Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : NL_two_levels Model description : Two-level NL model with socio-demographics on mode choice SP data Model run at : 2023-05-10 19:58:15 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -4.499366 Number of individuals : 500 Number of rows in database : 7000 Number of modelled outcomes : 7000 Number of cores used : 1 Model without mixing LL(start) : -4830.94 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : -6706.94 LL(final) : -4774.55 Rho-squared vs equal shares : 0.4175 Adj.Rho-squared vs equal shares : 0.4153 Rho-squared vs observed shares : 0.2881 Adj.Rho-squared vs observed shares : 0.2859 AIC : 9585.1 BIC : 9708.47 Estimated parameters : 18 Time taken (hh:mm:ss) : 00:00:23.3 pre-estimation : 00:00:0.59 estimation : 00:00:11.44 initial estimation : 00:00:10.56 estimation after rescaling : 00:00:0.88 post-estimation : 00:00:11.26 Iterations : 31 initial estimation : 28 estimation after rescaling : 3 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) t.rat(1) Rob.s.e. Rob.t.rat.(0) Rob.t.rat.(1) asc_car 0.000000 NA NA NA NA NA NA asc_bus 0.389998 0.436678 0.8931 -1.397 0.421992 0.9242 -1.446 asc_air -0.703746 0.301202 -2.3365 -5.656 0.292797 -2.4035 -5.819 asc_rail -1.666334 0.299917 -5.5560 -8.890 0.288935 -5.7672 -9.228 asc_bus_shift_female 0.269705 0.103713 2.6005 -7.042 0.113000 2.3868 -6.463 asc_air_shift_female 0.238200 0.077606 3.0693 -9.816 0.078306 3.0419 -9.728 asc_rail_shift_female 0.179786 0.067785 2.6523 -12.100 0.068430 2.6273 -11.986 b_tt_car -0.010496 7.2781e-04 -14.4217 -1388.410 7.2982e-04 -14.3819 -1384.576 b_tt_bus -0.016547 0.001244 -13.3000 -817.053 0.001221 -13.5487 -832.332 b_tt_air -0.012462 0.002028 -6.1440 -499.147 0.002040 -6.1089 -496.296 b_tt_rail -0.005176 0.001396 -3.7087 -720.286 0.001354 -3.8236 -742.600 b_tt_shift_business -0.006076 5.0779e-04 -11.9655 -1981.265 4.7318e-04 -12.8408 -2126.201 b_access -0.016973 0.002082 -8.1520 -488.440 0.002026 -8.3767 -501.903 b_cost -0.058410 0.002413 -24.2108 -438.708 0.002459 -23.7545 -430.440 b_cost_shift_business 0.024503 0.002280 10.7486 -427.907 0.002140 11.4489 -455.790 cost_income_elast -0.603005 0.028930 -20.8439 -55.410 0.029927 -20.1491 -53.564 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.771047 0.047051 16.3876 -4.866 0.048106 16.0283 -4.759 b_food 0.329419 0.040594 8.1150 -16.519 0.043124 7.6389 -15.550 lambda_PT 0.632446 0.028522 22.1739 -12.887 0.028226 22.4066 -13.022 Nesting structure for model component : Nest: root (1) |----Alternative: car '-Nest: PT (0.6324) |-Alternative: bus |-Alternative: air '-Alternative: rail Overview of choices for NL model component : car bus air rail Times available 5446.00 6314.00 5264.00 6118.00 Times chosen 1946.00 358.00 1522.00 3174.00 Percentage chosen overall 27.80 5.11 21.74 45.34 Percentage chosen when available 35.73 5.67 28.91 51.88 Classical covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.190687 0.036642 0.034186 -0.006259 asc_air 0.036642 0.090722 0.051278 -0.001790 asc_rail 0.034186 0.051278 0.089950 -0.001762 asc_bus_shift_female -0.006259 -0.001790 -0.001762 0.010756 asc_air_shift_female -0.001478 -0.002967 -0.002029 0.003416 asc_rail_shift_female -0.001619 -0.001691 -0.002339 0.003290 b_tt_car 1.0713e-04 1.4425e-04 1.5241e-04 -1.747e-06 b_tt_bus -4.2611e-04 3.978e-05 5.100e-05 -5.434e-07 b_tt_air -1.461e-05 -3.6996e-04 -1.466e-06 -2.675e-06 b_tt_rail 7.657e-06 7.205e-06 -2.7407e-04 -1.810e-06 b_tt_shift_business 6.165e-06 1.038e-05 1.575e-05 2.471e-07 b_access -1.231e-05 -3.0748e-04 -1.508e-05 -2.017e-07 b_cost -1.298e-05 -1.655e-05 4.130e-05 -1.483e-05 b_cost_shift_business 4.185e-05 -4.339e-05 -1.601e-05 1.232e-05 cost_income_elast -6.3730e-04 9.7071e-04 4.1061e-04 -1.3092e-04 b_wifi -1.4706e-04 -0.001630 -0.002053 1.4698e-04 b_food -2.0071e-04 -9.9044e-04 -0.001334 4.270e-05 lambda_PT 2.804e-05 -3.0127e-04 -0.001069 1.6945e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.001478 -0.001619 1.0713e-04 -4.2611e-04 asc_air -0.002967 -0.001691 1.4425e-04 3.978e-05 asc_rail -0.002029 -0.002339 1.5241e-04 5.100e-05 asc_bus_shift_female 0.003416 0.003290 -1.747e-06 -5.434e-07 asc_air_shift_female 0.006023 0.003677 -1.347e-06 -2.508e-06 asc_rail_shift_female 0.003677 0.004595 -6.248e-07 -8.708e-07 b_tt_car -1.347e-06 -6.248e-07 5.297e-07 2.408e-07 b_tt_bus -2.508e-06 -8.708e-07 2.408e-07 1.548e-06 b_tt_air -1.325e-06 -1.471e-06 7.979e-08 1.947e-07 b_tt_rail -5.683e-07 -2.145e-07 3.591e-08 9.186e-08 b_tt_shift_business -6.962e-07 -3.134e-07 -1.854e-08 -3.519e-08 b_access -3.009e-06 -2.497e-06 8.239e-08 9.287e-08 b_cost -8.367e-06 -3.964e-06 7.430e-07 1.266e-06 b_cost_shift_business 2.520e-06 1.547e-06 -4.930e-07 -9.082e-07 cost_income_elast 6.703e-06 -4.837e-06 -2.476e-07 2.365e-06 b_wifi 1.1242e-04 4.105e-05 -9.860e-06 -1.493e-05 b_food 4.532e-05 1.396e-05 -4.351e-06 -5.833e-06 lambda_PT 8.527e-05 3.381e-05 -7.123e-06 -1.315e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.461e-05 7.657e-06 6.165e-06 -1.231e-05 asc_air -3.6996e-04 7.205e-06 1.038e-05 -3.0748e-04 asc_rail -1.466e-06 -2.7407e-04 1.575e-05 -1.508e-05 asc_bus_shift_female -2.675e-06 -1.810e-06 2.471e-07 -2.017e-07 asc_air_shift_female -1.325e-06 -5.683e-07 -6.962e-07 -3.009e-06 asc_rail_shift_female -1.471e-06 -2.145e-07 -3.134e-07 -2.497e-06 b_tt_car 7.979e-08 3.591e-08 -1.854e-08 8.239e-08 b_tt_bus 1.947e-07 9.186e-08 -3.519e-08 9.287e-08 b_tt_air 4.114e-06 -6.939e-08 -4.996e-08 1.591e-06 b_tt_rail -6.939e-08 1.947e-06 -8.315e-08 -2.078e-07 b_tt_shift_business -4.996e-08 -8.315e-08 2.579e-07 6.099e-08 b_access 1.591e-06 -2.078e-07 6.099e-08 4.335e-06 b_cost 1.390e-06 8.687e-07 -2.161e-07 1.181e-06 b_cost_shift_business -4.593e-07 -5.914e-07 7.185e-07 -9.666e-08 cost_income_elast -6.542e-06 -2.093e-06 4.875e-07 -5.230e-06 b_wifi -1.286e-05 -9.151e-06 -2.154e-06 -1.411e-05 b_food -6.843e-06 -3.893e-06 -8.621e-07 -6.767e-06 lambda_PT -1.176e-05 -5.178e-06 -6.140e-07 -1.267e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -1.298e-05 4.185e-05 -6.3730e-04 -1.4706e-04 asc_air -1.655e-05 -4.339e-05 9.7071e-04 -0.001630 asc_rail 4.130e-05 -1.601e-05 4.1061e-04 -0.002053 asc_bus_shift_female -1.483e-05 1.232e-05 -1.3092e-04 1.4698e-04 asc_air_shift_female -8.367e-06 2.520e-06 6.703e-06 1.1242e-04 asc_rail_shift_female -3.964e-06 1.547e-06 -4.837e-06 4.105e-05 b_tt_car 7.430e-07 -4.930e-07 -2.476e-07 -9.860e-06 b_tt_bus 1.266e-06 -9.082e-07 2.365e-06 -1.493e-05 b_tt_air 1.390e-06 -4.593e-07 -6.542e-06 -1.286e-05 b_tt_rail 8.687e-07 -5.914e-07 -2.093e-06 -9.151e-06 b_tt_shift_business -2.161e-07 7.185e-07 4.875e-07 -2.154e-06 b_access 1.181e-06 -9.666e-08 -5.230e-06 -1.411e-05 b_cost 5.820e-06 -3.768e-06 -1.471e-05 -5.625e-05 b_cost_shift_business -3.768e-06 5.197e-06 2.925e-06 2.038e-05 cost_income_elast -1.471e-05 2.925e-06 8.3692e-04 6.762e-05 b_wifi -5.625e-05 2.038e-05 6.762e-05 0.002214 b_food -2.423e-05 7.779e-06 6.072e-05 0.001109 lambda_PT -4.982e-05 2.472e-05 -1.625e-05 6.7984e-04 b_food lambda_PT asc_bus -2.0071e-04 2.804e-05 asc_air -9.9044e-04 -3.0127e-04 asc_rail -0.001334 -0.001069 asc_bus_shift_female 4.270e-05 1.6945e-04 asc_air_shift_female 4.532e-05 8.527e-05 asc_rail_shift_female 1.396e-05 3.381e-05 b_tt_car -4.351e-06 -7.123e-06 b_tt_bus -5.833e-06 -1.315e-05 b_tt_air -6.843e-06 -1.176e-05 b_tt_rail -3.893e-06 -5.178e-06 b_tt_shift_business -8.621e-07 -6.140e-07 b_access -6.767e-06 -1.267e-05 b_cost -2.423e-05 -4.982e-05 b_cost_shift_business 7.779e-06 2.472e-05 cost_income_elast 6.072e-05 -1.625e-05 b_wifi 0.001109 6.7984e-04 b_food 0.001648 2.6223e-04 lambda_PT 2.6223e-04 8.1351e-04 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 0.178077 0.030533 0.032689 -0.005585 asc_air 0.030533 0.085730 0.048895 -0.001358 asc_rail 0.032689 0.048895 0.083484 -8.4818e-04 asc_bus_shift_female -0.005585 -0.001358 -8.4818e-04 0.012769 asc_air_shift_female 0.001044 -0.002314 -0.002886 0.003309 asc_rail_shift_female -6.5248e-04 -0.001137 -0.001633 0.003650 b_tt_car 1.0159e-04 1.3873e-04 1.4530e-04 -1.903e-07 b_tt_bus -3.9756e-04 4.926e-05 4.485e-05 -3.446e-06 b_tt_air -1.989e-05 -3.4309e-04 9.766e-06 1.239e-05 b_tt_rail -1.906e-06 7.266e-06 -2.4547e-04 -3.134e-06 b_tt_shift_business 1.598e-05 2.016e-05 2.793e-05 1.249e-06 b_access 7.347e-05 -2.8840e-04 -2.077e-05 -9.278e-06 b_cost -2.164e-05 -9.196e-06 3.164e-05 -2.373e-05 b_cost_shift_business 8.992e-05 -4.250e-05 2.487e-05 1.517e-05 cost_income_elast -9.8398e-04 0.001283 8.0050e-04 2.7830e-04 b_wifi -0.001314 -0.001573 -0.001765 1.0987e-04 b_food 4.719e-05 -9.3293e-04 -0.001099 2.7986e-04 lambda_PT -3.1587e-04 -1.2042e-04 -9.8030e-04 2.8879e-04 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.001044 -6.5248e-04 1.0159e-04 -3.9756e-04 asc_air -0.002314 -0.001137 1.3873e-04 4.926e-05 asc_rail -0.002886 -0.001633 1.4530e-04 4.485e-05 asc_bus_shift_female 0.003309 0.003650 -1.903e-07 -3.446e-06 asc_air_shift_female 0.006132 0.003940 -2.158e-06 -9.467e-06 asc_rail_shift_female 0.003940 0.004683 1.279e-06 -1.872e-06 b_tt_car -2.158e-06 1.279e-06 5.326e-07 2.581e-07 b_tt_bus -9.467e-06 -1.872e-06 2.581e-07 1.492e-06 b_tt_air -2.154e-06 3.396e-06 1.561e-07 2.685e-07 b_tt_rail 7.034e-06 1.650e-06 8.423e-08 1.818e-07 b_tt_shift_business 2.754e-07 4.605e-07 3.680e-09 -4.771e-08 b_access -7.341e-06 -3.024e-06 9.004e-08 -1.143e-07 b_cost -1.893e-05 -9.400e-06 7.837e-07 1.347e-06 b_cost_shift_business 1.408e-05 1.170e-05 -4.713e-07 -1.018e-06 cost_income_elast 1.8302e-04 1.6657e-04 6.714e-07 3.192e-06 b_wifi -4.340e-05 -6.840e-05 -9.918e-06 -1.190e-05 b_food -1.6352e-04 -8.021e-05 -5.035e-06 -7.812e-06 lambda_PT 1.0726e-04 3.907e-05 -7.013e-06 -1.197e-05 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -1.989e-05 -1.906e-06 1.598e-05 7.347e-05 asc_air -3.4309e-04 7.266e-06 2.016e-05 -2.8840e-04 asc_rail 9.766e-06 -2.4547e-04 2.793e-05 -2.077e-05 asc_bus_shift_female 1.239e-05 -3.134e-06 1.249e-06 -9.278e-06 asc_air_shift_female -2.154e-06 7.034e-06 2.754e-07 -7.341e-06 asc_rail_shift_female 3.396e-06 1.650e-06 4.605e-07 -3.024e-06 b_tt_car 1.561e-07 8.423e-08 3.680e-09 9.004e-08 b_tt_bus 2.685e-07 1.818e-07 -4.771e-08 -1.143e-07 b_tt_air 4.162e-06 3.515e-08 -7.142e-08 1.475e-06 b_tt_rail 3.515e-08 1.832e-06 -1.184e-07 -1.541e-07 b_tt_shift_business -7.142e-08 -1.184e-07 2.239e-07 5.906e-08 b_access 1.475e-06 -1.541e-07 5.906e-08 4.106e-06 b_cost 1.385e-06 1.003e-06 -2.379e-07 1.234e-06 b_cost_shift_business -3.466e-07 -8.363e-07 5.569e-07 -1.431e-07 cost_income_elast -7.954e-06 -3.409e-06 6.123e-07 -4.244e-06 b_wifi -1.661e-05 -1.158e-05 -2.555e-06 -9.182e-06 b_food -1.108e-05 -6.847e-06 -1.122e-06 -4.226e-06 lambda_PT -1.322e-05 -5.275e-06 -8.213e-07 -1.299e-05 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -2.164e-05 8.992e-05 -9.8398e-04 -0.001314 asc_air -9.196e-06 -4.250e-05 0.001283 -0.001573 asc_rail 3.164e-05 2.487e-05 8.0050e-04 -0.001765 asc_bus_shift_female -2.373e-05 1.517e-05 2.7830e-04 1.0987e-04 asc_air_shift_female -1.893e-05 1.408e-05 1.8302e-04 -4.340e-05 asc_rail_shift_female -9.400e-06 1.170e-05 1.6657e-04 -6.840e-05 b_tt_car 7.837e-07 -4.713e-07 6.714e-07 -9.918e-06 b_tt_bus 1.347e-06 -1.018e-06 3.192e-06 -1.190e-05 b_tt_air 1.385e-06 -3.466e-07 -7.954e-06 -1.661e-05 b_tt_rail 1.003e-06 -8.363e-07 -3.409e-06 -1.158e-05 b_tt_shift_business -2.379e-07 5.569e-07 6.123e-07 -2.555e-06 b_access 1.234e-06 -1.431e-07 -4.244e-06 -9.182e-06 b_cost 6.046e-06 -3.870e-06 -1.685e-05 -5.632e-05 b_cost_shift_business -3.870e-06 4.581e-06 2.958e-06 2.176e-05 cost_income_elast -1.685e-05 2.958e-06 8.9563e-04 8.193e-05 b_wifi -5.632e-05 2.176e-05 8.193e-05 0.002314 b_food -2.751e-05 9.884e-06 3.571e-06 0.001214 lambda_PT -5.120e-05 2.445e-05 6.660e-05 6.2621e-04 b_food lambda_PT asc_bus 4.719e-05 -3.1587e-04 asc_air -9.3293e-04 -1.2042e-04 asc_rail -0.001099 -9.8030e-04 asc_bus_shift_female 2.7986e-04 2.8879e-04 asc_air_shift_female -1.6352e-04 1.0726e-04 asc_rail_shift_female -8.021e-05 3.907e-05 b_tt_car -5.035e-06 -7.013e-06 b_tt_bus -7.812e-06 -1.197e-05 b_tt_air -1.108e-05 -1.322e-05 b_tt_rail -6.847e-06 -5.275e-06 b_tt_shift_business -1.122e-06 -8.213e-07 b_access -4.226e-06 -1.299e-05 b_cost -2.751e-05 -5.120e-05 b_cost_shift_business 9.884e-06 2.445e-05 cost_income_elast 3.571e-06 6.660e-05 b_wifi 0.001214 6.2621e-04 b_food 0.001860 2.8582e-04 lambda_PT 2.8582e-04 7.9670e-04 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.27859 0.261029 -0.138198 asc_air 0.278590 1.00000 0.567637 -0.057305 asc_rail 0.261029 0.56764 1.000000 -0.056634 asc_bus_shift_female -0.138198 -0.05731 -0.056634 1.000000 asc_air_shift_female -0.043620 -0.12693 -0.087157 0.424472 asc_rail_shift_female -0.054694 -0.08283 -0.115051 0.467916 b_tt_car 0.337094 0.65801 0.698233 -0.023141 b_tt_bus -0.784304 0.10615 0.136666 -0.004211 b_tt_air -0.016496 -0.60554 -0.002410 -0.012713 b_tt_rail 0.012565 0.01714 -0.654833 -0.012504 b_tt_shift_business 0.027802 0.06785 0.103416 0.004691 b_access -0.013544 -0.49030 -0.024154 -9.3417e-04 b_cost -0.012322 -0.02277 0.057076 -0.059286 b_cost_shift_business 0.042040 -0.06319 -0.023423 0.052090 cost_income_elast -0.050448 0.11140 0.047325 -0.043635 b_wifi -0.007157 -0.11501 -0.145482 0.030121 b_food -0.011323 -0.08101 -0.109541 0.010142 lambda_PT 0.002251 -0.03507 -0.124948 0.057282 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus -0.043620 -0.054694 0.33709 -0.784304 asc_air -0.126934 -0.082828 0.65801 0.106145 asc_rail -0.087157 -0.115051 0.69823 0.136666 asc_bus_shift_female 0.424472 0.467916 -0.02314 -0.004211 asc_air_shift_female 1.000000 0.698991 -0.02384 -0.025974 asc_rail_shift_female 0.698991 1.000000 -0.01266 -0.010325 b_tt_car -0.023844 -0.012664 1.00000 0.265887 b_tt_bus -0.025974 -0.010325 0.26589 1.000000 b_tt_air -0.008420 -0.010700 0.05405 0.077133 b_tt_rail -0.005248 -0.002267 0.03536 0.052907 b_tt_shift_business -0.017666 -0.009106 -0.05016 -0.055695 b_access -0.018622 -0.017693 0.05437 0.035851 b_cost -0.044688 -0.024242 0.42314 0.421688 b_cost_shift_business 0.014241 0.010014 -0.29713 -0.320218 cost_income_elast 0.002986 -0.002466 -0.01176 0.065705 b_wifi 0.030789 0.012872 -0.28793 -0.254975 b_food 0.014385 0.005074 -0.14725 -0.115500 lambda_PT 0.038525 0.017489 -0.34315 -0.370649 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.016496 0.012565 0.027802 -0.01354 asc_air -0.605541 0.017140 0.067848 -0.49030 asc_rail -0.002410 -0.654833 0.103416 -0.02415 asc_bus_shift_female -0.012713 -0.012504 0.004691 -9.3417e-04 asc_air_shift_female -0.008420 -0.005248 -0.017666 -0.01862 asc_rail_shift_female -0.010700 -0.002267 -0.009106 -0.01769 b_tt_car 0.054048 0.035358 -0.050160 0.05437 b_tt_bus 0.077133 0.052907 -0.055695 0.03585 b_tt_air 1.000000 -0.024514 -0.048507 0.37682 b_tt_rail -0.024514 1.000000 -0.117331 -0.07153 b_tt_shift_business -0.048507 -0.117331 1.000000 0.05768 b_access 0.376820 -0.071533 0.057683 1.00000 b_cost 0.283996 0.258025 -0.176432 0.23514 b_cost_shift_business -0.099327 -0.185882 0.620677 -0.02036 cost_income_elast -0.111492 -0.051855 0.033182 -0.08684 b_wifi -0.134788 -0.139364 -0.090157 -0.14406 b_food -0.083104 -0.068714 -0.041822 -0.08007 lambda_PT -0.203256 -0.130102 -0.042394 -0.21344 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.01232 0.04204 -0.050448 -0.007157 asc_air -0.02277 -0.06319 0.111401 -0.115012 asc_rail 0.05708 -0.02342 0.047325 -0.145482 asc_bus_shift_female -0.05929 0.05209 -0.043635 0.030121 asc_air_shift_female -0.04469 0.01424 0.002986 0.030789 asc_rail_shift_female -0.02424 0.01001 -0.002466 0.012872 b_tt_car 0.42314 -0.29713 -0.011761 -0.287932 b_tt_bus 0.42169 -0.32022 0.065705 -0.254975 b_tt_air 0.28400 -0.09933 -0.111492 -0.134788 b_tt_rail 0.25802 -0.18588 -0.051855 -0.139364 b_tt_shift_business -0.17643 0.62068 0.033182 -0.090157 b_access 0.23514 -0.02036 -0.086836 -0.144057 b_cost 1.00000 -0.68511 -0.210744 -0.495522 b_cost_shift_business -0.68511 1.00000 0.044357 0.190046 cost_income_elast -0.21074 0.04436 1.000000 0.049680 b_wifi -0.49552 0.19005 0.049680 1.000000 b_food -0.24738 0.08406 0.051707 0.580403 lambda_PT -0.72401 0.38014 -0.019690 0.506597 b_food lambda_PT asc_bus -0.011323 0.002251 asc_air -0.081005 -0.035068 asc_rail -0.109541 -0.124948 asc_bus_shift_female 0.010142 0.057282 asc_air_shift_female 0.014385 0.038525 asc_rail_shift_female 0.005074 0.017489 b_tt_car -0.147254 -0.343146 b_tt_bus -0.115500 -0.370649 b_tt_air -0.083104 -0.203256 b_tt_rail -0.068714 -0.130102 b_tt_shift_business -0.041822 -0.042394 b_access -0.080068 -0.213435 b_cost -0.247383 -0.724008 b_cost_shift_business 0.084059 0.380145 cost_income_elast 0.051707 -0.019690 b_wifi 0.580403 0.506597 b_food 1.000000 0.226486 lambda_PT 0.226486 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.24712 0.26810 -0.117122 asc_air 0.247118 1.00000 0.57796 -0.041039 asc_rail 0.268098 0.57796 1.00000 -0.025978 asc_bus_shift_female -0.117122 -0.04104 -0.02598 1.000000 asc_air_shift_female 0.031585 -0.10092 -0.12757 0.374002 asc_rail_shift_female -0.022595 -0.05675 -0.08259 0.472089 b_tt_car 0.329848 0.64921 0.68904 -0.002308 b_tt_bus -0.771382 0.13775 0.12710 -0.024966 b_tt_air -0.023106 -0.57439 0.01657 0.053739 b_tt_rail -0.003337 0.01833 -0.62764 -0.020491 b_tt_shift_business 0.080013 0.14552 0.20431 0.023368 b_access 0.085929 -0.48612 -0.03547 -0.040522 b_cost -0.020857 -0.01277 0.04454 -0.085415 b_cost_shift_business 0.099558 -0.06782 0.04022 0.062723 cost_income_elast -0.077914 0.14644 0.09258 0.082293 b_wifi -0.064752 -0.11165 -0.12698 0.020212 b_food 0.002593 -0.07389 -0.08822 0.057431 lambda_PT -0.026519 -0.01457 -0.12020 0.090543 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.031585 -0.02260 0.329848 -0.77138 asc_air -0.100917 -0.05675 0.649211 0.13775 asc_rail -0.127566 -0.08259 0.689043 0.12710 asc_bus_shift_female 0.374002 0.47209 -0.002308 -0.02497 asc_air_shift_female 1.000000 0.73536 -0.037763 -0.09899 asc_rail_shift_female 0.735357 1.00000 0.025612 -0.02240 b_tt_car -0.037763 0.02561 1.000000 0.28958 b_tt_bus -0.098985 -0.02240 0.289582 1.00000 b_tt_air -0.013485 0.02433 0.104856 0.10777 b_tt_rail 0.066366 0.01782 0.085263 0.11000 b_tt_shift_business 0.007434 0.01422 0.010655 -0.08256 b_access -0.046266 -0.02181 0.060890 -0.04619 b_cost -0.098307 -0.05587 0.436700 0.44841 b_cost_shift_business 0.084042 0.07990 -0.301745 -0.38938 cost_income_elast 0.078097 0.08134 0.030742 0.08734 b_wifi -0.011521 -0.02078 -0.282483 -0.20260 b_food -0.048425 -0.02718 -0.159994 -0.14833 lambda_PT 0.048526 0.02023 -0.340439 -0.34717 b_tt_air b_tt_rail b_tt_shift_business b_access asc_bus -0.02311 -0.003337 0.080013 0.08593 asc_air -0.57439 0.018334 0.145515 -0.48612 asc_rail 0.01657 -0.627644 0.204308 -0.03547 asc_bus_shift_female 0.05374 -0.020491 0.023368 -0.04052 asc_air_shift_female -0.01348 0.066366 0.007434 -0.04627 asc_rail_shift_female 0.02433 0.017817 0.014221 -0.02181 b_tt_car 0.10486 0.085263 0.010655 0.06089 b_tt_bus 0.10777 0.110000 -0.082560 -0.04619 b_tt_air 1.00000 0.012730 -0.073987 0.35683 b_tt_rail 0.01273 1.000000 -0.184817 -0.05618 b_tt_shift_business -0.07399 -0.184817 1.000000 0.06160 b_access 0.35683 -0.056182 0.061602 1.00000 b_cost 0.27603 0.301201 -0.204447 0.24760 b_cost_shift_business -0.07938 -0.288687 0.549890 -0.03300 cost_income_elast -0.13028 -0.084144 0.043237 -0.06999 b_wifi -0.16929 -0.177812 -0.112242 -0.09420 b_food -0.12589 -0.117307 -0.055000 -0.04836 lambda_PT -0.22955 -0.138064 -0.061494 -0.22713 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus -0.02086 0.09956 -0.077914 -0.06475 asc_air -0.01277 -0.06782 0.146437 -0.11165 asc_rail 0.04454 0.04022 0.092576 -0.12698 asc_bus_shift_female -0.08542 0.06272 0.082293 0.02021 asc_air_shift_female -0.09831 0.08404 0.078097 -0.01152 asc_rail_shift_female -0.05587 0.07990 0.081338 -0.02078 b_tt_car 0.43670 -0.30174 0.030742 -0.28248 b_tt_bus 0.44841 -0.38938 0.087337 -0.20260 b_tt_air 0.27603 -0.07938 -0.130284 -0.16929 b_tt_rail 0.30120 -0.28869 -0.084144 -0.17781 b_tt_shift_business -0.20445 0.54989 0.043237 -0.11224 b_access 0.24760 -0.03300 -0.069993 -0.09420 b_cost 1.00000 -0.73535 -0.228921 -0.47611 b_cost_shift_business -0.73535 1.00000 0.046179 0.21136 cost_income_elast -0.22892 0.04618 1.000000 0.05691 b_wifi -0.47611 0.21136 0.056912 1.00000 b_food -0.25941 0.10709 0.002767 0.58540 lambda_PT -0.73768 0.40473 0.078846 0.46119 b_food lambda_PT asc_bus 0.002593 -0.02652 asc_air -0.073886 -0.01457 asc_rail -0.088225 -0.12020 asc_bus_shift_female 0.057431 0.09054 asc_air_shift_female -0.048425 0.04853 asc_rail_shift_female -0.027183 0.02023 b_tt_car -0.159994 -0.34044 b_tt_bus -0.148331 -0.34717 b_tt_air -0.125891 -0.22955 b_tt_rail -0.117307 -0.13806 b_tt_shift_business -0.055000 -0.06149 b_access -0.048364 -0.22713 b_cost -0.259412 -0.73768 b_cost_shift_business 0.107089 0.40473 cost_income_elast 0.002767 0.07885 b_wifi 0.585404 0.46119 b_food 1.000000 0.23482 lambda_PT 0.234815 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.2315066 293 0.2341898 400 0.2350237 146 0.2625512 181 0.2693534 367 0.2733236 317 0.2755103 276 0.2769860 186 0.2886264 434 0.2896023 147 0.2906615 142 0.2914493 307 0.2927494 161 0.2939943 370 0.2942649 447 0.2982635 441 0.3004598 183 0.3005712 259 0.3026340 379 0.3051664 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000000 0.000000 0.000000 asc_bus 0.286548 0.389998 0.103450 asc_air -0.903342 -0.703746 0.199596 asc_rail -2.092649 -1.666334 0.426315 asc_bus_shift_female 0.340176 0.269705 -0.070472 asc_air_shift_female 0.268177 0.238200 -0.029978 asc_rail_shift_female 0.189615 0.179786 -0.009830 b_tt_car -0.013107 -0.010496 0.002611 b_tt_bus -0.021266 -0.016547 0.004719 b_tt_air -0.016578 -0.012462 0.004115 b_tt_rail -0.007051 -0.005176 0.001876 b_tt_shift_business -0.006234 -0.006076 1.5765e-04 b_access -0.021153 -0.016973 0.004179 b_cost -0.076190 -0.058410 0.017780 b_cost_shift_business 0.033381 0.024503 -0.008878 cost_income_elast -0.613795 -0.603005 0.010789 b_no_frills 0.000000 0.000000 0.000000 b_wifi 1.026713 0.771047 -0.255665 b_food 0.422069 0.329419 -0.092650 lambda_PT 1.000000 0.632446 -0.367554 Settings and functions used in model definition: apollo_control -------------- Value modelName "NL_two_levels" modelDescr "Two-level NL model with socio-demographics on mode choice SP 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 second derivative of LL (using numDeriv) Scaling in estimation --------------------- Value asc_bus 0.389999019 asc_air 0.703745478 asc_rail 1.666342088 asc_bus_shift_female 0.269704703 asc_air_shift_female 0.238199533 asc_rail_shift_female 0.179785551 b_tt_car 0.010496313 b_tt_bus 0.016546994 b_tt_air 0.012462425 b_tt_rail 0.005175645 b_tt_shift_business 0.006076032 b_access 0.016973226 b_cost 0.058410596 b_cost_shift_business 0.024503436 cost_income_elast 0.603006121 b_wifi 0.771046331 b_food 0.329418563 lambda_PT 0.632448333 Scaling used in computing Hessian --------------------------------- Value asc_bus 0.389998417 asc_air 0.703745756 asc_rail 1.666334393 asc_bus_shift_female 0.269704552 asc_air_shift_female 0.238199508 asc_rail_shift_female 0.179785613 b_tt_car 0.010496252 b_tt_bus 0.016547400 b_tt_air 0.012462432 b_tt_rail 0.005175634 b_tt_shift_business 0.006076029 b_access 0.016973237 b_cost 0.058410041 b_cost_shift_business 0.024503436 cost_income_elast 0.603005163 b_wifi 0.771047377 b_food 0.329418559 lambda_PT 0.632445772 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: these must use the same names as in nl_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 ) ### Specify nests for NL model nlNests = list(root=1, PT=lambda_PT) ### Specify tree structure for NL model nlStructure= list() nlStructure[["root"]] = c("car","PT") nlStructure[["PT"]] = c("bus","air","rail") ### Define settings for NL model nl_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, utilities = V, nlNests = nlNests, nlStructure = nlStructure ) ### Compute probabilities using NL model P[["model"]] = apollo_nl(nl_settings, functionality) ### Take product across observation for same individual P = apollo_panelProd(P, apollo_inputs, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }