Model run by stephane.hess using Apollo 0.3.6 on R 4.5.1 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 : MNL_RP_SP Model description : RP-SP model on mode choice data Model run at : 2025-09-19 11:37:57.326226 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -12.026772 reciprocal of condition number : 3.03709e-08 Number of individuals : 500 Number of rows in database : 8000 Number of modelled outcomes : 8000 RP : 1000 SP : 7000 Number of cores used : 1 Model without mixing LL(start) : -9366.88 LL (whole model) at equal shares, LL(0) : -9366.88 LL (whole model) at observed shares, LL(C) : -7792.08 LL(final, whole model) : -5802.64 Rho-squared vs equal shares : 0.3805 Adj.Rho-squared vs equal shares : 0.3786 Rho-squared vs observed shares : 0.2553 Adj.Rho-squared vs observed shares : 0.2538 AIC : 11641.29 BIC : 11729.63 LL(0,RP) : -1170.86 LL(final,RP) : -971.24 LL(0,SP) : -8196.02 LL(final,SP) : -4831.4 Estimated parameters : 18 Time taken (hh:mm:ss) : 00:00:4.46 pre-estimation : 00:00:0.92 estimation : 00:00:0.71 post-estimation : 00:00:2.83 Iterations : 12 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 0.124830 0.281040 0.4442 0.262028 0.4764 asc_air -0.396088 0.183661 -2.1566 0.177781 -2.2280 asc_rail -0.978687 0.180545 -5.4207 0.177524 -5.5130 asc_bus_interaction_female 0.181339 0.064656 2.8047 0.071405 2.5396 asc_air_interaction_female 0.134505 0.045471 2.9580 0.047351 2.8406 asc_rail_interaction_female 0.098189 0.036644 2.6796 0.038414 2.5561 b_tt_car -0.006425 5.0941e-04 -12.6116 4.9442e-04 -12.9942 b_tt_bus -0.010507 9.6109e-04 -10.9322 8.7333e-04 -12.0308 b_tt_air -0.008668 0.001466 -5.9138 0.001432 -6.0517 b_tt_rail -0.003838 9.2074e-04 -4.1682 8.9506e-04 -4.2878 b_tt_interaction_business -0.003203 3.4648e-04 -9.2440 3.4886e-04 -9.1808 b_access -0.010545 0.001531 -6.8858 0.001462 -7.2145 b_cost -0.038234 0.002461 -15.5359 0.002429 -15.7381 b_cost_interaction_business 0.016657 0.001634 10.1911 0.001551 10.7399 cost_income_elast -0.613150 0.029204 -20.9954 0.029760 -20.6034 b_no_frills 0.000000 NA NA NA NA b_wifi 0.523124 0.043044 12.1532 0.043594 11.9999 b_food 0.220074 0.030836 7.1369 0.031545 6.9765 mu_RP 1.000000 NA NA NA NA mu_SP 1.994744 0.126408 15.7802 0.122879 16.2334 Overview of choices for MNL model component RP: car bus air rail Times available 778.00 902.00 752.00 874.00 Times chosen 332.00 126.00 215.00 327.00 Percentage chosen overall 33.20 12.60 21.50 32.70 Percentage chosen when available 42.67 13.97 28.59 37.41 Overview of choices for MNL model component SP: 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_bus 0.078983 0.008702 asc_air 0.008702 0.033731 asc_rail 0.007860 0.015382 asc_bus_interaction_female -0.002408 -5.6910e-04 asc_air_interaction_female -3.1336e-04 -0.001117 asc_rail_interaction_female -3.4655e-04 -4.6732e-04 b_tt_car 2.494e-05 4.568e-05 b_tt_bus -1.9274e-04 2.559e-05 b_tt_air -4.400e-06 -1.6574e-04 b_tt_rail 2.440e-06 1.001e-05 b_tt_interaction_business 1.549e-06 5.553e-06 b_access -7.660e-06 -1.3496e-04 b_cost 1.326e-06 2.447e-05 b_cost_interaction_business 8.776e-06 -3.154e-05 cost_income_elast -4.1292e-04 6.1905e-04 b_wifi -5.635e-05 -0.001176 b_food -5.551e-05 -6.2408e-04 mu_SP -1.0255e-04 0.002198 asc_rail asc_bus_interaction_female asc_bus 0.007860 -0.002408 asc_air 0.015382 -5.6910e-04 asc_rail 0.032596 -8.8764e-04 asc_bus_interaction_female -8.8764e-04 0.004180 asc_air_interaction_female -8.6370e-04 8.2596e-04 asc_rail_interaction_female -9.6450e-04 7.4655e-04 b_tt_car 5.821e-05 -4.146e-06 b_tt_bus 4.310e-05 -5.481e-06 b_tt_air 1.925e-05 -6.093e-06 b_tt_rail -1.0210e-04 -2.982e-06 b_tt_interaction_business 1.414e-05 -1.825e-06 b_access 2.120e-05 -6.164e-06 b_cost 1.0621e-04 -2.663e-05 b_cost_interaction_business -4.348e-05 1.357e-05 cost_income_elast 1.9800e-04 -6.333e-05 b_wifi -0.002135 3.6652e-04 b_food -0.001160 1.5997e-04 mu_SP 0.006573 -0.001384 asc_air_interaction_female asc_rail_interaction_female asc_bus -3.1336e-04 -3.4655e-04 asc_air -0.001117 -4.6732e-04 asc_rail -8.6370e-04 -9.6450e-04 asc_bus_interaction_female 8.2596e-04 7.4655e-04 asc_air_interaction_female 0.002068 8.8623e-04 asc_rail_interaction_female 8.8623e-04 0.001343 b_tt_car -3.057e-06 -2.279e-06 b_tt_bus -4.872e-06 -3.524e-06 b_tt_air -4.160e-06 -3.586e-06 b_tt_rail -1.895e-06 -1.453e-06 b_tt_interaction_business -1.662e-06 -1.177e-06 b_access -5.391e-06 -4.386e-06 b_cost -1.863e-05 -1.402e-05 b_cost_interaction_business 7.386e-06 5.895e-06 cost_income_elast 1.343e-05 1.071e-05 b_wifi 2.7352e-04 1.9823e-04 b_food 1.2317e-04 8.614e-05 mu_SP -9.8585e-04 -7.4411e-04 b_tt_car b_tt_bus asc_bus 2.494e-05 -1.9274e-04 asc_air 4.568e-05 2.559e-05 asc_rail 5.821e-05 4.310e-05 asc_bus_interaction_female -4.146e-06 -5.481e-06 asc_air_interaction_female -3.057e-06 -4.872e-06 asc_rail_interaction_female -2.279e-06 -3.524e-06 b_tt_car 2.595e-07 2.575e-07 b_tt_bus 2.575e-07 9.237e-07 b_tt_air 1.791e-07 2.984e-07 b_tt_rail 8.303e-08 1.454e-07 b_tt_interaction_business 5.902e-08 9.176e-08 b_access 2.058e-07 2.967e-07 b_cost 9.241e-07 1.440e-06 b_cost_interaction_business -4.445e-07 -7.136e-07 cost_income_elast -7.524e-07 5.979e-07 b_wifi -1.351e-05 -2.054e-05 b_food -6.114e-06 -9.121e-06 mu_SP 4.581e-05 7.331e-05 b_tt_air b_tt_rail asc_bus -4.400e-06 2.440e-06 asc_air -1.6574e-04 1.001e-05 asc_rail 1.925e-05 -1.0210e-04 asc_bus_interaction_female -6.093e-06 -2.982e-06 asc_air_interaction_female -4.160e-06 -1.895e-06 asc_rail_interaction_female -3.586e-06 -1.453e-06 b_tt_car 1.791e-07 8.303e-08 b_tt_bus 2.984e-07 1.454e-07 b_tt_air 2.148e-06 6.463e-08 b_tt_rail 6.463e-08 8.478e-07 b_tt_interaction_business 8.522e-08 1.722e-08 b_access 9.720e-07 -2.241e-08 b_cost 1.469e-06 7.503e-07 b_cost_interaction_business -5.367e-07 -3.899e-07 cost_income_elast -5.266e-06 -1.884e-06 b_wifi -1.889e-05 -1.040e-05 b_food -9.404e-06 -4.592e-06 mu_SP 6.798e-05 3.038e-05 b_tt_interaction_business b_access asc_bus 1.549e-06 -7.660e-06 asc_air 5.553e-06 -1.3496e-04 asc_rail 1.414e-05 2.120e-05 asc_bus_interaction_female -1.825e-06 -6.164e-06 asc_air_interaction_female -1.662e-06 -5.391e-06 asc_rail_interaction_female -1.177e-06 -4.386e-06 b_tt_car 5.902e-08 2.058e-07 b_tt_bus 9.176e-08 2.967e-07 b_tt_air 8.522e-08 9.720e-07 b_tt_rail 1.722e-08 -2.241e-08 b_tt_interaction_business 1.200e-07 1.378e-07 b_access 1.378e-07 2.345e-06 b_cost 3.292e-07 1.503e-06 b_cost_interaction_business 1.027e-07 -4.496e-07 cost_income_elast -1.823e-07 -4.409e-06 b_wifi -6.778e-06 -2.165e-05 b_food -2.992e-06 -1.020e-05 mu_SP 2.374e-05 7.772e-05 b_cost b_cost_interaction_business asc_bus 1.326e-06 8.776e-06 asc_air 2.447e-05 -3.154e-05 asc_rail 1.0621e-04 -4.348e-05 asc_bus_interaction_female -2.663e-05 1.357e-05 asc_air_interaction_female -1.863e-05 7.386e-06 asc_rail_interaction_female -1.402e-05 5.895e-06 b_tt_car 9.241e-07 -4.445e-07 b_tt_bus 1.440e-06 -7.136e-07 b_tt_air 1.469e-06 -5.367e-07 b_tt_rail 7.503e-07 -3.899e-07 b_tt_interaction_business 3.292e-07 1.027e-07 b_access 1.503e-06 -4.496e-07 b_cost 6.057e-06 -2.955e-06 b_cost_interaction_business -2.955e-06 2.671e-06 cost_income_elast -1.316e-05 2.367e-06 b_wifi -7.907e-05 3.093e-05 b_food -3.562e-05 1.362e-05 mu_SP 2.8332e-04 -1.1989e-04 cost_income_elast b_wifi asc_bus -4.1292e-04 -5.635e-05 asc_air 6.1905e-04 -0.001176 asc_rail 1.9800e-04 -0.002135 asc_bus_interaction_female -6.333e-05 3.6652e-04 asc_air_interaction_female 1.343e-05 2.7352e-04 asc_rail_interaction_female 1.071e-05 1.9823e-04 b_tt_car -7.524e-07 -1.351e-05 b_tt_bus 5.979e-07 -2.054e-05 b_tt_air -5.266e-06 -1.889e-05 b_tt_rail -1.884e-06 -1.040e-05 b_tt_interaction_business -1.823e-07 -6.778e-06 b_access -4.409e-06 -2.165e-05 b_cost -1.316e-05 -7.907e-05 b_cost_interaction_business 2.367e-06 3.093e-05 cost_income_elast 8.5287e-04 9.464e-05 b_wifi 9.464e-05 0.001853 b_food 5.762e-05 8.8386e-04 mu_SP -1.5798e-04 -0.004170 b_food mu_SP asc_bus -5.551e-05 -1.0255e-04 asc_air -6.2408e-04 0.002198 asc_rail -0.001160 0.006573 asc_bus_interaction_female 1.5997e-04 -0.001384 asc_air_interaction_female 1.2317e-04 -9.8585e-04 asc_rail_interaction_female 8.614e-05 -7.4411e-04 b_tt_car -6.114e-06 4.581e-05 b_tt_bus -9.121e-06 7.331e-05 b_tt_air -9.404e-06 6.798e-05 b_tt_rail -4.592e-06 3.038e-05 b_tt_interaction_business -2.992e-06 2.374e-05 b_access -1.020e-05 7.772e-05 b_cost -3.562e-05 2.8332e-04 b_cost_interaction_business 1.362e-05 -1.1989e-04 cost_income_elast 5.762e-05 -1.5798e-04 b_wifi 8.8386e-04 -0.004170 b_food 9.5086e-04 -0.001849 mu_SP -0.001849 0.015979 Robust covariance matrix: asc_bus asc_air asc_bus 0.068659 0.008573 asc_air 0.008573 0.031606 asc_rail 0.008462 0.015656 asc_bus_interaction_female -0.003194 -4.4468e-04 asc_air_interaction_female 2.800e-05 -0.001061 asc_rail_interaction_female -4.9922e-04 -5.3889e-04 b_tt_car 2.972e-05 4.268e-05 b_tt_bus -1.5689e-04 1.906e-05 b_tt_air -8.534e-06 -1.5056e-04 b_tt_rail 6.559e-06 2.669e-06 b_tt_interaction_business 5.486e-06 7.260e-06 b_access 2.717e-05 -1.2538e-04 b_cost 1.377e-05 -2.217e-07 b_cost_interaction_business 1.303e-05 -1.872e-05 cost_income_elast -4.2750e-04 7.8995e-04 b_wifi -7.8215e-04 -6.3740e-04 b_food -1.2720e-04 -3.2754e-04 mu_SP 8.8345e-04 4.5488e-04 asc_rail asc_bus_interaction_female asc_bus 0.008462 -0.003194 asc_air 0.015656 -4.4468e-04 asc_rail 0.031515 -6.7182e-04 asc_bus_interaction_female -6.7182e-04 0.005099 asc_air_interaction_female -0.001433 0.001014 asc_rail_interaction_female -9.1404e-04 0.001042 b_tt_car 5.526e-05 -2.920e-06 b_tt_bus 3.508e-05 -2.346e-06 b_tt_air 1.705e-05 -1.926e-07 b_tt_rail -9.768e-05 -2.316e-06 b_tt_interaction_business 1.816e-05 -6.539e-07 b_access 1.245e-05 -9.228e-06 b_cost 8.272e-05 -2.400e-05 b_cost_interaction_business -1.823e-05 1.376e-05 cost_income_elast 1.8748e-04 1.0454e-04 b_wifi -0.001828 2.8999e-04 b_food -9.4214e-04 2.4406e-04 mu_SP 0.005331 -0.001071 asc_air_interaction_female asc_rail_interaction_female asc_bus 2.800e-05 -4.9922e-04 asc_air -0.001061 -5.3889e-04 asc_rail -0.001433 -9.1404e-04 asc_bus_interaction_female 0.001014 0.001042 asc_air_interaction_female 0.002242 0.001141 asc_rail_interaction_female 0.001141 0.001476 b_tt_car -3.564e-06 -8.446e-07 b_tt_bus -6.185e-06 -1.339e-06 b_tt_air -3.530e-06 6.661e-07 b_tt_rail 1.296e-06 8.443e-07 b_tt_interaction_business -1.390e-06 -4.422e-07 b_access -8.320e-06 -3.268e-06 b_cost -2.312e-05 -9.114e-06 b_cost_interaction_business 1.384e-05 7.037e-06 cost_income_elast 1.3036e-04 9.328e-05 b_wifi 2.4311e-04 1.0166e-04 b_food 8.897e-05 6.168e-05 mu_SP -9.9880e-04 -4.0576e-04 b_tt_car b_tt_bus asc_bus 2.972e-05 -1.5689e-04 asc_air 4.268e-05 1.906e-05 asc_rail 5.526e-05 3.508e-05 asc_bus_interaction_female -2.920e-06 -2.346e-06 asc_air_interaction_female -3.564e-06 -6.185e-06 asc_rail_interaction_female -8.446e-07 -1.339e-06 b_tt_car 2.444e-07 2.164e-07 b_tt_bus 2.164e-07 7.627e-07 b_tt_air 1.982e-07 3.322e-07 b_tt_rail 7.973e-08 1.305e-07 b_tt_interaction_business 6.553e-08 8.472e-08 b_access 1.885e-07 1.915e-07 b_cost 8.336e-07 1.293e-06 b_cost_interaction_business -3.886e-07 -6.616e-07 cost_income_elast -1.228e-06 -8.222e-07 b_wifi -1.237e-05 -1.743e-05 b_food -5.782e-06 -8.713e-06 mu_SP 4.024e-05 6.321e-05 b_tt_air b_tt_rail asc_bus -8.534e-06 6.559e-06 asc_air -1.5056e-04 2.669e-06 asc_rail 1.705e-05 -9.768e-05 asc_bus_interaction_female -1.926e-07 -2.316e-06 asc_air_interaction_female -3.530e-06 1.296e-06 asc_rail_interaction_female 6.661e-07 8.443e-07 b_tt_car 1.982e-07 7.973e-08 b_tt_bus 3.322e-07 1.305e-07 b_tt_air 2.051e-06 1.226e-07 b_tt_rail 1.226e-07 8.011e-07 b_tt_interaction_business 9.334e-08 3.721e-09 b_access 9.207e-07 2.157e-08 b_cost 1.553e-06 7.472e-07 b_cost_interaction_business -5.472e-07 -4.634e-07 cost_income_elast -7.565e-06 -2.642e-06 b_wifi -2.323e-05 -1.044e-05 b_food -1.243e-05 -5.420e-06 mu_SP 7.434e-05 2.822e-05 b_tt_interaction_business b_access asc_bus 5.486e-06 2.717e-05 asc_air 7.260e-06 -1.2538e-04 asc_rail 1.816e-05 1.245e-05 asc_bus_interaction_female -6.539e-07 -9.228e-06 asc_air_interaction_female -1.390e-06 -8.320e-06 asc_rail_interaction_female -4.422e-07 -3.268e-06 b_tt_car 6.553e-08 1.885e-07 b_tt_bus 8.472e-08 1.915e-07 b_tt_air 9.334e-08 9.207e-07 b_tt_rail 3.721e-09 2.157e-08 b_tt_interaction_business 1.217e-07 1.473e-07 b_access 1.473e-07 2.137e-06 b_cost 3.395e-07 1.505e-06 b_cost_interaction_business 4.806e-08 -4.580e-07 cost_income_elast -8.517e-07 -6.375e-06 b_wifi -7.312e-06 -2.028e-05 b_food -3.330e-06 -9.870e-06 mu_SP 2.429e-05 7.776e-05 b_cost b_cost_interaction_business asc_bus 1.377e-05 1.303e-05 asc_air -2.217e-07 -1.872e-05 asc_rail 8.272e-05 -1.823e-05 asc_bus_interaction_female -2.400e-05 1.376e-05 asc_air_interaction_female -2.312e-05 1.384e-05 asc_rail_interaction_female -9.114e-06 7.037e-06 b_tt_car 8.336e-07 -3.886e-07 b_tt_bus 1.293e-06 -6.616e-07 b_tt_air 1.553e-06 -5.472e-07 b_tt_rail 7.472e-07 -4.634e-07 b_tt_interaction_business 3.395e-07 4.806e-08 b_access 1.505e-06 -4.580e-07 b_cost 5.902e-06 -2.905e-06 b_cost_interaction_business -2.905e-06 2.405e-06 cost_income_elast -1.972e-05 4.749e-06 b_wifi -7.901e-05 3.117e-05 b_food -3.657e-05 1.407e-05 mu_SP 2.7177e-04 -1.1561e-04 cost_income_elast b_wifi asc_bus -4.2750e-04 -7.8215e-04 asc_air 7.8995e-04 -6.3740e-04 asc_rail 1.8748e-04 -0.001828 asc_bus_interaction_female 1.0454e-04 2.8999e-04 asc_air_interaction_female 1.3036e-04 2.4311e-04 asc_rail_interaction_female 9.328e-05 1.0166e-04 b_tt_car -1.228e-06 -1.237e-05 b_tt_bus -8.222e-07 -1.743e-05 b_tt_air -7.565e-06 -2.323e-05 b_tt_rail -2.642e-06 -1.044e-05 b_tt_interaction_business -8.517e-07 -7.312e-06 b_access -6.375e-06 -2.028e-05 b_cost -1.972e-05 -7.901e-05 b_cost_interaction_business 4.749e-06 3.117e-05 cost_income_elast 8.8564e-04 1.8853e-04 b_wifi 1.8853e-04 0.001900 b_food 6.013e-05 9.1015e-04 mu_SP -5.6825e-04 -0.004061 b_food mu_SP asc_bus -1.2720e-04 8.8345e-04 asc_air -3.2754e-04 4.5488e-04 asc_rail -9.4214e-04 0.005331 asc_bus_interaction_female 2.4406e-04 -0.001071 asc_air_interaction_female 8.897e-05 -9.9880e-04 asc_rail_interaction_female 6.168e-05 -4.0576e-04 b_tt_car -5.782e-06 4.024e-05 b_tt_bus -8.713e-06 6.321e-05 b_tt_air -1.243e-05 7.434e-05 b_tt_rail -5.420e-06 2.822e-05 b_tt_interaction_business -3.330e-06 2.429e-05 b_access -9.870e-06 7.776e-05 b_cost -3.657e-05 2.7177e-04 b_cost_interaction_business 1.407e-05 -1.1561e-04 cost_income_elast 6.013e-05 -5.6825e-04 b_wifi 9.1015e-04 -0.004061 b_food 9.9510e-04 -0.001812 mu_SP -0.001812 0.015099 Classical correlation matrix: asc_bus asc_air asc_bus 1.000000 0.16859 asc_air 0.168585 1.00000 asc_rail 0.154912 0.46390 asc_bus_interaction_female -0.132496 -0.04792 asc_air_interaction_female -0.024521 -0.13371 asc_rail_interaction_female -0.033651 -0.06944 b_tt_car 0.174179 0.48830 b_tt_bus -0.713579 0.14499 b_tt_air -0.010681 -0.61568 b_tt_rail 0.009429 0.05922 b_tt_interaction_business 0.015913 0.08726 b_access -0.017797 -0.47984 b_cost 0.001917 0.05415 b_cost_interaction_business 0.019106 -0.10508 cost_income_elast -0.050310 0.11542 b_wifi -0.004658 -0.14871 b_food -0.006406 -0.11020 mu_SP -0.002887 0.09469 asc_rail asc_bus_interaction_female asc_bus 0.15491 -0.13250 asc_air 0.46390 -0.04792 asc_rail 1.00000 -0.07604 asc_bus_interaction_female -0.07604 1.00000 asc_air_interaction_female -0.10521 0.28094 asc_rail_interaction_female -0.14579 0.31510 b_tt_car 0.63287 -0.12588 b_tt_bus 0.24839 -0.08820 b_tt_air 0.07274 -0.06430 b_tt_rail -0.61421 -0.05010 b_tt_interaction_business 0.22607 -0.08147 b_access 0.07666 -0.06225 b_cost 0.23903 -0.16737 b_cost_interaction_business -0.14734 0.12845 cost_income_elast 0.03755 -0.03354 b_wifi -0.27469 0.13170 b_food -0.20837 0.08024 mu_SP 0.28799 -0.16929 asc_air_interaction_female asc_rail_interaction_female asc_bus -0.02452 -0.03365 asc_air -0.13371 -0.06944 asc_rail -0.10521 -0.14579 asc_bus_interaction_female 0.28094 0.31510 asc_air_interaction_female 1.00000 0.53187 asc_rail_interaction_female 0.53187 1.00000 b_tt_car -0.13198 -0.12207 b_tt_bus -0.11148 -0.10006 b_tt_air -0.06242 -0.06676 b_tt_rail -0.04527 -0.04307 b_tt_interaction_business -0.10551 -0.09274 b_access -0.07741 -0.07816 b_cost -0.16648 -0.15551 b_cost_interaction_business 0.09938 0.09843 cost_income_elast 0.01012 0.01001 b_wifi 0.13975 0.12568 b_food 0.08784 0.07623 mu_SP -0.17151 -0.16064 b_tt_car b_tt_bus asc_bus 0.17418 -0.71358 asc_air 0.48830 0.14499 asc_rail 0.63287 0.24839 asc_bus_interaction_female -0.12588 -0.08820 asc_air_interaction_female -0.13198 -0.11148 asc_rail_interaction_female -0.12207 -0.10006 b_tt_car 1.00000 0.52585 b_tt_bus 0.52585 1.00000 b_tt_air 0.23981 0.21186 b_tt_rail 0.17703 0.16429 b_tt_interaction_business 0.33439 0.27556 b_access 0.26380 0.20160 b_cost 0.73710 0.60894 b_cost_interaction_business -0.53392 -0.45431 cost_income_elast -0.05057 0.02130 b_wifi -0.61609 -0.49658 b_food -0.38923 -0.30778 mu_SP 0.71142 0.60345 b_tt_air b_tt_rail asc_bus -0.01068 0.009429 asc_air -0.61568 0.059215 asc_rail 0.07274 -0.614210 asc_bus_interaction_female -0.06430 -0.050098 asc_air_interaction_female -0.06242 -0.045274 asc_rail_interaction_female -0.06676 -0.043071 b_tt_car 0.23981 0.177029 b_tt_bus 0.21186 0.164286 b_tt_air 1.00000 0.047894 b_tt_rail 0.04789 1.000000 b_tt_interaction_business 0.16781 0.053989 b_access 0.43305 -0.015889 b_cost 0.40719 0.331122 b_cost_interaction_business -0.22403 -0.259090 cost_income_elast -0.12302 -0.070052 b_wifi -0.29941 -0.262296 b_food -0.20807 -0.161719 mu_SP 0.36689 0.260987 b_tt_interaction_business b_access asc_bus 0.01591 -0.01780 asc_air 0.08726 -0.47984 asc_rail 0.22607 0.07666 asc_bus_interaction_female -0.08147 -0.06225 asc_air_interaction_female -0.10551 -0.07741 asc_rail_interaction_female -0.09274 -0.07816 b_tt_car 0.33439 0.26380 b_tt_bus 0.27556 0.20160 b_tt_air 0.16781 0.43305 b_tt_rail 0.05399 -0.01589 b_tt_interaction_business 1.00000 0.25974 b_access 0.25974 1.00000 b_cost 0.38604 0.39881 b_cost_interaction_business 0.18131 -0.17962 cost_income_elast -0.01801 -0.09858 b_wifi -0.45447 -0.32844 b_food -0.28001 -0.21597 mu_SP 0.54207 0.40146 b_cost b_cost_interaction_business asc_bus 0.001917 0.01911 asc_air 0.054147 -0.10508 asc_rail 0.239033 -0.14734 asc_bus_interaction_female -0.167373 0.12845 asc_air_interaction_female -0.166481 0.09938 asc_rail_interaction_female -0.155507 0.09843 b_tt_car 0.737099 -0.53392 b_tt_bus 0.608943 -0.45431 b_tt_air 0.407190 -0.22403 b_tt_rail 0.331122 -0.25909 b_tt_interaction_business 0.386040 0.18131 b_access 0.398811 -0.17962 b_cost 1.000000 -0.73463 b_cost_interaction_business -0.734632 1.00000 cost_income_elast -0.183097 0.04959 b_wifi -0.746431 0.43963 b_food -0.469363 0.27030 mu_SP 0.910736 -0.58029 cost_income_elast b_wifi asc_bus -0.05031 -0.004658 asc_air 0.11542 -0.148712 asc_rail 0.03755 -0.274688 asc_bus_interaction_female -0.03354 0.131697 asc_air_interaction_female 0.01012 0.139745 asc_rail_interaction_female 0.01001 0.125677 b_tt_car -0.05057 -0.616092 b_tt_bus 0.02130 -0.496584 b_tt_air -0.12302 -0.299408 b_tt_rail -0.07005 -0.262296 b_tt_interaction_business -0.01801 -0.454475 b_access -0.09858 -0.328438 b_cost -0.18310 -0.746431 b_cost_interaction_business 0.04959 0.439634 cost_income_elast 1.00000 0.075286 b_wifi 0.07529 1.000000 b_food 0.06398 0.665903 mu_SP -0.04279 -0.766368 b_food mu_SP asc_bus -0.006406 -0.002887 asc_air -0.110196 0.094687 asc_rail -0.208373 0.287993 asc_bus_interaction_female 0.080236 -0.169291 asc_air_interaction_female 0.087844 -0.171513 asc_rail_interaction_female 0.076234 -0.160644 b_tt_car -0.389232 0.711416 b_tt_bus -0.307775 0.603448 b_tt_air -0.208073 0.366891 b_tt_rail -0.161719 0.260987 b_tt_interaction_business -0.280007 0.542068 b_access -0.215969 0.401460 b_cost -0.469363 0.910736 b_cost_interaction_business 0.270299 -0.580288 cost_income_elast 0.063984 -0.042795 b_wifi 0.665903 -0.766368 b_food 1.000000 -0.474419 mu_SP -0.474419 1.000000 Robust correlation matrix: asc_bus asc_air asc_bus 1.000000 0.18403 asc_air 0.184026 1.00000 asc_rail 0.181908 0.49606 asc_bus_interaction_female -0.170711 -0.03503 asc_air_interaction_female 0.002257 -0.12602 asc_rail_interaction_female -0.049597 -0.07891 b_tt_car 0.229442 0.48560 b_tt_bus -0.685605 0.12277 b_tt_air -0.022740 -0.59126 b_tt_rail 0.027965 0.01677 b_tt_interaction_business 0.060010 0.11706 b_access 0.070940 -0.48248 b_cost 0.021633 -5.1324e-04 b_cost_interaction_business 0.032059 -0.06790 cost_income_elast -0.054823 0.14931 b_wifi -0.068473 -0.08224 b_food -0.015389 -0.05841 mu_SP 0.027438 0.02082 asc_rail asc_bus_interaction_female asc_bus 0.18191 -0.170711 asc_air 0.49606 -0.035029 asc_rail 1.00000 -0.052999 asc_bus_interaction_female -0.05300 1.000000 asc_air_interaction_female -0.17051 0.299951 asc_rail_interaction_female -0.13404 0.379959 b_tt_car 0.62955 -0.082703 b_tt_bus 0.22625 -0.037624 b_tt_air 0.06706 -0.001883 b_tt_rail -0.61472 -0.036232 b_tt_interaction_business 0.29327 -0.026249 b_access 0.04797 -0.088419 b_cost 0.19179 -0.138376 b_cost_interaction_business -0.06621 0.124244 cost_income_elast 0.03549 0.049195 b_wifi -0.23621 0.093158 b_food -0.16824 0.108351 mu_SP 0.24437 -0.122010 asc_air_interaction_female asc_rail_interaction_female asc_bus 0.002257 -0.04960 asc_air -0.126015 -0.07891 asc_rail -0.170510 -0.13404 asc_bus_interaction_female 0.299951 0.37996 asc_air_interaction_female 1.000000 0.62748 asc_rail_interaction_female 0.627478 1.00000 b_tt_car -0.152216 -0.04447 b_tt_bus -0.149560 -0.03990 b_tt_air -0.052042 0.01211 b_tt_rail 0.030575 0.02456 b_tt_interaction_business -0.084162 -0.03300 b_access -0.120203 -0.05820 b_cost -0.200960 -0.09766 b_cost_interaction_business 0.188525 0.11813 cost_income_elast 0.092510 0.08160 b_wifi 0.117772 0.06071 b_food 0.059565 0.05090 mu_SP -0.171659 -0.08596 b_tt_car b_tt_bus asc_bus 0.22944 -0.68560 asc_air 0.48560 0.12277 asc_rail 0.62955 0.22625 asc_bus_interaction_female -0.08270 -0.03762 asc_air_interaction_female -0.15222 -0.14956 asc_rail_interaction_female -0.04447 -0.03990 b_tt_car 1.00000 0.50114 b_tt_bus 0.50114 1.00000 b_tt_air 0.27991 0.26555 b_tt_rail 0.18016 0.16690 b_tt_interaction_business 0.37990 0.27808 b_access 0.26089 0.14998 b_cost 0.69402 0.60955 b_cost_interaction_business -0.50681 -0.48846 cost_income_elast -0.08348 -0.03164 b_wifi -0.57373 -0.45787 b_food -0.37069 -0.31627 mu_SP 0.66235 0.58906 b_tt_air b_tt_rail asc_bus -0.022740 0.02796 asc_air -0.591263 0.01677 asc_rail 0.067061 -0.61472 asc_bus_interaction_female -0.001883 -0.03623 asc_air_interaction_female -0.052042 0.03057 asc_rail_interaction_female 0.012107 0.02456 b_tt_car 0.279910 0.18016 b_tt_bus 0.265548 0.16690 b_tt_air 1.000000 0.09566 b_tt_rail 0.095663 1.00000 b_tt_interaction_business 0.186809 0.01192 b_access 0.439764 0.01649 b_cost 0.446438 0.34363 b_cost_interaction_business -0.246321 -0.33381 cost_income_elast -0.177486 -0.09919 b_wifi -0.372084 -0.26758 b_food -0.275026 -0.19195 mu_SP 0.422399 0.25661 b_tt_interaction_business b_access asc_bus 0.06001 0.07094 asc_air 0.11706 -0.48248 asc_rail 0.29327 0.04797 asc_bus_interaction_female -0.02625 -0.08842 asc_air_interaction_female -0.08416 -0.12020 asc_rail_interaction_female -0.03300 -0.05820 b_tt_car 0.37990 0.26089 b_tt_bus 0.27808 0.14998 b_tt_air 0.18681 0.43976 b_tt_rail 0.01192 0.01649 b_tt_interaction_business 1.00000 0.28892 b_access 0.28892 1.00000 b_cost 0.40062 0.42396 b_cost_interaction_business 0.08883 -0.20205 cost_income_elast -0.08203 -0.14655 b_wifi -0.48076 -0.31826 b_food -0.30257 -0.21406 mu_SP 0.56654 0.43295 b_cost b_cost_interaction_business asc_bus 0.02163 0.03206 asc_air -5.1324e-04 -0.06790 asc_rail 0.19179 -0.06621 asc_bus_interaction_female -0.13838 0.12424 asc_air_interaction_female -0.20096 0.18853 asc_rail_interaction_female -0.09766 0.11813 b_tt_car 0.69402 -0.50681 b_tt_bus 0.60955 -0.48846 b_tt_air 0.44644 -0.24632 b_tt_rail 0.34363 -0.33381 b_tt_interaction_business 0.40062 0.08883 b_access 0.42396 -0.20205 b_cost 1.00000 -0.77088 b_cost_interaction_business -0.77088 1.00000 cost_income_elast -0.27275 0.10290 b_wifi -0.74602 0.46104 b_food -0.47721 0.28763 mu_SP 0.91038 -0.60666 cost_income_elast b_wifi asc_bus -0.05482 -0.06847 asc_air 0.14931 -0.08224 asc_rail 0.03549 -0.23621 asc_bus_interaction_female 0.04919 0.09316 asc_air_interaction_female 0.09251 0.11777 asc_rail_interaction_female 0.08160 0.06071 b_tt_car -0.08348 -0.57373 b_tt_bus -0.03164 -0.45787 b_tt_air -0.17749 -0.37208 b_tt_rail -0.09919 -0.26758 b_tt_interaction_business -0.08203 -0.48076 b_access -0.14655 -0.31826 b_cost -0.27275 -0.74602 b_cost_interaction_business 0.10290 0.46104 cost_income_elast 1.00000 0.14532 b_wifi 0.14532 1.00000 b_food 0.06405 0.66184 mu_SP -0.15539 -0.75812 b_food mu_SP asc_bus -0.01539 0.02744 asc_air -0.05841 0.02082 asc_rail -0.16824 0.24437 asc_bus_interaction_female 0.10835 -0.12201 asc_air_interaction_female 0.05957 -0.17166 asc_rail_interaction_female 0.05090 -0.08596 b_tt_car -0.37069 0.66235 b_tt_bus -0.31627 0.58906 b_tt_air -0.27503 0.42240 b_tt_rail -0.19195 0.25661 b_tt_interaction_business -0.30257 0.56654 b_access -0.21406 0.43295 b_cost -0.47721 0.91038 b_cost_interaction_business 0.28763 -0.60666 cost_income_elast 0.06405 -0.15539 b_wifi 0.66184 -0.75812 b_food 1.00000 -0.46737 mu_SP -0.46737 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 146 0.2438954 400 0.2445125 317 0.2531967 464 0.2568683 186 0.2583054 293 0.2618956 181 0.2699403 441 0.2742193 307 0.2763105 276 0.2766698 259 0.2782719 498 0.2822857 367 0.2831478 434 0.2836230 227 0.2838150 142 0.2982998 447 0.3007373 23 0.3025851 147 0.3083391 86 0.3094483 Settings and functions used in model definition: apollo_control -------------- Value modelName "MNL_RP_SP" modelDescr "RP-SP model on mode choice data" indivID "ID" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian --------------------------------- Value asc_bus 0.124830089 asc_air 0.396088246 asc_rail 0.978686596 asc_bus_interaction_female 0.181339360 asc_air_interaction_female 0.134504527 asc_rail_interaction_female 0.098188773 b_tt_car 0.006424539 b_tt_bus 0.010506872 b_tt_air 0.008667767 b_tt_rail 0.003837876 b_tt_interaction_business 0.003202836 b_access 0.010545292 b_cost 0.038233932 b_cost_interaction_business 0.016656558 cost_income_elast 0.613149706 b_wifi 0.523123794 b_food 0.220073504 mu_SP 1.994743794 apollo_probabilities ---------------------- function(apollo_beta, apollo_inputs, functionality="estimate"){ ### Attach inputs and detach after function exit apollo_attach(apollo_beta, apollo_inputs) on.exit(apollo_detach(apollo_beta, apollo_inputs)) ### Create list of probabilities P P = list() ### Create alternative specific constants and coefficients using interactions with socio-demographics asc_bus_value = asc_bus + asc_bus_interaction_female * female asc_air_value = asc_air + asc_air_interaction_female * female asc_rail_value = asc_rail + asc_rail_interaction_female * female b_tt_car_value = b_tt_car + b_tt_interaction_business * business b_tt_bus_value = b_tt_bus + b_tt_interaction_business * business b_tt_air_value = b_tt_air + b_tt_interaction_business * business b_tt_rail_value = b_tt_rail + b_tt_interaction_business * business b_cost_value = ( b_cost + b_cost_interaction_business * business ) * ( income / mean_income ) ^ cost_income_elast ### List of utilities (before applying scales): these must use the same names as in mnl_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 ) ### Compute probabilities for the RP part of the data using MNL model mnl_settings_RP = 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 = list(car = mu_RP*V[["car"]], bus = mu_RP*V[["bus"]], air = mu_RP*V[["air"]], rail = mu_RP*V[["rail"]]), rows = (RP==1) ) P[["RP"]] = apollo_mnl(mnl_settings_RP, functionality) ### Compute probabilities for the SP part of the data using MNL model mnl_settings_SP = 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 = list(car = mu_SP*V[["car"]], bus = mu_SP*V[["bus"]], air = mu_SP*V[["air"]], rail = mu_SP*V[["rail"]]), rows = (SP==1) ) P[["SP"]] = apollo_mnl(mnl_settings_SP, functionality) ### Combined model P = apollo_combineModels(P, apollo_inputs, 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) }