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 : DFT_mode_choice Model description : DFT model on mode choice SP data Model run at : 2025-03-10 17:07:50.146436 Estimation method : bgw Model diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -0.01032 reciprocal of condition number : 2.02054e-12 Number of individuals : 500 Number of rows in database : 7000 Number of modelled outcomes : 7000 Number of cores used : 4 Model without mixing LL(start) : -7425.98 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : NA LL(final) : -4806.56 Rho-squared vs equal shares : 0.4135 Adj.Rho-squared vs equal shares : 0.4111 Rho-squared vs observed shares : Not applicable Adj.Rho-squared vs observed shares : Not applicable AIC : 9653.12 BIC : 9790.2 Estimated parameters : 20 Time taken (hh:mm:ss) : 00:03:54.14 pre-estimation : 00:00:6.74 estimation : 00:00:45.36 post-estimation : 00:03:2.05 Iterations : 20 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_car 0.000000 NA NA NA NA asc_bus 23.233659 8.953292 2.5950 10.723473 2.1666 asc_air 4.419460 5.758851 0.7674 8.053251 0.5488 asc_rail -16.586294 4.868139 -3.4071 5.521474 -3.0040 asc_bus_interaction_female 10.033688 5.291159 1.8963 6.567118 1.5279 asc_air_interaction_female 3.113534 2.534524 1.2284 2.589644 1.2023 asc_rail_interaction_female 2.139253 2.029404 1.0541 2.085884 1.0256 b_tt_car -0.001629 4.0971e-04 -3.9760 5.1781e-04 -3.1459 b_tt_bus -0.002931 7.2972e-04 -4.0167 9.1564e-04 -3.2011 b_tt_air -0.003187 7.3494e-04 -4.3363 7.9430e-04 -4.0122 b_tt_rail -0.001690 4.0503e-04 -4.1724 4.3576e-04 -3.8781 b_tt_interaction_business -0.001112 2.6282e-04 -4.2304 2.8500e-04 -3.9012 b_acc -0.003521 8.7791e-04 -4.0102 0.001041 -3.3814 b_cost -0.011896 0.002907 -4.0924 0.003634 -3.2732 b_cost_interaction_business 0.005336 0.001436 3.7170 0.001778 3.0013 cost_income_elast -0.667378 0.034510 -19.3388 0.037451 -17.8202 b_no_frills 0.000000 NA NA NA NA b_wifi 0.155046 0.036742 4.2198 0.045341 3.4195 b_food 0.063143 0.016887 3.7391 0.020490 3.0817 p_error_sd 1.000000 NA NA NA NA p_timesteps 5.895860 0.454480 12.9727 0.568066 10.3788 p_phi1 1.202562 0.572243 2.1015 0.720883 1.6682 p_phi2 -5.289266 0.414569 -12.7585 0.434064 -12.1854 Overview of choices for DFT 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 80.161433 22.096974 -9.901690 17.361423 asc_air 22.096974 33.164364 10.565710 16.006979 asc_rail -9.901690 10.565710 23.698772 1.607726 asc_bus_interaction_female 17.361423 16.006979 1.607726 27.996367 asc_air_interaction_female 4.897205 -1.067632 -3.501208 -1.369799 asc_rail_interaction_female 3.022253 -1.087903 -3.450183 -2.237935 b_tt_car 0.002560 0.001373 -5.9579e-04 0.001192 b_tt_bus 0.004003 0.002411 -0.001096 0.002051 b_tt_air 0.003804 9.7474e-04 -0.001719 0.001582 b_tt_rail 0.001894 4.8073e-04 -0.001369 6.4388e-04 b_tt_interaction_business 0.001399 5.8994e-04 -5.6698e-04 6.2310e-04 b_acc 0.004805 0.002121 -0.001383 0.002363 b_cost 0.016560 0.009832 -0.004275 0.008198 b_cost_interaction_business -0.007384 -0.004881 0.001840 -0.003749 cost_income_elast -0.033968 -0.017399 -0.026706 -0.017159 b_wifi -0.208268 -0.115550 0.054651 -0.101718 b_food -0.085168 -0.048629 0.020535 -0.042260 p_timesteps 2.711319 1.504343 -0.685304 1.331564 p_phi1 3.012226 1.978914 -0.691595 1.717205 p_phi2 -1.644567 -0.811740 0.982054 -0.754083 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 4.897205 3.022253 0.002560 0.004003 asc_air -1.067632 -1.087903 0.001373 0.002411 asc_rail -3.501208 -3.450183 -5.9579e-04 -0.001096 asc_bus_interaction_female -1.369799 -2.237935 0.001192 0.002051 asc_air_interaction_female 6.423812 3.867011 2.6588e-04 4.8997e-04 asc_rail_interaction_female 3.867011 4.118481 1.6056e-04 3.0109e-04 b_tt_car 2.6588e-04 1.6056e-04 1.679e-07 2.946e-07 b_tt_bus 4.8997e-04 3.0109e-04 2.946e-07 5.325e-07 b_tt_air 4.5169e-04 3.0241e-04 2.679e-07 4.725e-07 b_tt_rail 2.3596e-04 1.6795e-04 1.369e-07 2.366e-07 b_tt_interaction_business 1.9261e-04 1.2841e-04 9.410e-08 1.695e-07 b_acc 5.5521e-04 3.4323e-04 3.339e-07 5.931e-07 b_cost 0.001982 0.001226 1.170e-06 2.110e-06 b_cost_interaction_business -9.3972e-04 -5.9036e-04 -5.559e-07 -1.009e-06 cost_income_elast 0.010986 0.009739 8.817e-07 2.550e-06 b_wifi -0.024649 -0.015353 -1.442e-05 -2.599e-05 b_food -0.010061 -0.006310 -5.946e-06 -1.072e-05 p_timesteps 0.309880 0.188671 1.8201e-04 3.2864e-04 p_phi1 0.440558 0.274804 2.1530e-04 3.9090e-04 p_phi2 -0.304834 -0.217822 -1.4901e-04 -2.7518e-04 b_tt_air b_tt_rail b_tt_interaction_business b_acc asc_bus 0.003804 0.001894 0.001399 0.004805 asc_air 9.7474e-04 4.8073e-04 5.8994e-04 0.002121 asc_rail -0.001719 -0.001369 -5.6698e-04 -0.001383 asc_bus_interaction_female 0.001582 6.4388e-04 6.2310e-04 0.002363 asc_air_interaction_female 4.5169e-04 2.3596e-04 1.9261e-04 5.5521e-04 asc_rail_interaction_female 3.0241e-04 1.6795e-04 1.2841e-04 3.4323e-04 b_tt_car 2.679e-07 1.369e-07 9.410e-08 3.339e-07 b_tt_bus 4.725e-07 2.366e-07 1.695e-07 5.931e-07 b_tt_air 5.401e-07 2.600e-07 1.602e-07 5.317e-07 b_tt_rail 2.600e-07 1.640e-07 8.312e-08 2.671e-07 b_tt_interaction_business 1.602e-07 8.312e-08 6.908e-08 2.005e-07 b_acc 5.317e-07 2.671e-07 2.005e-07 7.707e-07 b_cost 1.844e-06 9.273e-07 6.765e-07 2.343e-06 b_cost_interaction_business -8.677e-07 -4.351e-07 -2.979e-07 -1.095e-06 cost_income_elast 3.399e-06 1.523e-06 1.659e-06 3.129e-06 b_wifi -2.336e-05 -1.162e-05 -8.544e-06 -2.941e-05 b_food -9.716e-06 -4.808e-06 -3.500e-06 -1.217e-05 p_timesteps 2.8965e-04 1.4155e-04 1.0748e-04 3.6946e-04 p_phi1 3.2851e-04 1.5767e-04 1.3069e-04 4.3816e-04 p_phi2 -2.6435e-04 -1.4102e-04 -9.741e-05 -3.0969e-04 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 0.016560 -0.007384 -0.033968 -0.208268 asc_air 0.009832 -0.004881 -0.017399 -0.115550 asc_rail -0.004275 0.001840 -0.026706 0.054651 asc_bus_interaction_female 0.008198 -0.003749 -0.017159 -0.101718 asc_air_interaction_female 0.001982 -9.3972e-04 0.010986 -0.024649 asc_rail_interaction_female 0.001226 -5.9036e-04 0.009739 -0.015353 b_tt_car 1.170e-06 -5.559e-07 8.817e-07 -1.442e-05 b_tt_bus 2.110e-06 -1.009e-06 2.550e-06 -2.599e-05 b_tt_air 1.844e-06 -8.677e-07 3.399e-06 -2.336e-05 b_tt_rail 9.273e-07 -4.351e-07 1.523e-06 -1.162e-05 b_tt_interaction_business 6.765e-07 -2.979e-07 1.659e-06 -8.544e-06 b_acc 2.343e-06 -1.095e-06 3.129e-06 -2.941e-05 b_cost 8.450e-06 -4.056e-06 7.812e-06 -1.0384e-04 b_cost_interaction_business -4.056e-06 2.061e-06 -4.802e-06 4.913e-05 cost_income_elast 7.812e-06 -4.802e-06 0.001191 -1.1969e-04 b_wifi -1.0384e-04 4.913e-05 -1.1969e-04 0.001350 b_food -4.301e-05 2.036e-05 -4.203e-05 5.6418e-04 p_timesteps 0.001310 -6.2099e-04 0.001548 -0.016236 p_phi1 0.001560 -7.3897e-04 0.003031 -0.019261 p_phi2 -0.001097 5.2657e-04 -0.003695 0.013659 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.085168 2.711319 3.012226 -1.644567 asc_air -0.048629 1.504343 1.978914 -0.811740 asc_rail 0.020535 -0.685304 -0.691595 0.982054 asc_bus_interaction_female -0.042260 1.331564 1.717205 -0.754083 asc_air_interaction_female -0.010061 0.309880 0.440558 -0.304834 asc_rail_interaction_female -0.006310 0.188671 0.274804 -0.217822 b_tt_car -5.946e-06 1.8201e-04 2.1530e-04 -1.4901e-04 b_tt_bus -1.072e-05 3.2864e-04 3.9090e-04 -2.7518e-04 b_tt_air -9.716e-06 2.8965e-04 3.2851e-04 -2.6435e-04 b_tt_rail -4.808e-06 1.4155e-04 1.5767e-04 -1.4102e-04 b_tt_interaction_business -3.500e-06 1.0748e-04 1.3069e-04 -9.741e-05 b_acc -1.217e-05 3.6946e-04 4.3816e-04 -3.0969e-04 b_cost -4.301e-05 0.001310 0.001560 -0.001097 b_cost_interaction_business 2.036e-05 -6.2099e-04 -7.3897e-04 5.2657e-04 cost_income_elast -4.203e-05 0.001548 0.003031 -0.003695 b_wifi 5.6418e-04 -0.016236 -0.019261 0.013659 b_food 2.8517e-04 -0.006703 -0.007968 0.005639 p_timesteps -0.006703 0.206552 0.244459 -0.170107 p_phi1 -0.007968 0.244459 0.327462 -0.197927 p_phi2 0.005639 -0.170107 -0.197927 0.171867 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 114.992881 58.317134 0.686695 37.805956 asc_air 58.317134 64.854857 21.315284 36.997013 asc_rail 0.686695 21.315284 30.486676 10.320301 asc_bus_interaction_female 37.805956 36.997013 10.320301 43.127036 asc_air_interaction_female 7.408020 1.402532 -3.509172 -0.396265 asc_rail_interaction_female 2.770466 -0.966899 -3.735174 -2.517638 b_tt_car 0.004398 0.003166 -5.813e-05 0.002332 b_tt_bus 0.007232 0.005527 -1.4328e-04 0.004031 b_tt_air 0.005386 0.002784 -0.001068 0.002820 b_tt_rail 0.002561 0.001019 -0.001425 9.7966e-04 b_tt_interaction_business 0.002039 0.001311 -3.1128e-04 0.001023 b_acc 0.007911 0.005316 -3.6792e-04 0.004273 b_cost 0.029393 0.022246 -4.2596e-04 0.015983 b_cost_interaction_business -0.013728 -0.010879 -2.101e-05 -0.007623 cost_income_elast -0.151792 -0.085808 -0.009843 -0.064477 b_wifi -0.361995 -0.266640 0.006314 -0.195448 b_food -0.151667 -0.112339 6.7742e-04 -0.079581 p_timesteps 4.714059 3.479131 -0.043385 2.543069 p_phi1 5.496866 4.532127 0.284984 3.227723 p_phi2 -2.397518 -1.593463 0.748944 -1.207626 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 7.408020 2.770466 0.004398 0.007232 asc_air 1.402532 -0.966899 0.003166 0.005527 asc_rail -3.509172 -3.735174 -5.813e-05 -1.4328e-04 asc_bus_interaction_female -0.396265 -2.517638 0.002332 0.004031 asc_air_interaction_female 6.706254 4.221102 3.9070e-04 7.0825e-04 asc_rail_interaction_female 4.221102 4.350910 1.7540e-04 3.2683e-04 b_tt_car 3.9070e-04 1.7540e-04 2.681e-07 4.699e-07 b_tt_bus 7.0825e-04 3.2683e-04 4.699e-07 8.384e-07 b_tt_air 5.7633e-04 3.2327e-04 3.657e-07 6.434e-07 b_tt_rail 3.2486e-04 2.1140e-04 1.735e-07 3.001e-07 b_tt_interaction_business 2.6409e-04 1.4802e-04 1.314e-07 2.355e-07 b_acc 7.8328e-04 3.8040e-04 5.124e-07 9.074e-07 b_cost 0.002850 0.001322 1.861e-06 3.316e-06 b_cost_interaction_business -0.001320 -5.9898e-04 -8.933e-07 -1.595e-06 cost_income_elast 0.009095 0.012312 -4.292e-06 -6.368e-06 b_wifi -0.037303 -0.017821 -2.278e-05 -4.061e-05 b_food -0.016578 -0.008201 -9.554e-06 -1.701e-05 p_timesteps 0.452819 0.203689 2.8996e-04 5.1697e-04 p_phi1 0.613258 0.283786 3.5213e-04 6.3025e-04 p_phi2 -0.401853 -0.261689 -1.9254e-04 -3.5192e-04 b_tt_air b_tt_rail b_tt_interaction_business b_acc asc_bus 0.005386 0.002561 0.002039 0.007911 asc_air 0.002784 0.001019 0.001311 0.005316 asc_rail -0.001068 -0.001425 -3.1128e-04 -3.6792e-04 asc_bus_interaction_female 0.002820 9.7966e-04 0.001023 0.004273 asc_air_interaction_female 5.7633e-04 3.2486e-04 2.6409e-04 7.8328e-04 asc_rail_interaction_female 3.2327e-04 2.1140e-04 1.4802e-04 3.8040e-04 b_tt_car 3.657e-07 1.735e-07 1.314e-07 5.124e-07 b_tt_bus 6.434e-07 3.001e-07 2.355e-07 9.074e-07 b_tt_air 6.309e-07 2.920e-07 1.930e-07 7.106e-07 b_tt_rail 2.920e-07 1.899e-07 9.410e-08 3.323e-07 b_tt_interaction_business 1.930e-07 9.410e-08 8.122e-08 2.665e-07 b_acc 7.106e-07 3.323e-07 2.665e-07 1.084e-06 b_cost 2.509e-06 1.171e-06 9.367e-07 3.583e-06 b_cost_interaction_business -1.194e-06 -5.547e-07 -4.320e-07 -1.707e-06 cost_income_elast -2.919e-06 -2.382e-06 -9.458e-07 -6.044e-06 b_wifi -3.152e-05 -1.449e-05 -1.170e-05 -4.415e-05 b_food -1.338e-05 -6.097e-06 -4.883e-06 -1.852e-05 p_timesteps 3.9229e-04 1.7829e-04 1.4788e-04 5.6086e-04 p_phi1 4.6337e-04 1.9786e-04 1.8344e-04 6.7859e-04 p_phi2 -3.0193e-04 -1.5556e-04 -1.1305e-04 -3.9105e-04 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 0.029393 -0.013728 -0.151792 -0.361995 asc_air 0.022246 -0.010879 -0.085808 -0.266640 asc_rail -4.2596e-04 -2.101e-05 -0.009843 0.006314 asc_bus_interaction_female 0.015983 -0.007623 -0.064477 -0.195448 asc_air_interaction_female 0.002850 -0.001320 0.009095 -0.037303 asc_rail_interaction_female 0.001322 -5.9898e-04 0.012312 -0.017821 b_tt_car 1.861e-06 -8.933e-07 -4.292e-06 -2.278e-05 b_tt_bus 3.316e-06 -1.595e-06 -6.368e-06 -4.061e-05 b_tt_air 2.509e-06 -1.194e-06 -2.919e-06 -3.152e-05 b_tt_rail 1.171e-06 -5.547e-07 -2.382e-06 -1.449e-05 b_tt_interaction_business 9.367e-07 -4.320e-07 -9.458e-07 -1.170e-05 b_acc 3.583e-06 -1.707e-06 -6.044e-06 -4.415e-05 b_cost 1.321e-05 -6.370e-06 -2.761e-05 -1.6156e-04 b_cost_interaction_business -6.370e-06 3.161e-06 1.153e-05 7.728e-05 cost_income_elast -2.761e-05 1.153e-05 0.001403 3.0690e-04 b_wifi -1.6156e-04 7.728e-05 3.0690e-04 0.002056 b_food -6.782e-05 3.244e-05 1.1831e-04 8.6642e-04 p_timesteps 0.002054 -9.8283e-04 -0.004197 -0.025241 p_phi1 0.002510 -0.001203 -0.003297 -0.030894 p_phi2 -0.001396 6.7058e-04 -4.5144e-04 0.017302 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.151667 4.714059 5.496866 -2.397518 asc_air -0.112339 3.479131 4.532127 -1.593463 asc_rail 6.7742e-04 -0.043385 0.284984 0.748944 asc_bus_interaction_female -0.079581 2.543069 3.227723 -1.207626 asc_air_interaction_female -0.016578 0.452819 0.613258 -0.401853 asc_rail_interaction_female -0.008201 0.203689 0.283786 -0.261689 b_tt_car -9.554e-06 2.8996e-04 3.5213e-04 -1.9254e-04 b_tt_bus -1.701e-05 5.1697e-04 6.3025e-04 -3.5192e-04 b_tt_air -1.338e-05 3.9229e-04 4.6337e-04 -3.0193e-04 b_tt_rail -6.097e-06 1.7829e-04 1.9786e-04 -1.5556e-04 b_tt_interaction_business -4.883e-06 1.4788e-04 1.8344e-04 -1.1305e-04 b_acc -1.852e-05 5.6086e-04 6.7859e-04 -3.9105e-04 b_cost -6.782e-05 0.002054 0.002510 -0.001396 b_cost_interaction_business 3.244e-05 -9.8283e-04 -0.001203 6.7058e-04 cost_income_elast 1.1831e-04 -0.004197 -0.003297 -4.5144e-04 b_wifi 8.6642e-04 -0.025241 -0.030894 0.017302 b_food 4.1983e-04 -0.010569 -0.013015 0.007224 p_timesteps -0.010569 0.322699 0.392965 -0.216368 p_phi1 -0.013015 0.392965 0.519672 -0.259675 p_phi2 0.007224 -0.216368 -0.259675 0.188412 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.0000 0.42856 -0.22718 0.36648 asc_air 0.4286 1.00000 0.37688 0.52532 asc_rail -0.2272 0.37688 1.00000 0.06242 asc_bus_interaction_female 0.3665 0.52532 0.06242 1.00000 asc_air_interaction_female 0.2158 -0.07315 -0.28376 -0.10214 asc_rail_interaction_female 0.1663 -0.09309 -0.34923 -0.20841 b_tt_car 0.6978 0.58210 -0.29872 0.54970 b_tt_bus 0.6126 0.57365 -0.30858 0.53131 b_tt_air 0.5781 0.23030 -0.48059 0.40694 b_tt_rail 0.5222 0.20610 -0.69417 0.30045 b_tt_interaction_business 0.5947 0.38977 -0.44314 0.44807 b_acc 0.6112 0.41962 -0.32351 0.50877 b_cost 0.6363 0.58736 -0.30212 0.53301 b_cost_interaction_business -0.5744 -0.59032 0.26321 -0.49348 cost_income_elast -0.1099 -0.08755 -0.15897 -0.09397 b_wifi -0.6331 -0.54609 0.30554 -0.52321 b_food -0.5633 -0.50004 0.24980 -0.47296 p_timesteps 0.6663 0.57477 -0.30975 0.55373 p_phi1 0.5879 0.60050 -0.24826 0.56714 p_phi2 -0.4431 -0.34000 0.48660 -0.34377 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 0.21581 0.16633 0.69781 0.6126 asc_air -0.07315 -0.09309 0.58210 0.5736 asc_rail -0.28376 -0.34923 -0.29872 -0.3086 asc_bus_interaction_female -0.10214 -0.20841 0.54970 0.5313 asc_air_interaction_female 1.00000 0.75181 0.25605 0.2649 asc_rail_interaction_female 0.75181 1.00000 0.19311 0.2033 b_tt_car 0.25605 0.19311 1.00000 0.9853 b_tt_bus 0.26492 0.20332 0.98529 1.0000 b_tt_air 0.24249 0.20276 0.88972 0.8810 b_tt_rail 0.22985 0.20432 0.82504 0.8004 b_tt_interaction_business 0.28914 0.24075 0.87390 0.8839 b_acc 0.24952 0.19265 0.92835 0.9259 b_cost 0.26900 0.20791 0.98203 0.9947 b_cost_interaction_business -0.25825 -0.20262 -0.94503 -0.9634 cost_income_elast 0.12561 0.13906 0.06236 0.1012 b_wifi -0.26469 -0.20590 -0.95804 -0.9692 b_food -0.23507 -0.18412 -0.85945 -0.8702 p_timesteps 0.26902 0.20456 0.97749 0.9910 p_phi1 0.30376 0.23663 0.91831 0.9361 p_phi2 -0.29012 -0.25890 -0.87729 -0.9096 b_tt_air b_tt_rail b_tt_interaction_business b_acc asc_bus 0.5781 0.5222 0.5947 0.6112 asc_air 0.2303 0.2061 0.3898 0.4196 asc_rail -0.4806 -0.6942 -0.4431 -0.3235 asc_bus_interaction_female 0.4069 0.3005 0.4481 0.5088 asc_air_interaction_female 0.2425 0.2299 0.2891 0.2495 asc_rail_interaction_female 0.2028 0.2043 0.2408 0.1926 b_tt_car 0.8897 0.8250 0.8739 0.9283 b_tt_bus 0.8810 0.8004 0.8839 0.9259 b_tt_air 1.0000 0.8735 0.8295 0.8241 b_tt_rail 0.8735 1.0000 0.7808 0.7512 b_tt_interaction_business 0.8295 0.7808 1.0000 0.8689 b_acc 0.8241 0.7512 0.8689 1.0000 b_cost 0.8630 0.7876 0.8855 0.9180 b_cost_interaction_business -0.8223 -0.7482 -0.7894 -0.8691 cost_income_elast 0.1340 0.1090 0.1829 0.1033 b_wifi -0.8651 -0.7805 -0.8848 -0.9118 b_food -0.7829 -0.7029 -0.7887 -0.8207 p_timesteps 0.8672 0.7690 0.8998 0.9260 p_phi1 0.7811 0.6803 0.8690 0.8722 p_phi2 -0.8676 -0.8398 -0.8940 -0.8509 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 0.63630 -0.57441 -0.10994 -0.63310 asc_air 0.58736 -0.59032 -0.08755 -0.54609 asc_rail -0.30212 0.26321 -0.15897 0.30554 asc_bus_interaction_female 0.53301 -0.49348 -0.09397 -0.52321 asc_air_interaction_female 0.26900 -0.25825 0.12561 -0.26469 asc_rail_interaction_female 0.20791 -0.20262 0.13906 -0.20590 b_tt_car 0.98203 -0.94503 0.06236 -0.95804 b_tt_bus 0.99467 -0.96339 0.10124 -0.96924 b_tt_air 0.86298 -0.82234 0.13403 -0.86513 b_tt_rail 0.78761 -0.74819 0.10897 -0.78052 b_tt_interaction_business 0.88555 -0.78945 0.18291 -0.88475 b_acc 0.91802 -0.86909 0.10328 -0.91176 b_cost 1.00000 -0.97200 0.07787 -0.97223 b_cost_interaction_business -0.97200 1.00000 -0.09693 0.93145 cost_income_elast 0.07787 -0.09693 1.00000 -0.09439 b_wifi -0.97223 0.93145 -0.09439 1.00000 b_food -0.87618 0.83992 -0.07211 0.90927 p_timesteps 0.99132 -0.95173 0.09872 -0.97230 p_phi1 0.93782 -0.89947 0.15351 -0.91607 p_phi2 -0.91063 0.88470 -0.25829 0.89671 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.56330 0.66632 0.5879 -0.4431 asc_air -0.50004 0.57477 0.6005 -0.3400 asc_rail 0.24980 -0.30975 -0.2483 0.4866 asc_bus_interaction_female -0.47296 0.55373 0.5671 -0.3438 asc_air_interaction_female -0.23507 0.26902 0.3038 -0.2901 asc_rail_interaction_female -0.18412 0.20456 0.2366 -0.2589 b_tt_car -0.85945 0.97749 0.9183 -0.8773 b_tt_bus -0.87015 0.99096 0.9361 -0.9096 b_tt_air -0.78289 0.86717 0.7811 -0.8676 b_tt_rail -0.70290 0.76896 0.6803 -0.8398 b_tt_interaction_business -0.78869 0.89982 0.8690 -0.8940 b_acc -0.82071 0.92598 0.8722 -0.8509 b_cost -0.87618 0.99132 0.9378 -0.9106 b_cost_interaction_business 0.83992 -0.95173 -0.8995 0.8847 cost_income_elast -0.07211 0.09872 0.1535 -0.2583 b_wifi 0.90927 -0.97230 -0.9161 0.8967 b_food 1.00000 -0.87337 -0.8245 0.8054 p_timesteps -0.87337 1.00000 0.9400 -0.9028 p_phi1 -0.82454 0.93996 1.0000 -0.8343 p_phi2 0.80542 -0.90284 -0.8343 1.0000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_interaction_female asc_bus 1.00000 0.67529 0.011598 0.53685 asc_air 0.67529 1.00000 0.479363 0.69955 asc_rail 0.01160 0.47936 1.000000 0.28462 asc_bus_interaction_female 0.53685 0.69955 0.284618 1.00000 asc_air_interaction_female 0.26676 0.06725 -0.245420 -0.02330 asc_rail_interaction_female 0.12386 -0.05756 -0.324314 -0.18379 b_tt_car 0.79196 0.75931 -0.020331 0.68564 b_tt_bus 0.73658 0.74958 -0.028340 0.67035 b_tt_air 0.63233 0.43528 -0.243520 0.54058 b_tt_rail 0.54799 0.29035 -0.592294 0.34234 b_tt_interaction_business 0.66728 0.57119 -0.197811 0.54646 b_acc 0.70854 0.63401 -0.064000 0.62488 b_cost 0.75420 0.76007 -0.021227 0.66966 b_cost_interaction_business -0.72000 -0.75979 -0.002140 -0.65282 cost_income_elast -0.37797 -0.28451 -0.047601 -0.26216 b_wifi -0.74451 -0.73023 0.025222 -0.65639 b_food -0.69027 -0.68081 0.005988 -0.59142 p_timesteps 0.77386 0.76050 -0.013832 0.68169 p_phi1 0.71107 0.78067 0.071598 0.68180 p_phi2 -0.51508 -0.45584 0.312493 -0.42365 asc_air_interaction_female asc_rail_interaction_female b_tt_car b_tt_bus asc_bus 0.26676 0.12386 0.79196 0.73658 asc_air 0.06725 -0.05756 0.75931 0.74958 asc_rail -0.24542 -0.32431 -0.02033 -0.02834 asc_bus_interaction_female -0.02330 -0.18379 0.68564 0.67035 asc_air_interaction_female 1.00000 0.78144 0.29136 0.29869 asc_rail_interaction_female 0.78144 1.00000 0.16240 0.17112 b_tt_car 0.29136 0.16240 1.00000 0.99104 b_tt_bus 0.29869 0.17112 0.99104 1.00000 b_tt_air 0.28019 0.19511 0.88905 0.88471 b_tt_rail 0.28788 0.23257 0.76902 0.75213 b_tt_interaction_business 0.35782 0.24899 0.89038 0.90255 b_acc 0.29050 0.17516 0.95049 0.95179 b_cost 0.30284 0.17433 0.98873 0.99641 b_cost_interaction_business -0.28672 -0.16150 -0.97020 -0.97967 cost_income_elast 0.09378 0.15761 -0.22133 -0.18570 b_wifi -0.31769 -0.18843 -0.97035 -0.97815 b_food -0.31244 -0.19188 -0.90045 -0.90686 p_timesteps 0.30781 0.17190 0.98573 0.99389 p_phi1 0.32850 0.18873 0.94334 0.95482 p_phi2 -0.35750 -0.28903 -0.85665 -0.88545 b_tt_air b_tt_rail b_tt_interaction_business b_acc asc_bus 0.63233 0.5480 0.66728 0.70854 asc_air 0.43528 0.2903 0.57119 0.63401 asc_rail -0.24352 -0.5923 -0.19781 -0.06400 asc_bus_interaction_female 0.54058 0.3423 0.54646 0.62488 asc_air_interaction_female 0.28019 0.2879 0.35782 0.29050 asc_rail_interaction_female 0.19511 0.2326 0.24899 0.17516 b_tt_car 0.88905 0.7690 0.89038 0.95049 b_tt_bus 0.88471 0.7521 0.90255 0.95179 b_tt_air 1.00000 0.8436 0.85268 0.85929 b_tt_rail 0.84359 1.0000 0.75770 0.73235 b_tt_interaction_business 0.85268 0.7577 1.00000 0.89796 b_acc 0.85929 0.7323 0.89796 1.00000 b_cost 0.86918 0.7392 0.90433 0.94684 b_cost_interaction_business -0.84552 -0.7160 -0.85243 -0.92193 cost_income_elast -0.09813 -0.1459 -0.08861 -0.15501 b_wifi -0.87508 -0.7334 -0.90558 -0.93520 b_food -0.82234 -0.6828 -0.83618 -0.86812 p_timesteps 0.86942 0.7203 0.91339 0.94827 p_phi1 0.80924 0.6299 0.89285 0.90411 p_phi2 -0.87574 -0.8224 -0.91389 -0.86527 b_cost b_cost_interaction_business cost_income_elast b_wifi asc_bus 0.75420 -0.720003 -0.37797 -0.74451 asc_air 0.76007 -0.759789 -0.28451 -0.73023 asc_rail -0.02123 -0.002140 -0.04760 0.02522 asc_bus_interaction_female 0.66966 -0.652819 -0.26216 -0.65639 asc_air_interaction_female 0.30284 -0.286718 0.09378 -0.31769 asc_rail_interaction_female 0.17433 -0.161503 0.15761 -0.18843 b_tt_car 0.98873 -0.970202 -0.22133 -0.97035 b_tt_bus 0.99641 -0.979670 -0.18570 -0.97815 b_tt_air 0.86918 -0.845524 -0.09813 -0.87508 b_tt_rail 0.73925 -0.715963 -0.14594 -0.73342 b_tt_interaction_business 0.90433 -0.852435 -0.08861 -0.90558 b_acc 0.94684 -0.921928 -0.15501 -0.93520 b_cost 1.00000 -0.985715 -0.20283 -0.98045 b_cost_interaction_business -0.98572 1.000000 0.17309 0.95854 cost_income_elast -0.20283 0.173091 1.00000 0.18074 b_wifi -0.98045 0.958538 0.18074 1.00000 b_food -0.91074 0.890490 0.15418 0.93261 p_timesteps 0.99476 -0.973059 -0.19730 -0.97999 p_phi1 0.95793 -0.938551 -0.12211 -0.94518 p_phi2 -0.88478 0.868870 -0.02777 0.87913 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.690273 0.77386 0.71107 -0.51508 asc_air -0.680810 0.76050 0.78067 -0.45584 asc_rail 0.005988 -0.01383 0.07160 0.31249 asc_bus_interaction_female -0.591425 0.68169 0.68180 -0.42365 asc_air_interaction_female -0.312438 0.30781 0.32850 -0.35750 asc_rail_interaction_female -0.191882 0.17190 0.18873 -0.28903 b_tt_car -0.900450 0.98573 0.94334 -0.85665 b_tt_bus -0.906861 0.99389 0.95482 -0.88545 b_tt_air -0.822335 0.86942 0.80924 -0.87574 b_tt_rail -0.682814 0.72026 0.62987 -0.82241 b_tt_interaction_business -0.836179 0.91339 0.89285 -0.91389 b_acc -0.868117 0.94827 0.90411 -0.86527 b_cost -0.910742 0.99476 0.95793 -0.88478 b_cost_interaction_business 0.890490 -0.97306 -0.93855 0.86887 cost_income_elast 0.154182 -0.19730 -0.12211 -0.02777 b_wifi 0.932608 -0.97999 -0.94518 0.87913 b_food 1.000000 -0.90804 -0.88116 0.81222 p_timesteps -0.908036 1.00000 0.95960 -0.87749 p_phi1 -0.881162 0.95960 1.00000 -0.82987 p_phi2 0.812216 -0.87749 -0.82987 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2378115 464 0.2521121 146 0.2568402 293 0.2614053 186 0.2704926 276 0.2781970 317 0.2828237 467 0.2892157 263 0.2923598 370 0.2940592 181 0.2941080 183 0.2956476 161 0.2984972 441 0.3008148 367 0.3029091 259 0.3038128 133 0.3069201 434 0.3118567 307 0.3130002 379 0.3149432 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.00000 0.000000 0.000000 asc_bus 0.00000 23.233659 23.233659 asc_air 0.00000 4.419460 4.419460 asc_rail 0.00000 -16.586294 -16.586294 asc_bus_interaction_female 0.00000 10.033688 10.033688 asc_air_interaction_female 0.00000 3.113534 3.113534 asc_rail_interaction_female 0.00000 2.139253 2.139253 b_tt_car -0.01000 -0.001629 0.008371 b_tt_bus -0.01000 -0.002931 0.007069 b_tt_air -0.01000 -0.003187 0.006813 b_tt_rail -0.01000 -0.001690 0.008310 b_tt_interaction_business 0.00000 -0.001112 -0.001112 b_acc -0.01000 -0.003521 0.006479 b_cost -0.01000 -0.011896 -0.001896 b_cost_interaction_business 0.00000 0.005336 0.005336 cost_income_elast 0.00000 -0.667378 -0.667378 b_no_frills 0.00000 0.000000 0.000000 b_wifi -0.01000 0.155046 0.165046 b_food -0.01000 0.063143 0.073143 p_error_sd 1.00000 1.000000 0.000000 p_timesteps 1.00000 5.895860 4.895860 p_phi1 -2.00000 1.202562 3.202562 p_phi2 -2.00000 -5.289266 -3.289266 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "DFT model on mode choice SP data" indivID "ID" nCores "4" outputDirectory "output/" debug "FALSE" modelName "DFT_mode_choice" 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 23.233659456 asc_air 4.419459767 asc_rail 16.586293575 asc_bus_interaction_female 10.033688443 asc_air_interaction_female 3.113534133 asc_rail_interaction_female 2.139253266 b_tt_car 0.001628995 b_tt_bus 0.002931035 b_tt_air 0.003186888 b_tt_rail 0.001689919 b_tt_interaction_business 0.001111842 b_acc 0.003520613 b_cost 0.011895996 b_cost_interaction_business 0.005336477 cost_income_elast 0.667377969 b_wifi 0.155046195 b_food 0.063142794 p_timesteps 5.895859707 p_phi1 1.202562490 p_phi2 5.289266243 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 attribute values attrValues = list() attrValues[["car"]] = list(time=time_car , access=0 , cost=cost_car , wifi=0 , food=0 ) attrValues[["bus"]] = list(time=time_bus , access=access_bus , cost=cost_bus , wifi=0 , food=0 ) attrValues[["air"]] = list(time=time_air , access=access_air , cost=cost_air , wifi=1*(service_air == 2), food=1*(service_air == 3)) attrValues[["rail"]] = list(time=time_rail, access=access_rail, cost=cost_rail, wifi=1*(service_rail == 2), food=1*(service_rail == 3)) ### List of initial preference values altStart = list() altStart[["car"]] = asc_car altStart[["bus"]] = asc_bus_value altStart[["air"]] = asc_air_value altStart[["rail"]] = asc_rail_value ### List of attribute scaling factors attrScalings = list(time = list(car = b_tt_car_value, bus = b_tt_bus_value, air = b_tt_air_value, rail = b_tt_rail_value), access = b_acc, cost = b_cost_value, wifi = b_wifi, food = b_food) ### List of process parameters procPars = list( error_sd = p_error_sd, timesteps = 1+exp(p_timesteps), phi1 = exp(p_phi1), phi2 = exp(p_phi2)/(1+exp(p_phi2)) ) ### Define settings for DFT model component dft_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, attrValues = attrValues, altStart = altStart, attrWeights = 1, ### Using scaling factors, so attrWeights must be set to 1. attrScalings = attrScalings, procPars = procPars ) ### Compute choice probabilities using DFT model P[["model"]] = apollo_dft(dft_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) }