Model run by stephane.hess using Apollo 0.3.4 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 : MNL_RP_SP Model description : RP-SP model on mode choice data Model run at : 2024-09-27 15:30:52.334228 Estimation method : bgw Model 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) : 00:00:4.29 pre-estimation : 00:00:0.86 estimation : 00:00:0.6 post-estimation : 00:00:2.84 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_shift_female 0.181339 0.064656 2.8047 0.071405 2.5396 asc_air_shift_female 0.134505 0.045471 2.9580 0.047351 2.8406 asc_rail_shift_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_shift_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_shift_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_rail asc_bus 0.078983 0.008702 0.007860 asc_air 0.008702 0.033731 0.015382 asc_rail 0.007860 0.015382 0.032596 asc_bus_shift_female -0.002408 -5.6910e-04 -8.8764e-04 asc_air_shift_female -3.1336e-04 -0.001117 -8.6370e-04 asc_rail_shift_female -3.4655e-04 -4.6732e-04 -9.6450e-04 b_tt_car 2.494e-05 4.568e-05 5.821e-05 b_tt_bus -1.9274e-04 2.559e-05 4.310e-05 b_tt_air -4.400e-06 -1.6574e-04 1.925e-05 b_tt_rail 2.440e-06 1.001e-05 -1.0210e-04 b_tt_shift_business 1.549e-06 5.553e-06 1.414e-05 b_access -7.660e-06 -1.3496e-04 2.120e-05 b_cost 1.326e-06 2.447e-05 1.0621e-04 b_cost_shift_business 8.776e-06 -3.154e-05 -4.348e-05 cost_income_elast -4.1292e-04 6.1905e-04 1.9800e-04 b_wifi -5.635e-05 -0.001176 -0.002135 b_food -5.551e-05 -6.2408e-04 -0.001160 mu_SP -1.0255e-04 0.002198 0.006573 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.002408 -3.1336e-04 -3.4655e-04 asc_air -5.6910e-04 -0.001117 -4.6732e-04 asc_rail -8.8764e-04 -8.6370e-04 -9.6450e-04 asc_bus_shift_female 0.004180 8.2596e-04 7.4655e-04 asc_air_shift_female 8.2596e-04 0.002068 8.8623e-04 asc_rail_shift_female 7.4655e-04 8.8623e-04 0.001343 b_tt_car -4.146e-06 -3.057e-06 -2.279e-06 b_tt_bus -5.481e-06 -4.872e-06 -3.524e-06 b_tt_air -6.093e-06 -4.160e-06 -3.586e-06 b_tt_rail -2.982e-06 -1.895e-06 -1.453e-06 b_tt_shift_business -1.825e-06 -1.662e-06 -1.177e-06 b_access -6.164e-06 -5.391e-06 -4.386e-06 b_cost -2.663e-05 -1.863e-05 -1.402e-05 b_cost_shift_business 1.357e-05 7.386e-06 5.895e-06 cost_income_elast -6.333e-05 1.343e-05 1.071e-05 b_wifi 3.6652e-04 2.7352e-04 1.9823e-04 b_food 1.5997e-04 1.2317e-04 8.614e-05 mu_SP -0.001384 -9.8585e-04 -7.4411e-04 b_tt_car b_tt_bus b_tt_air asc_bus 2.494e-05 -1.9274e-04 -4.400e-06 asc_air 4.568e-05 2.559e-05 -1.6574e-04 asc_rail 5.821e-05 4.310e-05 1.925e-05 asc_bus_shift_female -4.146e-06 -5.481e-06 -6.093e-06 asc_air_shift_female -3.057e-06 -4.872e-06 -4.160e-06 asc_rail_shift_female -2.279e-06 -3.524e-06 -3.586e-06 b_tt_car 2.595e-07 2.575e-07 1.791e-07 b_tt_bus 2.575e-07 9.237e-07 2.984e-07 b_tt_air 1.791e-07 2.984e-07 2.148e-06 b_tt_rail 8.303e-08 1.454e-07 6.463e-08 b_tt_shift_business 5.902e-08 9.176e-08 8.522e-08 b_access 2.058e-07 2.967e-07 9.720e-07 b_cost 9.241e-07 1.440e-06 1.469e-06 b_cost_shift_business -4.445e-07 -7.136e-07 -5.367e-07 cost_income_elast -7.524e-07 5.979e-07 -5.266e-06 b_wifi -1.351e-05 -2.054e-05 -1.889e-05 b_food -6.114e-06 -9.121e-06 -9.404e-06 mu_SP 4.581e-05 7.331e-05 6.798e-05 b_tt_rail b_tt_shift_business b_access asc_bus 2.440e-06 1.549e-06 -7.660e-06 asc_air 1.001e-05 5.553e-06 -1.3496e-04 asc_rail -1.0210e-04 1.414e-05 2.120e-05 asc_bus_shift_female -2.982e-06 -1.825e-06 -6.164e-06 asc_air_shift_female -1.895e-06 -1.662e-06 -5.391e-06 asc_rail_shift_female -1.453e-06 -1.177e-06 -4.386e-06 b_tt_car 8.303e-08 5.902e-08 2.058e-07 b_tt_bus 1.454e-07 9.176e-08 2.967e-07 b_tt_air 6.463e-08 8.522e-08 9.720e-07 b_tt_rail 8.478e-07 1.722e-08 -2.241e-08 b_tt_shift_business 1.722e-08 1.200e-07 1.378e-07 b_access -2.241e-08 1.378e-07 2.345e-06 b_cost 7.503e-07 3.292e-07 1.503e-06 b_cost_shift_business -3.899e-07 1.027e-07 -4.496e-07 cost_income_elast -1.884e-06 -1.823e-07 -4.409e-06 b_wifi -1.040e-05 -6.778e-06 -2.165e-05 b_food -4.592e-06 -2.992e-06 -1.020e-05 mu_SP 3.038e-05 2.374e-05 7.772e-05 b_cost b_cost_shift_business cost_income_elast asc_bus 1.326e-06 8.776e-06 -4.1292e-04 asc_air 2.447e-05 -3.154e-05 6.1905e-04 asc_rail 1.0621e-04 -4.348e-05 1.9800e-04 asc_bus_shift_female -2.663e-05 1.357e-05 -6.333e-05 asc_air_shift_female -1.863e-05 7.386e-06 1.343e-05 asc_rail_shift_female -1.402e-05 5.895e-06 1.071e-05 b_tt_car 9.241e-07 -4.445e-07 -7.524e-07 b_tt_bus 1.440e-06 -7.136e-07 5.979e-07 b_tt_air 1.469e-06 -5.367e-07 -5.266e-06 b_tt_rail 7.503e-07 -3.899e-07 -1.884e-06 b_tt_shift_business 3.292e-07 1.027e-07 -1.823e-07 b_access 1.503e-06 -4.496e-07 -4.409e-06 b_cost 6.057e-06 -2.955e-06 -1.316e-05 b_cost_shift_business -2.955e-06 2.671e-06 2.367e-06 cost_income_elast -1.316e-05 2.367e-06 8.5287e-04 b_wifi -7.907e-05 3.093e-05 9.464e-05 b_food -3.562e-05 1.362e-05 5.762e-05 mu_SP 2.8332e-04 -1.1989e-04 -1.5798e-04 b_wifi b_food mu_SP asc_bus -5.635e-05 -5.551e-05 -1.0255e-04 asc_air -0.001176 -6.2408e-04 0.002198 asc_rail -0.002135 -0.001160 0.006573 asc_bus_shift_female 3.6652e-04 1.5997e-04 -0.001384 asc_air_shift_female 2.7352e-04 1.2317e-04 -9.8585e-04 asc_rail_shift_female 1.9823e-04 8.614e-05 -7.4411e-04 b_tt_car -1.351e-05 -6.114e-06 4.581e-05 b_tt_bus -2.054e-05 -9.121e-06 7.331e-05 b_tt_air -1.889e-05 -9.404e-06 6.798e-05 b_tt_rail -1.040e-05 -4.592e-06 3.038e-05 b_tt_shift_business -6.778e-06 -2.992e-06 2.374e-05 b_access -2.165e-05 -1.020e-05 7.772e-05 b_cost -7.907e-05 -3.562e-05 2.8332e-04 b_cost_shift_business 3.093e-05 1.362e-05 -1.1989e-04 cost_income_elast 9.464e-05 5.762e-05 -1.5798e-04 b_wifi 0.001853 8.8386e-04 -0.004170 b_food 8.8386e-04 9.5086e-04 -0.001849 mu_SP -0.004170 -0.001849 0.015979 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus 0.068659 0.008573 0.008462 asc_air 0.008573 0.031606 0.015656 asc_rail 0.008462 0.015656 0.031515 asc_bus_shift_female -0.003194 -4.4468e-04 -6.7182e-04 asc_air_shift_female 2.800e-05 -0.001061 -0.001433 asc_rail_shift_female -4.9922e-04 -5.3889e-04 -9.1404e-04 b_tt_car 2.972e-05 4.268e-05 5.526e-05 b_tt_bus -1.5689e-04 1.906e-05 3.508e-05 b_tt_air -8.534e-06 -1.5056e-04 1.705e-05 b_tt_rail 6.559e-06 2.669e-06 -9.768e-05 b_tt_shift_business 5.486e-06 7.260e-06 1.816e-05 b_access 2.717e-05 -1.2538e-04 1.245e-05 b_cost 1.377e-05 -2.217e-07 8.272e-05 b_cost_shift_business 1.303e-05 -1.872e-05 -1.823e-05 cost_income_elast -4.2750e-04 7.8995e-04 1.8748e-04 b_wifi -7.8215e-04 -6.3740e-04 -0.001828 b_food -1.2720e-04 -3.2754e-04 -9.4214e-04 mu_SP 8.8345e-04 4.5488e-04 0.005331 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.003194 2.800e-05 -4.9922e-04 asc_air -4.4468e-04 -0.001061 -5.3889e-04 asc_rail -6.7182e-04 -0.001433 -9.1404e-04 asc_bus_shift_female 0.005099 0.001014 0.001042 asc_air_shift_female 0.001014 0.002242 0.001141 asc_rail_shift_female 0.001042 0.001141 0.001476 b_tt_car -2.920e-06 -3.564e-06 -8.446e-07 b_tt_bus -2.346e-06 -6.185e-06 -1.339e-06 b_tt_air -1.926e-07 -3.530e-06 6.661e-07 b_tt_rail -2.316e-06 1.296e-06 8.443e-07 b_tt_shift_business -6.539e-07 -1.390e-06 -4.422e-07 b_access -9.228e-06 -8.320e-06 -3.268e-06 b_cost -2.400e-05 -2.312e-05 -9.114e-06 b_cost_shift_business 1.376e-05 1.384e-05 7.037e-06 cost_income_elast 1.0454e-04 1.3036e-04 9.328e-05 b_wifi 2.8999e-04 2.4311e-04 1.0166e-04 b_food 2.4406e-04 8.897e-05 6.168e-05 mu_SP -0.001071 -9.9880e-04 -4.0576e-04 b_tt_car b_tt_bus b_tt_air asc_bus 2.972e-05 -1.5689e-04 -8.534e-06 asc_air 4.268e-05 1.906e-05 -1.5056e-04 asc_rail 5.526e-05 3.508e-05 1.705e-05 asc_bus_shift_female -2.920e-06 -2.346e-06 -1.926e-07 asc_air_shift_female -3.564e-06 -6.185e-06 -3.530e-06 asc_rail_shift_female -8.446e-07 -1.339e-06 6.661e-07 b_tt_car 2.444e-07 2.164e-07 1.982e-07 b_tt_bus 2.164e-07 7.627e-07 3.322e-07 b_tt_air 1.982e-07 3.322e-07 2.051e-06 b_tt_rail 7.973e-08 1.305e-07 1.226e-07 b_tt_shift_business 6.553e-08 8.472e-08 9.334e-08 b_access 1.885e-07 1.915e-07 9.207e-07 b_cost 8.336e-07 1.293e-06 1.553e-06 b_cost_shift_business -3.886e-07 -6.616e-07 -5.472e-07 cost_income_elast -1.228e-06 -8.222e-07 -7.565e-06 b_wifi -1.237e-05 -1.743e-05 -2.323e-05 b_food -5.782e-06 -8.713e-06 -1.243e-05 mu_SP 4.024e-05 6.321e-05 7.434e-05 b_tt_rail b_tt_shift_business b_access asc_bus 6.559e-06 5.486e-06 2.717e-05 asc_air 2.669e-06 7.260e-06 -1.2538e-04 asc_rail -9.768e-05 1.816e-05 1.245e-05 asc_bus_shift_female -2.316e-06 -6.539e-07 -9.228e-06 asc_air_shift_female 1.296e-06 -1.390e-06 -8.320e-06 asc_rail_shift_female 8.443e-07 -4.422e-07 -3.268e-06 b_tt_car 7.973e-08 6.553e-08 1.885e-07 b_tt_bus 1.305e-07 8.472e-08 1.915e-07 b_tt_air 1.226e-07 9.334e-08 9.207e-07 b_tt_rail 8.011e-07 3.721e-09 2.157e-08 b_tt_shift_business 3.721e-09 1.217e-07 1.473e-07 b_access 2.157e-08 1.473e-07 2.137e-06 b_cost 7.472e-07 3.395e-07 1.505e-06 b_cost_shift_business -4.634e-07 4.806e-08 -4.580e-07 cost_income_elast -2.642e-06 -8.517e-07 -6.375e-06 b_wifi -1.044e-05 -7.312e-06 -2.028e-05 b_food -5.420e-06 -3.330e-06 -9.870e-06 mu_SP 2.822e-05 2.429e-05 7.776e-05 b_cost b_cost_shift_business cost_income_elast asc_bus 1.377e-05 1.303e-05 -4.2750e-04 asc_air -2.217e-07 -1.872e-05 7.8995e-04 asc_rail 8.272e-05 -1.823e-05 1.8748e-04 asc_bus_shift_female -2.400e-05 1.376e-05 1.0454e-04 asc_air_shift_female -2.312e-05 1.384e-05 1.3036e-04 asc_rail_shift_female -9.114e-06 7.037e-06 9.328e-05 b_tt_car 8.336e-07 -3.886e-07 -1.228e-06 b_tt_bus 1.293e-06 -6.616e-07 -8.222e-07 b_tt_air 1.553e-06 -5.472e-07 -7.565e-06 b_tt_rail 7.472e-07 -4.634e-07 -2.642e-06 b_tt_shift_business 3.395e-07 4.806e-08 -8.517e-07 b_access 1.505e-06 -4.580e-07 -6.375e-06 b_cost 5.902e-06 -2.905e-06 -1.972e-05 b_cost_shift_business -2.905e-06 2.405e-06 4.749e-06 cost_income_elast -1.972e-05 4.749e-06 8.8564e-04 b_wifi -7.901e-05 3.117e-05 1.8853e-04 b_food -3.657e-05 1.407e-05 6.013e-05 mu_SP 2.7177e-04 -1.1561e-04 -5.6825e-04 b_wifi b_food mu_SP asc_bus -7.8215e-04 -1.2720e-04 8.8345e-04 asc_air -6.3740e-04 -3.2754e-04 4.5488e-04 asc_rail -0.001828 -9.4214e-04 0.005331 asc_bus_shift_female 2.8999e-04 2.4406e-04 -0.001071 asc_air_shift_female 2.4311e-04 8.897e-05 -9.9880e-04 asc_rail_shift_female 1.0166e-04 6.168e-05 -4.0576e-04 b_tt_car -1.237e-05 -5.782e-06 4.024e-05 b_tt_bus -1.743e-05 -8.713e-06 6.321e-05 b_tt_air -2.323e-05 -1.243e-05 7.434e-05 b_tt_rail -1.044e-05 -5.420e-06 2.822e-05 b_tt_shift_business -7.312e-06 -3.330e-06 2.429e-05 b_access -2.028e-05 -9.870e-06 7.776e-05 b_cost -7.901e-05 -3.657e-05 2.7177e-04 b_cost_shift_business 3.117e-05 1.407e-05 -1.1561e-04 cost_income_elast 1.8853e-04 6.013e-05 -5.6825e-04 b_wifi 0.001900 9.1015e-04 -0.004061 b_food 9.1015e-04 9.9510e-04 -0.001812 mu_SP -0.004061 -0.001812 0.015099 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus 1.000000 0.16859 0.15491 asc_air 0.168585 1.00000 0.46390 asc_rail 0.154912 0.46390 1.00000 asc_bus_shift_female -0.132496 -0.04792 -0.07604 asc_air_shift_female -0.024521 -0.13371 -0.10521 asc_rail_shift_female -0.033651 -0.06944 -0.14579 b_tt_car 0.174179 0.48830 0.63287 b_tt_bus -0.713579 0.14499 0.24839 b_tt_air -0.010681 -0.61568 0.07274 b_tt_rail 0.009429 0.05922 -0.61421 b_tt_shift_business 0.015913 0.08726 0.22607 b_access -0.017797 -0.47984 0.07666 b_cost 0.001917 0.05415 0.23903 b_cost_shift_business 0.019106 -0.10508 -0.14734 cost_income_elast -0.050310 0.11542 0.03755 b_wifi -0.004658 -0.14871 -0.27469 b_food -0.006406 -0.11020 -0.20837 mu_SP -0.002887 0.09469 0.28799 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.13250 -0.02452 -0.03365 asc_air -0.04792 -0.13371 -0.06944 asc_rail -0.07604 -0.10521 -0.14579 asc_bus_shift_female 1.00000 0.28094 0.31510 asc_air_shift_female 0.28094 1.00000 0.53187 asc_rail_shift_female 0.31510 0.53187 1.00000 b_tt_car -0.12588 -0.13198 -0.12207 b_tt_bus -0.08820 -0.11148 -0.10006 b_tt_air -0.06430 -0.06242 -0.06676 b_tt_rail -0.05010 -0.04527 -0.04307 b_tt_shift_business -0.08147 -0.10551 -0.09274 b_access -0.06225 -0.07741 -0.07816 b_cost -0.16737 -0.16648 -0.15551 b_cost_shift_business 0.12845 0.09938 0.09843 cost_income_elast -0.03354 0.01012 0.01001 b_wifi 0.13170 0.13975 0.12568 b_food 0.08024 0.08784 0.07623 mu_SP -0.16929 -0.17151 -0.16064 b_tt_car b_tt_bus b_tt_air asc_bus 0.17418 -0.71358 -0.01068 asc_air 0.48830 0.14499 -0.61568 asc_rail 0.63287 0.24839 0.07274 asc_bus_shift_female -0.12588 -0.08820 -0.06430 asc_air_shift_female -0.13198 -0.11148 -0.06242 asc_rail_shift_female -0.12207 -0.10006 -0.06676 b_tt_car 1.00000 0.52585 0.23981 b_tt_bus 0.52585 1.00000 0.21186 b_tt_air 0.23981 0.21186 1.00000 b_tt_rail 0.17703 0.16429 0.04789 b_tt_shift_business 0.33439 0.27556 0.16781 b_access 0.26380 0.20160 0.43305 b_cost 0.73710 0.60894 0.40719 b_cost_shift_business -0.53392 -0.45431 -0.22403 cost_income_elast -0.05057 0.02130 -0.12302 b_wifi -0.61609 -0.49658 -0.29941 b_food -0.38923 -0.30778 -0.20807 mu_SP 0.71142 0.60345 0.36689 b_tt_rail b_tt_shift_business b_access asc_bus 0.009429 0.01591 -0.01780 asc_air 0.059215 0.08726 -0.47984 asc_rail -0.614210 0.22607 0.07666 asc_bus_shift_female -0.050098 -0.08147 -0.06225 asc_air_shift_female -0.045274 -0.10551 -0.07741 asc_rail_shift_female -0.043071 -0.09274 -0.07816 b_tt_car 0.177029 0.33439 0.26380 b_tt_bus 0.164286 0.27556 0.20160 b_tt_air 0.047894 0.16781 0.43305 b_tt_rail 1.000000 0.05399 -0.01589 b_tt_shift_business 0.053989 1.00000 0.25974 b_access -0.015889 0.25974 1.00000 b_cost 0.331122 0.38604 0.39881 b_cost_shift_business -0.259090 0.18131 -0.17962 cost_income_elast -0.070052 -0.01801 -0.09858 b_wifi -0.262296 -0.45447 -0.32844 b_food -0.161719 -0.28001 -0.21597 mu_SP 0.260987 0.54207 0.40146 b_cost b_cost_shift_business cost_income_elast asc_bus 0.001917 0.01911 -0.05031 asc_air 0.054147 -0.10508 0.11542 asc_rail 0.239033 -0.14734 0.03755 asc_bus_shift_female -0.167373 0.12845 -0.03354 asc_air_shift_female -0.166481 0.09938 0.01012 asc_rail_shift_female -0.155507 0.09843 0.01001 b_tt_car 0.737099 -0.53392 -0.05057 b_tt_bus 0.608943 -0.45431 0.02130 b_tt_air 0.407190 -0.22403 -0.12302 b_tt_rail 0.331122 -0.25909 -0.07005 b_tt_shift_business 0.386040 0.18131 -0.01801 b_access 0.398811 -0.17962 -0.09858 b_cost 1.000000 -0.73463 -0.18310 b_cost_shift_business -0.734632 1.00000 0.04959 cost_income_elast -0.183097 0.04959 1.00000 b_wifi -0.746431 0.43963 0.07529 b_food -0.469363 0.27030 0.06398 mu_SP 0.910736 -0.58029 -0.04279 b_wifi b_food mu_SP asc_bus -0.004658 -0.006406 -0.002887 asc_air -0.148712 -0.110196 0.094687 asc_rail -0.274688 -0.208373 0.287993 asc_bus_shift_female 0.131697 0.080236 -0.169291 asc_air_shift_female 0.139745 0.087844 -0.171513 asc_rail_shift_female 0.125677 0.076234 -0.160644 b_tt_car -0.616092 -0.389232 0.711416 b_tt_bus -0.496584 -0.307775 0.603448 b_tt_air -0.299408 -0.208073 0.366891 b_tt_rail -0.262296 -0.161719 0.260987 b_tt_shift_business -0.454475 -0.280007 0.542068 b_access -0.328438 -0.215969 0.401460 b_cost -0.746431 -0.469363 0.910736 b_cost_shift_business 0.439634 0.270299 -0.580288 cost_income_elast 0.075286 0.063984 -0.042795 b_wifi 1.000000 0.665903 -0.766368 b_food 0.665903 1.000000 -0.474419 mu_SP -0.766368 -0.474419 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus 1.000000 0.18403 0.18191 asc_air 0.184026 1.00000 0.49606 asc_rail 0.181908 0.49606 1.00000 asc_bus_shift_female -0.170711 -0.03503 -0.05300 asc_air_shift_female 0.002257 -0.12602 -0.17051 asc_rail_shift_female -0.049597 -0.07891 -0.13404 b_tt_car 0.229442 0.48560 0.62955 b_tt_bus -0.685605 0.12277 0.22625 b_tt_air -0.022740 -0.59126 0.06706 b_tt_rail 0.027965 0.01677 -0.61472 b_tt_shift_business 0.060010 0.11706 0.29327 b_access 0.070940 -0.48248 0.04797 b_cost 0.021633 -5.1324e-04 0.19179 b_cost_shift_business 0.032059 -0.06790 -0.06621 cost_income_elast -0.054823 0.14931 0.03549 b_wifi -0.068473 -0.08224 -0.23621 b_food -0.015389 -0.05841 -0.16824 mu_SP 0.027438 0.02082 0.24437 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.170711 0.002257 -0.04960 asc_air -0.035029 -0.126015 -0.07891 asc_rail -0.052999 -0.170510 -0.13404 asc_bus_shift_female 1.000000 0.299951 0.37996 asc_air_shift_female 0.299951 1.000000 0.62748 asc_rail_shift_female 0.379959 0.627478 1.00000 b_tt_car -0.082703 -0.152216 -0.04447 b_tt_bus -0.037624 -0.149560 -0.03990 b_tt_air -0.001883 -0.052042 0.01211 b_tt_rail -0.036232 0.030575 0.02456 b_tt_shift_business -0.026249 -0.084162 -0.03300 b_access -0.088419 -0.120203 -0.05820 b_cost -0.138376 -0.200960 -0.09766 b_cost_shift_business 0.124244 0.188525 0.11813 cost_income_elast 0.049195 0.092510 0.08160 b_wifi 0.093158 0.117772 0.06071 b_food 0.108351 0.059565 0.05090 mu_SP -0.122010 -0.171659 -0.08596 b_tt_car b_tt_bus b_tt_air asc_bus 0.22944 -0.68560 -0.022740 asc_air 0.48560 0.12277 -0.591263 asc_rail 0.62955 0.22625 0.067061 asc_bus_shift_female -0.08270 -0.03762 -0.001883 asc_air_shift_female -0.15222 -0.14956 -0.052042 asc_rail_shift_female -0.04447 -0.03990 0.012107 b_tt_car 1.00000 0.50114 0.279910 b_tt_bus 0.50114 1.00000 0.265548 b_tt_air 0.27991 0.26555 1.000000 b_tt_rail 0.18016 0.16690 0.095663 b_tt_shift_business 0.37990 0.27808 0.186809 b_access 0.26089 0.14998 0.439764 b_cost 0.69402 0.60955 0.446438 b_cost_shift_business -0.50681 -0.48846 -0.246321 cost_income_elast -0.08348 -0.03164 -0.177486 b_wifi -0.57373 -0.45787 -0.372084 b_food -0.37069 -0.31627 -0.275026 mu_SP 0.66235 0.58906 0.422399 b_tt_rail b_tt_shift_business b_access asc_bus 0.02796 0.06001 0.07094 asc_air 0.01677 0.11706 -0.48248 asc_rail -0.61472 0.29327 0.04797 asc_bus_shift_female -0.03623 -0.02625 -0.08842 asc_air_shift_female 0.03057 -0.08416 -0.12020 asc_rail_shift_female 0.02456 -0.03300 -0.05820 b_tt_car 0.18016 0.37990 0.26089 b_tt_bus 0.16690 0.27808 0.14998 b_tt_air 0.09566 0.18681 0.43976 b_tt_rail 1.00000 0.01192 0.01649 b_tt_shift_business 0.01192 1.00000 0.28892 b_access 0.01649 0.28892 1.00000 b_cost 0.34363 0.40062 0.42396 b_cost_shift_business -0.33381 0.08883 -0.20205 cost_income_elast -0.09919 -0.08203 -0.14655 b_wifi -0.26758 -0.48076 -0.31826 b_food -0.19195 -0.30257 -0.21406 mu_SP 0.25661 0.56654 0.43295 b_cost b_cost_shift_business cost_income_elast asc_bus 0.02163 0.03206 -0.05482 asc_air -5.1324e-04 -0.06790 0.14931 asc_rail 0.19179 -0.06621 0.03549 asc_bus_shift_female -0.13838 0.12424 0.04919 asc_air_shift_female -0.20096 0.18853 0.09251 asc_rail_shift_female -0.09766 0.11813 0.08160 b_tt_car 0.69402 -0.50681 -0.08348 b_tt_bus 0.60955 -0.48846 -0.03164 b_tt_air 0.44644 -0.24632 -0.17749 b_tt_rail 0.34363 -0.33381 -0.09919 b_tt_shift_business 0.40062 0.08883 -0.08203 b_access 0.42396 -0.20205 -0.14655 b_cost 1.00000 -0.77088 -0.27275 b_cost_shift_business -0.77088 1.00000 0.10290 cost_income_elast -0.27275 0.10290 1.00000 b_wifi -0.74602 0.46104 0.14532 b_food -0.47721 0.28763 0.06405 mu_SP 0.91038 -0.60666 -0.15539 b_wifi b_food mu_SP asc_bus -0.06847 -0.01539 0.02744 asc_air -0.08224 -0.05841 0.02082 asc_rail -0.23621 -0.16824 0.24437 asc_bus_shift_female 0.09316 0.10835 -0.12201 asc_air_shift_female 0.11777 0.05957 -0.17166 asc_rail_shift_female 0.06071 0.05090 -0.08596 b_tt_car -0.57373 -0.37069 0.66235 b_tt_bus -0.45787 -0.31627 0.58906 b_tt_air -0.37208 -0.27503 0.42240 b_tt_rail -0.26758 -0.19195 0.25661 b_tt_shift_business -0.48076 -0.30257 0.56654 b_access -0.31826 -0.21406 0.43295 b_cost -0.74602 -0.47721 0.91038 b_cost_shift_business 0.46104 0.28763 -0.60666 cost_income_elast 0.14532 0.06405 -0.15539 b_wifi 1.00000 0.66184 -0.75812 b_food 0.66184 1.00000 -0.46737 mu_SP -0.75812 -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 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000 0.000000 0.000000 asc_bus 0.000 0.124830 0.124830 asc_air 0.000 -0.396088 -0.396088 asc_rail 0.000 -0.978687 -0.978687 asc_bus_shift_female 0.000 0.181339 0.181339 asc_air_shift_female 0.000 0.134505 0.134505 asc_rail_shift_female 0.000 0.098189 0.098189 b_tt_car 0.000 -0.006425 -0.006425 b_tt_bus 0.000 -0.010507 -0.010507 b_tt_air 0.000 -0.008668 -0.008668 b_tt_rail 0.000 -0.003838 -0.003838 b_tt_shift_business 0.000 -0.003203 -0.003203 b_access 0.000 -0.010545 -0.010545 b_cost 0.000 -0.038234 -0.038234 b_cost_shift_business 0.000 0.016657 0.016657 cost_income_elast 0.000 -0.613150 -0.613150 b_no_frills 0.000 0.000000 0.000000 b_wifi 0.000 0.523124 0.523124 b_food 0.000 0.220074 0.220074 mu_RP 1.000 1.000000 0.000000 mu_SP 1.000 1.994744 0.994744 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_shift_female 0.181339360 asc_air_shift_female 0.134504527 asc_rail_shift_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_shift_business 0.003202836 b_access 0.010545292 b_cost 0.038233932 b_cost_shift_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_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 (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) }