Model run using Apollo for R, version 0.2.3 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : Apollo_example_22 Model description : RP-SP model on mode choice data Model run at : 2021-02-04 19:03:44 Estimation method : bfgs Model diagnosis : successful convergence 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) : -9366.881 LL(0, whole model) : -9366.881 LL(final, whole model) : -5802.644 Rho-square (0) : 0.3805 Adj.Rho-square (0) : 0.3786 AIC : 11641.29 BIC : 11767.06 LL(0,RP) : -1170.86 LL(final,RP) : -971.2441 LL(0,SP) : -8196.021 LL(final,SP) : -4831.4 Estimated parameters : 18 Time taken (hh:mm:ss) : 00:00:47.13 pre-estimation : 00:00:0.77 estimation : 00:00:30.79 post-estimation : 00:00:15.57 Iterations : 63 Min abs eigenvalue of Hessian : 12.02662 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 0.281042 0.4443 0.262032 0.4765 asc_air -0.396083 0.183661 -2.1566 0.177781 -2.2279 asc_rail -0.978683 0.180545 -5.4207 0.177525 -5.5129 asc_bus_shift_female 0.181337 0.064657 2.8046 0.071407 2.5395 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 5.0942e-04 -12.6114 4.9442e-04 -12.9939 b_tt_bus -0.010507 9.6111e-04 -10.9321 8.7337e-04 -12.0304 b_tt_air -0.008668 0.001466 -5.9139 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 3.4887e-04 -9.1806 b_access -0.010545 0.001531 -6.8857 0.001462 -7.2143 b_cost -0.038234 0.002461 -15.5356 0.002429 -15.7376 b_cost_shift_business 0.016656 0.001634 10.1910 0.001551 10.7398 cost_income_elast -0.613155 0.029204 -20.9954 0.029760 -20.6033 b_no_frills 0.000000 NA NA NA NA b_wifi 0.523122 0.043045 12.1530 0.043595 11.9995 b_food 0.220074 0.030836 7.1369 0.031546 6.9764 mu_RP 1.000000 NA NA NA NA mu_SP 1.994746 0.126412 15.7798 0.122886 16.2325 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 0.078985 0.008702 0.007860 asc_air 0.008702 0.033731 0.015382 asc_rail 0.007860 0.015382 0.032597 asc_bus_shift_female -0.002408 -5.6911e-04 -8.8765e-04 asc_air_shift_female -3.1334e-04 -0.001117 -8.6372e-04 asc_rail_shift_female -3.4653e-04 -4.6733e-04 -9.6451e-04 b_tt_car 2.494e-05 4.569e-05 5.821e-05 b_tt_bus -1.9275e-04 2.559e-05 4.310e-05 b_tt_air -4.401e-06 -1.6573e-04 1.925e-05 b_tt_rail 2.439e-06 1.001e-05 -1.0210e-04 b_tt_shift_business 1.549e-06 5.553e-06 1.414e-05 b_access -7.662e-06 -1.3496e-04 2.120e-05 b_cost 1.318e-06 2.447e-05 1.0621e-04 b_cost_shift_business 8.779e-06 -3.154e-05 -4.348e-05 cost_income_elast -4.1294e-04 6.1907e-04 1.9804e-04 b_wifi -5.624e-05 -0.001176 -0.002135 b_food -5.547e-05 -6.2409e-04 -0.001160 mu_SP -1.0297e-04 0.002198 0.006573 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.002408 -3.1334e-04 -3.4653e-04 asc_air -5.6911e-04 -0.001117 -4.6733e-04 asc_rail -8.8765e-04 -8.6372e-04 -9.6451e-04 asc_bus_shift_female 0.004181 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 -6.094e-06 -4.160e-06 -3.586e-06 b_tt_rail -2.982e-06 -1.896e-06 -1.453e-06 b_tt_shift_business -1.825e-06 -1.662e-06 -1.178e-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 3.6654e-04 2.7353e-04 1.9824e-04 b_food 1.5998e-04 1.2318e-04 8.614e-05 mu_SP -0.001384 -9.8591e-04 -7.4414e-04 b_tt_car b_tt_bus b_tt_air asc_bus 2.494e-05 -1.9275e-04 -4.401e-06 asc_air 4.569e-05 2.559e-05 -1.6573e-04 asc_rail 5.821e-05 4.310e-05 1.925e-05 asc_bus_shift_female -4.146e-06 -5.481e-06 -6.094e-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 2.985e-07 b_tt_air 1.791e-07 2.985e-07 2.148e-06 b_tt_rail 8.303e-08 1.454e-07 6.464e-08 b_tt_shift_business 5.902e-08 9.177e-08 8.523e-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 -7.137e-07 -5.367e-07 cost_income_elast -7.521e-07 5.984e-07 -5.265e-06 b_wifi -1.351e-05 -2.054e-05 -1.889e-05 b_food -6.114e-06 -9.122e-06 -9.405e-06 mu_SP 4.581e-05 7.332e-05 6.798e-05 b_tt_rail b_tt_shift_business b_access asc_bus 2.439e-06 1.549e-06 -7.662e-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 -1.896e-06 -1.662e-06 -5.391e-06 asc_rail_shift_female -1.453e-06 -1.178e-06 -4.386e-06 b_tt_car 8.303e-08 5.902e-08 2.058e-07 b_tt_bus 1.454e-07 9.177e-08 2.967e-07 b_tt_air 6.464e-08 8.523e-08 9.720e-07 b_tt_rail 8.478e-07 1.723e-08 -2.241e-08 b_tt_shift_business 1.723e-08 1.201e-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 -1.883e-06 -1.822e-07 -4.408e-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 1.318e-06 8.779e-06 -4.1294e-04 asc_air 2.447e-05 -3.154e-05 6.1907e-04 asc_rail 1.0621e-04 -4.348e-05 1.9804e-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 -7.521e-07 b_tt_bus 1.440e-06 -7.137e-07 5.984e-07 b_tt_air 1.469e-06 -5.367e-07 -5.265e-06 b_tt_rail 7.503e-07 -3.899e-07 -1.883e-06 b_tt_shift_business 3.292e-07 1.027e-07 -1.822e-07 b_access 1.503e-06 -4.496e-07 -4.408e-06 b_cost 6.057e-06 -2.955e-06 -1.316e-05 b_cost_shift_business -2.955e-06 2.671e-06 2.366e-06 cost_income_elast -1.316e-05 2.366e-06 8.5289e-04 b_wifi -7.907e-05 3.093e-05 9.462e-05 b_food -3.562e-05 1.362e-05 5.761e-05 mu_SP 2.8333e-04 -1.1989e-04 -1.5790e-04 b_wifi b_food mu_SP asc_bus -5.624e-05 -5.547e-05 -1.0297e-04 asc_air -0.001176 -6.2409e-04 0.002198 asc_rail -0.002135 -0.001160 0.006573 asc_bus_shift_female 3.6654e-04 1.5998e-04 -0.001384 asc_air_shift_female 2.7353e-04 1.2318e-04 -9.8591e-04 asc_rail_shift_female 1.9824e-04 8.614e-05 -7.4414e-04 b_tt_car -1.351e-05 -6.114e-06 4.581e-05 b_tt_bus -2.054e-05 -9.122e-06 7.332e-05 b_tt_air -1.889e-05 -9.405e-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 2.8333e-04 b_cost_shift_business 3.093e-05 1.362e-05 -1.1989e-04 cost_income_elast 9.462e-05 5.761e-05 -1.5790e-04 b_wifi 0.001853 8.8388e-04 -0.004170 b_food 8.8388e-04 9.5087e-04 -0.001849 mu_SP -0.004170 -0.001849 0.015980 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus 0.068661 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 -4.4466e-04 -6.7185e-04 asc_air_shift_female 2.803e-05 -0.001061 -0.001433 asc_rail_shift_female -4.9923e-04 -5.3889e-04 -9.1404e-04 b_tt_car 2.972e-05 4.268e-05 5.526e-05 b_tt_bus -1.5690e-04 1.906e-05 3.508e-05 b_tt_air -8.537e-06 -1.5055e-04 1.705e-05 b_tt_rail 6.557e-06 2.669e-06 -9.768e-05 b_tt_shift_business 5.485e-06 7.261e-06 1.816e-05 b_access 2.717e-05 -1.2538e-04 1.245e-05 b_cost 1.376e-05 -2.204e-07 8.272e-05 b_cost_shift_business 1.303e-05 -1.872e-05 -1.823e-05 cost_income_elast -4.2753e-04 7.8997e-04 1.8753e-04 b_wifi -7.8204e-04 -6.3743e-04 -0.001828 b_food -1.2715e-04 -3.2756e-04 -9.4222e-04 mu_SP 8.8301e-04 4.5499e-04 0.005331 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.003194 2.803e-05 -4.9923e-04 asc_air -4.4466e-04 -0.001061 -5.3889e-04 asc_rail -6.7185e-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 -1.931e-07 -3.530e-06 6.658e-07 b_tt_rail -2.316e-06 1.296e-06 8.442e-07 b_tt_shift_business -6.540e-07 -1.390e-06 -4.423e-07 b_access -9.229e-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 1.385e-05 7.037e-06 cost_income_elast 1.0453e-04 1.3036e-04 9.328e-05 b_wifi 2.8999e-04 2.4313e-04 1.0167e-04 b_food 2.4407e-04 8.899e-05 6.169e-05 mu_SP -0.001071 -9.9889e-04 -4.0579e-04 b_tt_car b_tt_bus b_tt_air asc_bus 2.972e-05 -1.5690e-04 -8.537e-06 asc_air 4.268e-05 1.906e-05 -1.5055e-04 asc_rail 5.526e-05 3.508e-05 1.705e-05 asc_bus_shift_female -2.920e-06 -2.346e-06 -1.931e-07 asc_air_shift_female -3.564e-06 -6.185e-06 -3.530e-06 asc_rail_shift_female -8.446e-07 -1.339e-06 6.658e-07 b_tt_car 2.445e-07 2.164e-07 1.982e-07 b_tt_bus 2.164e-07 7.628e-07 3.322e-07 b_tt_air 1.982e-07 3.322e-07 2.052e-06 b_tt_rail 7.973e-08 1.305e-07 1.227e-07 b_tt_shift_business 6.554e-08 8.474e-08 9.336e-08 b_access 1.885e-07 1.915e-07 9.207e-07 b_cost 8.336e-07 1.293e-06 1.554e-06 b_cost_shift_business -3.886e-07 -6.616e-07 -5.472e-07 cost_income_elast -1.228e-06 -8.215e-07 -7.565e-06 b_wifi -1.237e-05 -1.743e-05 -2.324e-05 b_food -5.782e-06 -8.714e-06 -1.243e-05 mu_SP 4.024e-05 6.322e-05 7.435e-05 b_tt_rail b_tt_shift_business b_access asc_bus 6.557e-06 5.485e-06 2.717e-05 asc_air 2.669e-06 7.261e-06 -1.2538e-04 asc_rail -9.768e-05 1.816e-05 1.245e-05 asc_bus_shift_female -2.316e-06 -6.540e-07 -9.229e-06 asc_air_shift_female 1.296e-06 -1.390e-06 -8.320e-06 asc_rail_shift_female 8.442e-07 -4.423e-07 -3.268e-06 b_tt_car 7.973e-08 6.554e-08 1.885e-07 b_tt_bus 1.305e-07 8.474e-08 1.915e-07 b_tt_air 1.227e-07 9.336e-08 9.207e-07 b_tt_rail 8.011e-07 3.727e-09 2.157e-08 b_tt_shift_business 3.727e-09 1.217e-07 1.473e-07 b_access 2.157e-08 1.473e-07 2.137e-06 b_cost 7.472e-07 3.396e-07 1.505e-06 b_cost_shift_business -4.634e-07 4.804e-08 -4.580e-07 cost_income_elast -2.642e-06 -8.515e-07 -6.374e-06 b_wifi -1.044e-05 -7.313e-06 -2.028e-05 b_food -5.420e-06 -3.330e-06 -9.871e-06 mu_SP 2.822e-05 2.429e-05 7.777e-05 b_cost b_cost_shift_business cost_income_elast asc_bus 1.376e-05 1.303e-05 -4.2753e-04 asc_air -2.204e-07 -1.872e-05 7.8997e-04 asc_rail 8.272e-05 -1.823e-05 1.8753e-04 asc_bus_shift_female -2.400e-05 1.376e-05 1.0453e-04 asc_air_shift_female -2.312e-05 1.385e-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 -8.215e-07 b_tt_air 1.554e-06 -5.472e-07 -7.565e-06 b_tt_rail 7.472e-07 -4.634e-07 -2.642e-06 b_tt_shift_business 3.396e-07 4.804e-08 -8.515e-07 b_access 1.505e-06 -4.580e-07 -6.374e-06 b_cost 5.902e-06 -2.905e-06 -1.972e-05 b_cost_shift_business -2.905e-06 2.405e-06 4.748e-06 cost_income_elast -1.972e-05 4.748e-06 8.8566e-04 b_wifi -7.901e-05 3.117e-05 1.8850e-04 b_food -3.657e-05 1.407e-05 6.012e-05 mu_SP 2.7179e-04 -1.1562e-04 -5.6813e-04 b_wifi b_food mu_SP asc_bus -7.8204e-04 -1.2715e-04 8.8301e-04 asc_air -6.3743e-04 -3.2756e-04 4.5499e-04 asc_rail -0.001828 -9.4222e-04 0.005331 asc_bus_shift_female 2.8999e-04 2.4407e-04 -0.001071 asc_air_shift_female 2.4313e-04 8.899e-05 -9.9889e-04 asc_rail_shift_female 1.0167e-04 6.169e-05 -4.0579e-04 b_tt_car -1.237e-05 -5.782e-06 4.024e-05 b_tt_bus -1.743e-05 -8.714e-06 6.322e-05 b_tt_air -2.324e-05 -1.243e-05 7.435e-05 b_tt_rail -1.044e-05 -5.420e-06 2.822e-05 b_tt_shift_business -7.313e-06 -3.330e-06 2.429e-05 b_access -2.028e-05 -9.871e-06 7.777e-05 b_cost -7.901e-05 -3.657e-05 2.7179e-04 b_cost_shift_business 3.117e-05 1.407e-05 -1.1562e-04 cost_income_elast 1.8850e-04 6.012e-05 -5.6813e-04 b_wifi 0.001901 9.1020e-04 -0.004062 b_food 9.1020e-04 9.9512e-04 -0.001812 mu_SP -0.004062 -0.001812 0.015101 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus 1.000000 0.16858 0.15491 asc_air 0.168583 1.00000 0.46390 asc_rail 0.154907 0.46390 1.00000 asc_bus_shift_female -0.132495 -0.04792 -0.07604 asc_air_shift_female -0.024519 -0.13371 -0.10521 asc_rail_shift_female -0.033649 -0.06944 -0.14579 b_tt_car 0.174168 0.48830 0.63287 b_tt_bus -0.713579 0.14499 0.24839 b_tt_air -0.010685 -0.61568 0.07274 b_tt_rail 0.009426 0.05922 -0.61421 b_tt_shift_business 0.015906 0.08726 0.22608 b_access -0.017801 -0.47984 0.07666 b_cost 0.001906 0.05415 0.23904 b_cost_shift_business 0.019112 -0.10508 -0.14735 cost_income_elast -0.050312 0.11542 0.03756 b_wifi -0.004649 -0.14871 -0.27469 b_food -0.006400 -0.11020 -0.20838 mu_SP -0.002898 0.09469 0.28800 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.13249 -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 0.53188 asc_rail_shift_female 0.31510 0.53188 1.00000 b_tt_car -0.12588 -0.13198 -0.12207 b_tt_bus -0.08821 -0.11148 -0.10007 b_tt_air -0.06430 -0.06242 -0.06677 b_tt_rail -0.05010 -0.04528 -0.04307 b_tt_shift_business -0.08148 -0.10551 -0.09274 b_access -0.06225 -0.07741 -0.07816 b_cost -0.16737 -0.16649 -0.15551 b_cost_shift_business 0.12845 0.09938 0.09843 cost_income_elast -0.03354 0.01011 0.01001 b_wifi 0.13170 0.13975 0.12568 b_food 0.08024 0.08785 0.07624 mu_SP -0.16929 -0.17152 -0.16064 b_tt_car b_tt_bus b_tt_air asc_bus 0.17417 -0.71358 -0.01069 asc_air 0.48830 0.14499 -0.61568 asc_rail 0.63287 0.24839 0.07274 asc_bus_shift_female -0.12588 -0.08821 -0.06430 asc_air_shift_female -0.13198 -0.11148 -0.06242 asc_rail_shift_female -0.12207 -0.10007 -0.06677 b_tt_car 1.00000 0.52586 0.23982 b_tt_bus 0.52586 1.00000 0.21188 b_tt_air 0.23982 0.21188 1.00000 b_tt_rail 0.17703 0.16429 0.04790 b_tt_shift_business 0.33441 0.27559 0.16783 b_access 0.26379 0.20160 0.43305 b_cost 0.73710 0.60895 0.40721 b_cost_shift_business -0.53392 -0.45432 -0.22404 cost_income_elast -0.05056 0.02132 -0.12301 b_wifi -0.61610 -0.49660 -0.29942 b_food -0.38924 -0.30779 -0.20809 mu_SP 0.71142 0.60346 0.36691 b_tt_rail b_tt_shift_business b_access asc_bus 0.009426 0.01591 -0.01780 asc_air 0.059215 0.08726 -0.47984 asc_rail -0.614207 0.22608 0.07666 asc_bus_shift_female -0.050098 -0.08148 -0.06225 asc_air_shift_female -0.045275 -0.10551 -0.07741 asc_rail_shift_female -0.043071 -0.09274 -0.07816 b_tt_car 0.177030 0.33441 0.26379 b_tt_bus 0.164289 0.27559 0.20160 b_tt_air 0.047899 0.16783 0.43305 b_tt_rail 1.000000 0.05400 -0.01589 b_tt_shift_business 0.053997 1.00000 0.25974 b_access -0.015892 0.25974 1.00000 b_cost 0.331122 0.38606 0.39880 b_cost_shift_business -0.259091 0.18129 -0.17962 cost_income_elast -0.070046 -0.01800 -0.09857 b_wifi -0.262297 -0.45449 -0.32843 b_food -0.161722 -0.28002 -0.21597 mu_SP 0.260988 0.54209 0.40145 b_cost b_cost_shift_business cost_income_elast asc_bus 0.001906 0.01911 -0.05031 asc_air 0.054148 -0.10508 0.11542 asc_rail 0.239039 -0.14735 0.03756 asc_bus_shift_female -0.167374 0.12845 -0.03354 asc_air_shift_female -0.166486 0.09938 0.01011 asc_rail_shift_female -0.155508 0.09843 0.01001 b_tt_car 0.737102 -0.53392 -0.05056 b_tt_bus 0.608953 -0.45432 0.02132 b_tt_air 0.407206 -0.22404 -0.12301 b_tt_rail 0.331122 -0.25909 -0.07005 b_tt_shift_business 0.386063 0.18129 -0.01800 b_access 0.398804 -0.17962 -0.09857 b_cost 1.000000 -0.73464 -0.18308 b_cost_shift_business -0.734635 1.00000 0.04958 cost_income_elast -0.183075 0.04958 1.00000 b_wifi -0.746438 0.43964 0.07527 b_food -0.469374 0.27031 0.06397 mu_SP 0.910738 -0.58029 -0.04277 b_wifi b_food mu_SP asc_bus -0.004649 -0.006400 -0.002898 asc_air -0.148712 -0.110197 0.094688 asc_rail -0.274694 -0.208379 0.287999 asc_bus_shift_female 0.131699 0.080238 -0.169291 asc_air_shift_female 0.139750 0.087849 -0.171518 asc_rail_shift_female 0.125679 0.076236 -0.160644 b_tt_car -0.616099 -0.389242 0.711420 b_tt_bus -0.496596 -0.307788 0.603460 b_tt_air -0.299425 -0.208086 0.366908 b_tt_rail -0.262297 -0.161722 0.260988 b_tt_shift_business -0.454495 -0.280024 0.542089 b_access -0.328434 -0.215970 0.401452 b_cost -0.746438 -0.469374 0.910738 b_cost_shift_business 0.439643 0.270309 -0.580294 cost_income_elast 0.075267 0.063973 -0.042771 b_wifi 1.000000 0.665909 -0.766375 b_food 0.665909 1.000000 -0.474432 mu_SP -0.766375 -0.474432 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus 1.000000 0.18402 0.18190 asc_air 0.184022 1.00000 0.49606 asc_rail 0.181903 0.49606 1.00000 asc_bus_shift_female -0.170713 -0.03503 -0.05300 asc_air_shift_female 0.002259 -0.12602 -0.17051 asc_rail_shift_female -0.049598 -0.07891 -0.13404 b_tt_car 0.229426 0.48559 0.62955 b_tt_bus -0.685602 0.12277 0.22626 b_tt_air -0.022745 -0.59125 0.06707 b_tt_rail 0.027959 0.01677 -0.61471 b_tt_shift_business 0.060002 0.11707 0.29328 b_access 0.070935 -0.48248 0.04797 b_cost 0.021619 -5.1033e-04 0.19181 b_cost_shift_business 0.032069 -0.06790 -0.06623 cost_income_elast -0.054826 0.14931 0.03550 b_wifi -0.068460 -0.08224 -0.23623 b_food -0.015383 -0.05841 -0.16825 mu_SP 0.027423 0.02083 0.24438 asc_bus_shift_female asc_air_shift_female asc_rail_shift_female asc_bus -0.170713 0.002259 -0.04960 asc_air -0.035027 -0.126016 -0.07891 asc_rail -0.052999 -0.170513 -0.13404 asc_bus_shift_female 1.000000 0.299948 0.37996 asc_air_shift_female 0.299948 1.000000 0.62748 asc_rail_shift_female 0.379956 0.627481 1.00000 b_tt_car -0.082700 -0.152221 -0.04447 b_tt_bus -0.037621 -0.149564 -0.03990 b_tt_air -0.001888 -0.052050 0.01210 b_tt_rail -0.036229 0.030572 0.02455 b_tt_shift_business -0.026254 -0.084171 -0.03300 b_access -0.088418 -0.120205 -0.05820 b_cost -0.138372 -0.200966 -0.09767 b_cost_shift_business 0.124240 0.188529 0.11813 cost_income_elast 0.049188 0.092504 0.08160 b_wifi 0.093156 0.117780 0.06071 b_food 0.108351 0.059573 0.05091 mu_SP -0.122008 -0.171665 -0.08596 b_tt_car b_tt_bus b_tt_air asc_bus 0.22943 -0.68560 -0.022745 asc_air 0.48559 0.12277 -0.591250 asc_rail 0.62955 0.22626 0.067074 asc_bus_shift_female -0.08270 -0.03762 -0.001888 asc_air_shift_female -0.15222 -0.14956 -0.052050 asc_rail_shift_female -0.04447 -0.03990 0.012102 b_tt_car 1.00000 0.50116 0.279935 b_tt_bus 0.50116 1.00000 0.265574 b_tt_air 0.27994 0.26557 1.000000 b_tt_rail 0.18016 0.16691 0.095673 b_tt_shift_business 0.37994 0.27812 0.186843 b_access 0.26089 0.14999 0.439773 b_cost 0.69403 0.60956 0.446466 b_cost_shift_business -0.50682 -0.48847 -0.246346 cost_income_elast -0.08345 -0.03161 -0.177471 b_wifi -0.57375 -0.45790 -0.372111 b_food -0.37071 -0.31629 -0.275049 mu_SP 0.66236 0.58908 0.422429 b_tt_rail b_tt_shift_business b_access asc_bus 0.02796 0.06000 0.07093 asc_air 0.01677 0.11707 -0.48248 asc_rail -0.61471 0.29328 0.04797 asc_bus_shift_female -0.03623 -0.02625 -0.08842 asc_air_shift_female 0.03057 -0.08417 -0.12021 asc_rail_shift_female 0.02455 -0.03300 -0.05820 b_tt_car 0.18016 0.37994 0.26089 b_tt_bus 0.16691 0.27812 0.14999 b_tt_air 0.09567 0.18684 0.43977 b_tt_rail 1.00000 0.01193 0.01649 b_tt_shift_business 0.01193 1.00000 0.28893 b_access 0.01649 0.28893 1.00000 b_cost 0.34364 0.40066 0.42395 b_cost_shift_business -0.33382 0.08878 -0.20205 cost_income_elast -0.09918 -0.08201 -0.14653 b_wifi -0.26758 -0.48080 -0.31826 b_food -0.19196 -0.30260 -0.21407 mu_SP 0.25661 0.56657 0.43294 b_cost b_cost_shift_business cost_income_elast asc_bus 0.02162 0.03207 -0.05483 asc_air -5.1033e-04 -0.06790 0.14931 asc_rail 0.19181 -0.06623 0.03550 asc_bus_shift_female -0.13837 0.12424 0.04919 asc_air_shift_female -0.20097 0.18853 0.09250 asc_rail_shift_female -0.09767 0.11813 0.08160 b_tt_car 0.69403 -0.50682 -0.08345 b_tt_bus 0.60956 -0.48847 -0.03161 b_tt_air 0.44647 -0.24635 -0.17747 b_tt_rail 0.34364 -0.33382 -0.09918 b_tt_shift_business 0.40066 0.08878 -0.08201 b_access 0.42395 -0.20205 -0.14653 b_cost 1.00000 -0.77089 -0.27270 b_cost_shift_business -0.77089 1.00000 0.10288 cost_income_elast -0.27270 0.10288 1.00000 b_wifi -0.74604 0.46106 0.14529 b_food -0.47723 0.28765 0.06404 mu_SP 0.91039 -0.60668 -0.15535 b_wifi b_food mu_SP asc_bus -0.06846 -0.01538 0.02742 asc_air -0.08224 -0.05841 0.02083 asc_rail -0.23623 -0.16825 0.24438 asc_bus_shift_female 0.09316 0.10835 -0.12201 asc_air_shift_female 0.11778 0.05957 -0.17167 asc_rail_shift_female 0.06071 0.05091 -0.08596 b_tt_car -0.57375 -0.37071 0.66236 b_tt_bus -0.45790 -0.31629 0.58908 b_tt_air -0.37211 -0.27505 0.42243 b_tt_rail -0.26758 -0.19196 0.25661 b_tt_shift_business -0.48080 -0.30260 0.56657 b_access -0.31826 -0.21407 0.43294 b_cost -0.74604 -0.47723 0.91039 b_cost_shift_business 0.46106 0.28765 -0.60668 cost_income_elast 0.14529 0.06404 -0.15535 b_wifi 1.00000 0.66185 -0.75814 b_food 0.66185 1.00000 -0.46739 mu_SP -0.75814 -0.46739 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 146 0.2438962 400 0.2445136 317 0.2531977 464 0.2568655 186 0.2583050 293 0.2618943 181 0.2699412 441 0.2742182 307 0.2763118 276 0.2766688 259 0.2782703 498 0.2822853 367 0.2831485 434 0.2836219 227 0.2838160 142 0.2982986 447 0.3007371 23 0.3025844 147 0.3083372 86 0.3094490 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 1.994746 0.994746 Settings and functions used in model definition: apollo_control -------------- Value modelName "Apollo_example_22" modelDescr "RP-SP model on mode choice data" indivID "ID" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" panelData "TRUE" analyticGrad "TRUE" Hessian routines attempted -------------- numerical second derivative of LL (using numDeriv) Scaling used in computing Hessian -------------- Value asc_bus 0.124860021 asc_air 0.396083041 asc_rail 0.978682543 asc_bus_shift_female 0.181337355 asc_air_shift_female 0.134504558 asc_rail_shift_female 0.098187484 b_tt_car 0.006424487 b_tt_bus 0.010506942 b_tt_air 0.008667900 b_tt_rail 0.003837828 b_tt_shift_business 0.003202885 b_access 0.010545032 b_cost 0.038233580 b_cost_shift_business 0.016656426 cost_income_elast 0.613155210 b_wifi 0.523121758 b_food 0.220073719 mu_SP 1.994745622 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 = list( alternatives = c(car=1, bus=2, air=3, rail=4), avail = list(car=av_car, bus=av_bus, air=av_air, rail=av_rail), choiceVar = choice, V = lapply(V, "*", mu_RP), rows = (RP==1) ) P[['RP']] = apollo_mnl(mnl_settings, functionality) ### Compute probabilities for the SP part of the data using MNL model mnl_settings$V = lapply(V, "*", mu_SP) mnl_settings$rows = (SP==1) P[['SP']] = apollo_mnl(mnl_settings, 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)