.057587 0.018599 b_cost_shift_business 0.033379 0.023263 -0.010116 cost_income_elast -0.613842 -0.620989 -0.007147 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026703 0.774403 -0.252300 b_food 0.422063 0.337786 -0.084277 lambda_fastPT 0.950000 0.401203 -0.548797 lambda_groundPT 0.950000 0.528465 -0.421535 alpha0_rail_fastPT 0.000000 -0.028439 -0.028439 alpha0_rail_groundPT 0.000000 0.000000 0.000000 Settings and functions used in model definition: apollo_control -------------- Value modelName "Apollo_example_6" modelDescr "CNL model with socio-demographics on mode choice SP data" indivID "ID" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" panelData "TRUE" analyticGrad "TRUE" Hessian routines attempted -------------- numerical second derivative of LL (using numDeriv) Scaling used in computing Hessian -------------- Value asc_bus 0.298994534 asc_air 0.646329250 asc_rail 1.563473637 asc_bus_shift_female 0.273662175 asc_air_shift_female 0.240313642 asc_rail_shift_female 0.178820352 b_tt_car 0.010390864 b_tt_bus 0.016554824 b_tt_air 0.013074453 b_tt_rail 0.005459918 b_tt_shift_business 0.006009800 b_access 0.017829980 b_cost 0.057587435 b_cost_shift_business 0.023262585 cost_income_elast 0.620988593 b_wifi 0.774403247 b_food 0.337785913 lambda_fastPT 0.401203193 lambda_groundPT 0.528465197 alpha0_rail_fastPT 0.028438738 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(fastPT=lambda_fastPT, groundPT=lambda_groundPT, car=1) ### Specify nest allocation parameters for alternatives included in multiple nests alpha_rail_fastPT = exp(alpha0_rail_fastPT)/(exp(alpha0_rail_fastPT) + exp(alpha0_rail_groundPT)) 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( 0, 0, 1, alpha_rail_fastPT ) # fastPT cnlStructure[2,] = c( 0, 1, 0, alpha_rail_groundPT) # groundPT cnlStructure[3,] = c( 1, 0, 0, 0 ) # car ### 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, V = 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)