Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : MNL_RP_SP Model description : RP-SP model on mode choice data Model run at : 2023-05-10 19:50:01 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -12.02687 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) : 00:00:22.02 pre-estimation : 00:00:3.91 estimation : 00:00:8.92 initial estimation : 00:00:8.61 estimation after rescaling : 00:00:0.31 post-estimation : 00:00:9.2 Iterations : 63 initial estimation : 62 estimation after rescaling : 1 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 0.124860 0.281039 0.4443 0.262026 0.4765 asc_air -0.396083 0.183661 -2.1566 0.177780 -2.2279 asc_rail -0.978683 0.180544 -5.4207 0.177523 -5.5130 asc_bus_shift_female 0.181337 0.064656 2.8046 0.071405 2.5396 asc_air_shift_female 0.134505 0.045471 2.9580 0.047351 2.8406 asc_rail_shift_female 0.098187 0.036644 2.6795 0.038414 2.5561 b_tt_car -0.006424 5.0940e-04 -12.6118 4.9440e-04 -12.9945 b_tt_bus -0.010507 9.6108e-04 -10.9324 8.7332e-04 -12.0310 b_tt_air -0.008668 0.001466 -5.9139 0.001432 -6.0518 b_tt_rail -0.003838 9.2074e-04 -4.1682 8.9505e-04 -4.2878 b_tt_shift_business -0.003203 3.4648e-04 -9.2441 3.4886e-04 -9.1810 b_access -0.010545 0.001531 -6.8858 0.001462 -7.2145 b_cost -0.038234 0.002461 -15.5362 0.002429 -15.7388 b_cost_shift_business 0.016656 0.001634 10.1912 0.001551 10.7401 cost_income_elast -0.613155 0.029204 -20.9956 0.029760 -20.6035 b_no_frills 0.000000 NA NA NA NA b_wifi 0.523122 0.043043 12.1534 0.043593 12.0003 b_food 0.220074 0.030836 7.1369 0.031545 6.9765 mu_RP 1.000000 NA NA NA NA mu_SP 1.994745 0.126405 15.7806 0.122872 16.2343 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_shift_female asc_bus 0.078983 0.008702 0.007860 -0.002408 asc_air 0.008702 0.033731 0.015382 -5.6908e-04 asc_rail 0.007860 0.015382 0.032596 -8.8759e-04 asc_bus_shift_female -0.002408 -5.6908e-04 -8.8759e-04 0.004180 asc_air_shift_female -3.1334e-04 -0.001117 -8.6368e-04 8.2595e-04 asc_rail_shift_female -3.4653e-04 -4.6731e-04 -9.6448e-04 7.4654e-04 b_tt_car 2.494e-05 4.568e-05 5.821e-05 -4.146e-06 b_tt_bus -1.9274e-04 2.559e-05 4.310e-05 -5.481e-06 b_tt_air -4.401e-06 -1.6574e-04 1.925e-05 -6.093e-06 b_tt_rail 2.439e-06 1.001e-05 -1.0210e-04 -2.982e-06 b_tt_shift_business 1.549e-06 5.552e-06 1.414e-05 -1.825e-06 b_access -7.662e-06 -1.3496e-04 2.119e-05 -6.164e-06 b_cost 1.318e-06 2.447e-05 1.0620e-04 -2.663e-05 b_cost_shift_business 8.779e-06 -3.154e-05 -4.348e-05 1.357e-05 cost_income_elast -4.1292e-04 6.1905e-04 1.9801e-04 -6.333e-05 b_wifi -5.624e-05 -0.001176 -0.002135 3.6649e-04 b_food -5.547e-05 -6.2406e-04 -0.001160 1.5996e-04 mu_SP -1.0296e-04 0.002198 0.006572 -0.001384 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -3.1334e-04 -3.4653e-04 2.494e-05 -1.9274e-04 asc_air -0.001117 -4.6731e-04 4.568e-05 2.559e-05 asc_rail -8.6368e-04 -9.6448e-04 5.821e-05 4.310e-05 asc_bus_shift_female 8.2595e-04 7.4654e-04 -4.146e-06 -5.481e-06 asc_air_shift_female 0.002068 8.8623e-04 -3.057e-06 -4.872e-06 asc_rail_shift_female 8.8623e-04 0.001343 -2.278e-06 -3.524e-06 b_tt_car -3.057e-06 -2.278e-06 2.595e-07 2.574e-07 b_tt_bus -4.872e-06 -3.524e-06 2.574e-07 9.237e-07 b_tt_air -4.160e-06 -3.586e-06 1.790e-07 2.984e-07 b_tt_rail -1.895e-06 -1.453e-06 8.303e-08 1.454e-07 b_tt_shift_business -1.662e-06 -1.177e-06 5.902e-08 9.176e-08 b_access -5.390e-06 -4.386e-06 2.058e-07 2.967e-07 b_cost -1.863e-05 -1.402e-05 9.240e-07 1.440e-06 b_cost_shift_business 7.385e-06 5.895e-06 -4.445e-07 -7.136e-07 cost_income_elast 1.343e-05 1.071e-05 -7.524e-07 5.980e-07 b_wifi 2.7351e-04 1.9821e-04 -1.351e-05 -2.054e-05 b_food 1.2317e-04 8.613e-05 -6.114e-06 -9.121e-06 mu_SP -9.8580e-04 -7.4406e-04 4.581e-05 7.331e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -4.401e-06 2.439e-06 1.549e-06 -7.662e-06 asc_air -1.6574e-04 1.001e-05 5.552e-06 -1.3496e-04 asc_rail 1.925e-05 -1.0210e-04 1.414e-05 2.119e-05 asc_bus_shift_female -6.093e-06 -2.982e-06 -1.825e-06 -6.164e-06 asc_air_shift_female -4.160e-06 -1.895e-06 -1.662e-06 -5.390e-06 asc_rail_shift_female -3.586e-06 -1.453e-06 -1.177e-06 -4.386e-06 b_tt_car 1.790e-07 8.303e-08 5.902e-08 2.058e-07 b_tt_bus 2.984e-07 1.454e-07 9.176e-08 2.967e-07 b_tt_air 2.148e-06 6.463e-08 8.522e-08 9.720e-07 b_tt_rail 6.463e-08 8.478e-07 1.722e-08 -2.242e-08 b_tt_shift_business 8.522e-08 1.722e-08 1.200e-07 1.378e-07 b_access 9.720e-07 -2.242e-08 1.378e-07 2.345e-06 b_cost 1.469e-06 7.503e-07 3.292e-07 1.503e-06 b_cost_shift_business -5.366e-07 -3.899e-07 1.027e-07 -4.495e-07 cost_income_elast -5.266e-06 -1.884e-06 -1.823e-07 -4.409e-06 b_wifi -1.889e-05 -1.039e-05 -6.778e-06 -2.165e-05 b_food -9.404e-06 -4.591e-06 -2.992e-06 -1.020e-05 mu_SP 6.797e-05 3.037e-05 2.374e-05 7.771e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 1.318e-06 8.779e-06 -4.1292e-04 -5.624e-05 asc_air 2.447e-05 -3.154e-05 6.1905e-04 -0.001176 asc_rail 1.0620e-04 -4.348e-05 1.9801e-04 -0.002135 asc_bus_shift_female -2.663e-05 1.357e-05 -6.333e-05 3.6649e-04 asc_air_shift_female -1.863e-05 7.385e-06 1.343e-05 2.7351e-04 asc_rail_shift_female -1.402e-05 5.895e-06 1.071e-05 1.9821e-04 b_tt_car 9.240e-07 -4.445e-07 -7.524e-07 -1.351e-05 b_tt_bus 1.440e-06 -7.136e-07 5.980e-07 -2.054e-05 b_tt_air 1.469e-06 -5.366e-07 -5.266e-06 -1.889e-05 b_tt_rail 7.503e-07 -3.899e-07 -1.884e-06 -1.039e-05 b_tt_shift_business 3.292e-07 1.027e-07 -1.823e-07 -6.778e-06 b_access 1.503e-06 -4.495e-07 -4.409e-06 -2.165e-05 b_cost 6.056e-06 -2.955e-06 -1.316e-05 -7.907e-05 b_cost_shift_business -2.955e-06 2.671e-06 2.367e-06 3.093e-05 cost_income_elast -1.316e-05 2.367e-06 8.5288e-04 9.464e-05 b_wifi -7.907e-05 3.093e-05 9.464e-05 0.001853 b_food -3.562e-05 1.362e-05 5.762e-05 8.8383e-04 mu_SP 2.8331e-04 -1.1988e-04 -1.5798e-04 -0.004170 b_food mu_SP asc_bus -5.547e-05 -1.0296e-04 asc_air -6.2406e-04 0.002198 asc_rail -0.001160 0.006572 asc_bus_shift_female 1.5996e-04 -0.001384 asc_air_shift_female 1.2317e-04 -9.8580e-04 asc_rail_shift_female 8.613e-05 -7.4406e-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 6.797e-05 b_tt_rail -4.591e-06 3.037e-05 b_tt_shift_business -2.992e-06 2.374e-05 b_access -1.020e-05 7.771e-05 b_cost -3.562e-05 2.8331e-04 b_cost_shift_business 1.362e-05 -1.1988e-04 cost_income_elast 5.762e-05 -1.5798e-04 b_wifi 8.8383e-04 -0.004170 b_food 9.5085e-04 -0.001849 mu_SP -0.001849 0.015978 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.068658 0.008573 0.008461 -0.003194 asc_air 0.008573 0.031606 0.015656 -4.4465e-04 asc_rail 0.008461 0.015656 0.031514 -6.7174e-04 asc_bus_shift_female -0.003194 -4.4465e-04 -6.7174e-04 0.005099 asc_air_shift_female 2.805e-05 -0.001061 -0.001433 0.001014 asc_rail_shift_female -4.9919e-04 -5.3888e-04 -9.1400e-04 0.001042 b_tt_car 2.972e-05 4.268e-05 5.525e-05 -2.919e-06 b_tt_bus -1.5689e-04 1.906e-05 3.508e-05 -2.346e-06 b_tt_air -8.538e-06 -1.5056e-04 1.705e-05 -1.920e-07 b_tt_rail 6.557e-06 2.668e-06 -9.768e-05 -2.315e-06 b_tt_shift_business 5.485e-06 7.260e-06 1.816e-05 -6.537e-07 b_access 2.717e-05 -1.2538e-04 1.244e-05 -9.227e-06 b_cost 1.376e-05 -2.271e-07 8.270e-05 -2.400e-05 b_cost_shift_business 1.303e-05 -1.872e-05 -1.822e-05 1.376e-05 cost_income_elast -4.2747e-04 7.8997e-04 1.8749e-04 1.0453e-04 b_wifi -7.8195e-04 -6.3732e-04 -0.001828 2.8993e-04 b_food -1.2712e-04 -3.2751e-04 -9.4206e-04 2.4404e-04 mu_SP 8.8275e-04 4.5459e-04 0.005330 -0.001070 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 2.805e-05 -4.9919e-04 2.972e-05 -1.5689e-04 asc_air -0.001061 -5.3888e-04 4.268e-05 1.906e-05 asc_rail -0.001433 -9.1400e-04 5.525e-05 3.508e-05 asc_bus_shift_female 0.001014 0.001042 -2.919e-06 -2.346e-06 asc_air_shift_female 0.002242 0.001141 -3.563e-06 -6.184e-06 asc_rail_shift_female 0.001141 0.001476 -8.443e-07 -1.338e-06 b_tt_car -3.563e-06 -8.443e-07 2.444e-07 2.164e-07 b_tt_bus -6.184e-06 -1.338e-06 2.164e-07 7.627e-07 b_tt_air -3.529e-06 6.664e-07 1.982e-07 3.322e-07 b_tt_rail 1.296e-06 8.445e-07 7.971e-08 1.304e-07 b_tt_shift_business -1.390e-06 -4.421e-07 6.552e-08 8.472e-08 b_access -8.319e-06 -3.267e-06 1.885e-07 1.914e-07 b_cost -2.312e-05 -9.113e-06 8.335e-07 1.293e-06 b_cost_shift_business 1.384e-05 7.037e-06 -3.886e-07 -6.615e-07 cost_income_elast 1.3036e-04 9.328e-05 -1.228e-06 -8.222e-07 b_wifi 2.4308e-04 1.0163e-04 -1.236e-05 -1.743e-05 b_food 8.896e-05 6.168e-05 -5.781e-06 -8.712e-06 mu_SP -9.9869e-04 -4.0567e-04 4.023e-05 6.321e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -8.538e-06 6.557e-06 5.485e-06 2.717e-05 asc_air -1.5056e-04 2.668e-06 7.260e-06 -1.2538e-04 asc_rail 1.705e-05 -9.768e-05 1.816e-05 1.244e-05 asc_bus_shift_female -1.920e-07 -2.315e-06 -6.537e-07 -9.227e-06 asc_air_shift_female -3.529e-06 1.296e-06 -1.390e-06 -8.319e-06 asc_rail_shift_female 6.664e-07 8.445e-07 -4.421e-07 -3.267e-06 b_tt_car 1.982e-07 7.971e-08 6.552e-08 1.885e-07 b_tt_bus 3.322e-07 1.304e-07 8.472e-08 1.914e-07 b_tt_air 2.051e-06 1.226e-07 9.334e-08 9.206e-07 b_tt_rail 1.226e-07 8.011e-07 3.717e-09 2.154e-08 b_tt_shift_business 9.334e-08 3.717e-09 1.217e-07 1.473e-07 b_access 9.206e-07 2.154e-08 1.473e-07 2.136e-06 b_cost 1.553e-06 7.471e-07 3.395e-07 1.505e-06 b_cost_shift_business -5.471e-07 -4.634e-07 4.808e-08 -4.579e-07 cost_income_elast -7.565e-06 -2.642e-06 -8.516e-07 -6.375e-06 b_wifi -2.323e-05 -1.044e-05 -7.311e-06 -2.028e-05 b_food -1.243e-05 -5.419e-06 -3.330e-06 -9.869e-06 mu_SP 7.434e-05 2.822e-05 2.428e-05 7.775e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 1.376e-05 1.303e-05 -4.2747e-04 -7.8195e-04 asc_air -2.271e-07 -1.872e-05 7.8997e-04 -6.3732e-04 asc_rail 8.270e-05 -1.822e-05 1.8749e-04 -0.001828 asc_bus_shift_female -2.400e-05 1.376e-05 1.0453e-04 2.8993e-04 asc_air_shift_female -2.312e-05 1.384e-05 1.3036e-04 2.4308e-04 asc_rail_shift_female -9.113e-06 7.037e-06 9.328e-05 1.0163e-04 b_tt_car 8.335e-07 -3.886e-07 -1.228e-06 -1.236e-05 b_tt_bus 1.293e-06 -6.615e-07 -8.222e-07 -1.743e-05 b_tt_air 1.553e-06 -5.471e-07 -7.565e-06 -2.323e-05 b_tt_rail 7.471e-07 -4.634e-07 -2.642e-06 -1.044e-05 b_tt_shift_business 3.395e-07 4.808e-08 -8.516e-07 -7.311e-06 b_access 1.505e-06 -4.579e-07 -6.375e-06 -2.028e-05 b_cost 5.901e-06 -2.904e-06 -1.972e-05 -7.900e-05 b_cost_shift_business -2.904e-06 2.405e-06 4.749e-06 3.117e-05 cost_income_elast -1.972e-05 4.749e-06 8.8565e-04 1.8852e-04 b_wifi -7.900e-05 3.117e-05 1.8852e-04 0.001900 b_food -3.657e-05 1.407e-05 6.013e-05 9.1010e-04 mu_SP 2.7174e-04 -1.1560e-04 -5.6822e-04 -0.004061 b_food mu_SP asc_bus -1.2712e-04 8.8275e-04 asc_air -3.2751e-04 4.5459e-04 asc_rail -9.4206e-04 0.005330 asc_bus_shift_female 2.4404e-04 -0.001070 asc_air_shift_female 8.896e-05 -9.9869e-04 asc_rail_shift_female 6.168e-05 -4.0567e-04 b_tt_car -5.781e-06 4.023e-05 b_tt_bus -8.712e-06 6.321e-05 b_tt_air -1.243e-05 7.434e-05 b_tt_rail -5.419e-06 2.822e-05 b_tt_shift_business -3.330e-06 2.428e-05 b_access -9.869e-06 7.775e-05 b_cost -3.657e-05 2.7174e-04 b_cost_shift_business 1.407e-05 -1.1560e-04 cost_income_elast 6.013e-05 -5.6822e-04 b_wifi 9.1010e-04 -0.004061 b_food 9.9508e-04 -0.001811 mu_SP -0.001811 0.015098 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.16858 0.15491 -0.13249 asc_air 0.168585 1.00000 0.46390 -0.04792 asc_rail 0.154910 0.46390 1.00000 -0.07604 asc_bus_shift_female -0.132494 -0.04792 -0.07604 1.00000 asc_air_shift_female -0.024519 -0.13371 -0.10520 0.28094 asc_rail_shift_female -0.033649 -0.06944 -0.14578 0.31510 b_tt_car 0.174175 0.48830 0.63287 -0.12587 b_tt_bus -0.713590 0.14498 0.24838 -0.08820 b_tt_air -0.010685 -0.61569 0.07273 -0.06430 b_tt_rail 0.009426 0.05921 -0.61422 -0.05009 b_tt_shift_business 0.015906 0.08725 0.22607 -0.08147 b_access -0.017802 -0.47985 0.07665 -0.06225 b_cost 0.001906 0.05414 0.23902 -0.16737 b_cost_shift_business 0.019113 -0.10508 -0.14733 0.12844 cost_income_elast -0.050311 0.11542 0.03755 -0.03354 b_wifi -0.004649 -0.14871 -0.27468 0.13169 b_food -0.006401 -0.11019 -0.20837 0.08023 mu_SP -0.002898 0.09468 0.28798 -0.16928 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.02452 -0.03365 0.17417 -0.71359 asc_air -0.13371 -0.06944 0.48830 0.14498 asc_rail -0.10520 -0.14578 0.63287 0.24838 asc_bus_shift_female 0.28094 0.31510 -0.12587 -0.08820 asc_air_shift_female 1.00000 0.53187 -0.13198 -0.11147 asc_rail_shift_female 0.53187 1.00000 -0.12206 -0.10006 b_tt_car -0.13198 -0.12206 1.00000 0.52584 b_tt_bus -0.11147 -0.10006 0.52584 1.00000 b_tt_air -0.06242 -0.06676 0.23981 0.21186 b_tt_rail -0.04527 -0.04307 0.17702 0.16428 b_tt_shift_business -0.10551 -0.09274 0.33438 0.27556 b_access -0.07740 -0.07816 0.26377 0.20158 b_cost -0.16648 -0.15550 0.73709 0.60894 b_cost_shift_business 0.09937 0.09842 -0.53390 -0.45430 cost_income_elast 0.01011 0.01001 -0.05057 0.02130 b_wifi 0.13974 0.12567 -0.61608 -0.49657 b_food 0.08784 0.07623 -0.38922 -0.30777 mu_SP -0.17151 -0.16064 0.71140 0.60344 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.01069 0.009426 0.01591 -0.01780 asc_air -0.61569 0.059213 0.08725 -0.47985 asc_rail 0.07273 -0.614219 0.22607 0.07665 asc_bus_shift_female -0.06430 -0.050094 -0.08147 -0.06225 asc_air_shift_female -0.06242 -0.045271 -0.10551 -0.07740 asc_rail_shift_female -0.06676 -0.043067 -0.09274 -0.07816 b_tt_car 0.23981 0.177017 0.33438 0.26377 b_tt_bus 0.21186 0.164278 0.27556 0.20158 b_tt_air 1.00000 0.047891 0.16781 0.43304 b_tt_rail 0.04789 1.000000 0.05398 -0.01590 b_tt_shift_business 0.16781 0.053984 1.00000 0.25972 b_access 0.43304 -0.015902 0.25972 1.00000 b_cost 0.40719 0.331114 0.38604 0.39879 b_cost_shift_business -0.22402 -0.259081 0.18133 -0.17960 cost_income_elast -0.12302 -0.070053 -0.01801 -0.09858 b_wifi -0.29941 -0.262286 -0.45447 -0.32842 b_food -0.20807 -0.161712 -0.28000 -0.21596 mu_SP 0.36689 0.260976 0.54207 0.40144 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.001906 0.01911 -0.05031 -0.004649 asc_air 0.054139 -0.10508 0.11542 -0.148707 asc_rail 0.239022 -0.14733 0.03755 -0.274679 asc_bus_shift_female -0.167366 0.12844 -0.03354 0.131690 asc_air_shift_female -0.166477 0.09937 0.01011 0.139741 asc_rail_shift_female -0.155499 0.09842 0.01001 0.125670 b_tt_car 0.737086 -0.53390 -0.05057 -0.616076 b_tt_bus 0.608935 -0.45430 0.02130 -0.496573 b_tt_air 0.407193 -0.22402 -0.12302 -0.299408 b_tt_rail 0.331114 -0.25908 -0.07005 -0.262286 b_tt_shift_business 0.386035 0.18133 -0.01801 -0.454471 b_access 0.398788 -0.17960 -0.09858 -0.328416 b_cost 1.000000 -0.73462 -0.18310 -0.746420 b_cost_shift_business -0.734624 1.00000 0.04959 0.439616 cost_income_elast -0.183103 0.04959 1.00000 0.075286 b_wifi -0.746420 0.43962 0.07529 1.000000 b_food -0.469354 0.27029 0.06398 0.665899 mu_SP 0.910730 -0.58027 -0.04279 -0.766358 b_food mu_SP asc_bus -0.006401 -0.002898 asc_air -0.110192 0.094680 asc_rail -0.208367 0.287984 asc_bus_shift_female 0.080231 -0.169283 asc_air_shift_female 0.087841 -0.171509 asc_rail_shift_female 0.076229 -0.160636 b_tt_car -0.389220 0.711401 b_tt_bus -0.307767 0.603440 b_tt_air -0.208072 0.366893 b_tt_rail -0.161712 0.260976 b_tt_shift_business -0.280004 0.542069 b_access -0.215955 0.401436 b_cost -0.469354 0.910730 b_cost_shift_business 0.270287 -0.580273 cost_income_elast 0.063984 -0.042794 b_wifi 0.665899 -0.766358 b_food 1.000000 -0.474411 mu_SP -0.474411 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.18403 0.18191 -0.170707 asc_air 0.184026 1.00000 0.49606 -0.035028 asc_rail 0.181905 0.49606 1.00000 -0.052993 asc_bus_shift_female -0.170707 -0.03503 -0.05299 1.000000 asc_air_shift_female 0.002260 -0.12601 -0.17051 0.299952 asc_rail_shift_female -0.049595 -0.07891 -0.13403 0.379959 b_tt_car 0.229437 0.48560 0.62955 -0.082689 b_tt_bus -0.685627 0.12277 0.22624 -0.037614 b_tt_air -0.022749 -0.59127 0.06705 -0.001878 b_tt_rail 0.027958 0.01677 -0.61474 -0.036226 b_tt_shift_business 0.060000 0.11706 0.29326 -0.026240 b_access 0.070931 -0.48249 0.04795 -0.088408 b_cost 0.021614 -5.2587e-04 0.19177 -0.138364 b_cost_shift_business 0.032073 -0.06789 -0.06619 0.124234 cost_income_elast -0.054819 0.14931 0.03549 0.049192 b_wifi -0.068457 -0.08224 -0.23620 0.093145 b_food -0.015379 -0.05840 -0.16823 0.108344 mu_SP 0.027418 0.02081 0.24435 -0.121997 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.002260 -0.04959 0.22944 -0.68563 asc_air -0.126013 -0.07891 0.48560 0.12277 asc_rail -0.170505 -0.13403 0.62955 0.22624 asc_bus_shift_female 0.299952 0.37996 -0.08269 -0.03761 asc_air_shift_female 1.000000 0.62748 -0.15221 -0.14955 asc_rail_shift_female 0.627476 1.00000 -0.04446 -0.03989 b_tt_car -0.152205 -0.04446 1.00000 0.50112 b_tt_bus -0.149552 -0.03989 0.50112 1.00000 b_tt_air -0.052038 0.01211 0.27990 0.26554 b_tt_rail 0.030581 0.02456 0.18014 0.16688 b_tt_shift_business -0.084156 -0.03299 0.37989 0.27807 b_access -0.120194 -0.05819 0.26085 0.14995 b_cost -0.200953 -0.09765 0.69399 0.60953 b_cost_shift_business 0.188517 0.11812 -0.50678 -0.48843 cost_income_elast 0.092509 0.08160 -0.08348 -0.03163 b_wifi 0.117761 0.06069 -0.57370 -0.45785 b_food 0.059558 0.05090 -0.37067 -0.31625 mu_SP -0.171651 -0.08595 0.66232 0.58904 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.022749 0.02796 0.06000 0.07093 asc_air -0.591268 0.01677 0.11706 -0.48249 asc_rail 0.067054 -0.61474 0.29326 0.04795 asc_bus_shift_female -0.001878 -0.03623 -0.02624 -0.08841 asc_air_shift_female -0.052038 0.03058 -0.08416 -0.12019 asc_rail_shift_female 0.012112 0.02456 -0.03299 -0.05819 b_tt_car 0.279898 0.18014 0.37989 0.26085 b_tt_bus 0.265541 0.16688 0.27807 0.14995 b_tt_air 1.000000 0.09565 0.18681 0.43975 b_tt_rail 0.095655 1.00000 0.01190 0.01647 b_tt_shift_business 0.186808 0.01190 1.00000 0.28890 b_access 0.439754 0.01647 0.28890 1.00000 b_cost 0.446438 0.34362 0.40060 0.42392 b_cost_shift_business -0.246309 -0.33380 0.08886 -0.20201 cost_income_elast -0.177487 -0.09919 -0.08203 -0.14655 b_wifi -0.372078 -0.26756 -0.48075 -0.31822 b_food -0.275021 -0.19194 -0.30256 -0.21404 mu_SP 0.422399 0.25659 0.56653 0.43291 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.02161 0.03207 -0.05482 -0.06846 asc_air -5.2587e-04 -0.06789 0.14931 -0.08224 asc_rail 0.19177 -0.06619 0.03549 -0.23620 asc_bus_shift_female -0.13836 0.12423 0.04919 0.09315 asc_air_shift_female -0.20095 0.18852 0.09251 0.11776 asc_rail_shift_female -0.09765 0.11812 0.08160 0.06069 b_tt_car 0.69399 -0.50678 -0.08348 -0.57370 b_tt_bus 0.60953 -0.48843 -0.03163 -0.45785 b_tt_air 0.44644 -0.24631 -0.17749 -0.37208 b_tt_rail 0.34362 -0.33380 -0.09919 -0.26756 b_tt_shift_business 0.40060 0.08886 -0.08203 -0.48075 b_access 0.42392 -0.20201 -0.14655 -0.31822 b_cost 1.00000 -0.77087 -0.27275 -0.74600 b_cost_shift_business -0.77087 1.00000 0.10290 0.46101 cost_income_elast -0.27275 0.10290 1.00000 0.14532 b_wifi -0.74600 0.46101 0.14532 1.00000 b_food -0.47719 0.28761 0.06405 0.66183 mu_SP 0.91037 -0.60664 -0.15539 -0.75811 b_food mu_SP asc_bus -0.01538 0.02742 asc_air -0.05840 0.02081 asc_rail -0.16823 0.24435 asc_bus_shift_female 0.10834 -0.12200 asc_air_shift_female 0.05956 -0.17165 asc_rail_shift_female 0.05090 -0.08595 b_tt_car -0.37067 0.66232 b_tt_bus -0.31625 0.58904 b_tt_air -0.27502 0.42240 b_tt_rail -0.19194 0.25659 b_tt_shift_business -0.30256 0.56653 b_access -0.21404 0.43291 b_cost -0.47719 0.91037 b_cost_shift_business 0.28761 -0.60664 cost_income_elast 0.06405 -0.15539 b_wifi 0.66183 -0.75811 b_food 1.00000 -0.46735 mu_SP -0.46735 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 146 0.2438962 400 0.2445128 317 0.2531972 464 0.2568689 186 0.2583061 293 0.2618963 181 0.2699404 441 0.2742187 307 0.2763107 276 0.2766703 259 0.2782715 498 0.2822862 367 0.2831473 434 0.2836223 227 0.2838154 142 0.2983000 447 0.3007382 23 0.3025847 147 0.3083405 86 0.3094485 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000 0.000000 0.000000 asc_bus 0.000 0.124860 0.124860 asc_air 0.000 -0.396083 -0.396083 asc_rail 0.000 -0.978683 -0.978683 asc_bus_shift_female 0.000 0.181337 0.181337 asc_air_shift_female 0.000 0.134505 0.134505 asc_rail_shift_female 0.000 0.098187 0.098187 b_tt_car 0.000 -0.006424 -0.006424 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 0.016656 0.016656 cost_income_elast 0.000 -0.613155 -0.613155 b_no_frills 0.000 0.000000 0.000000 b_wifi 0.000 0.523122 0.523122 b_food 0.000 0.220074 0.220074 mu_RP 1.000 1.000000 0.000000 mu_SP 1.000 1.994745 0.994745 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" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling in estimation --------------------- Value asc_bus 0.124859528 asc_air 0.396082882 asc_rail 0.978682315 asc_bus_shift_female 0.181337332 asc_air_shift_female 0.134504537 asc_rail_shift_female 0.098187469 b_tt_car 0.006424486 b_tt_bus 0.010506939 b_tt_air 0.008667899 b_tt_rail 0.003837827 b_tt_shift_business 0.003202885 b_access 0.010545031 b_cost 0.038233574 b_cost_shift_business 0.016656423 cost_income_elast 0.613155210 b_wifi 0.523121676 b_food 0.220073683 mu_SP 1.994745912 Scaling used in computing Hessian --------------------------------- Value asc_bus 0.124859548 asc_air 0.396082945 asc_rail 0.978683378 asc_bus_shift_female 0.181337352 asc_air_shift_female 0.134504533 asc_rail_shift_female 0.098187464 b_tt_car 0.006424483 b_tt_bus 0.010506890 b_tt_air 0.008667900 b_tt_rail 0.003837830 b_tt_shift_business 0.003202884 b_access 0.010545034 b_cost 0.038233704 b_cost_shift_business 0.016656416 cost_income_elast 0.613155384 b_wifi 0.523121542 b_food 0.220073655 mu_SP 1.994745054 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) }