Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : DFT_mode_choice Model description : DFT model on mode choice SP data Model run at : 2023-05-10 20:25:48 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -0.010444 Number of individuals : 500 Number of rows in database : 7000 Number of modelled outcomes : 7000 Number of cores used : 4 Model without mixing LL(start) : -7425.98 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : NA LL(final) : -4806.56 Rho-squared vs equal shares : 0.4135 Adj.Rho-squared vs equal shares : 0.4111 Rho-squared vs observed shares : Not applicable Adj.Rho-squared vs observed shares : Not applicable AIC : 9653.12 BIC : 9790.2 Estimated parameters : 20 Time taken (hh:mm:ss) : 00:56:11.68 pre-estimation : 00:00:22.55 estimation : 00:44:20.31 initial estimation : 00:33:27.48 estimation after rescaling : 00:10:52.83 post-estimation : 00:11:28.83 Iterations : 137 initial estimation : 102 estimation after rescaling : 35 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 23.185539 8.904767 2.6037 10.619730 2.1833 asc_air 4.416363 5.740023 0.7694 8.004454 0.5517 asc_rail -16.567332 4.862336 -3.4073 5.517219 -3.0028 asc_bus_shift_female 10.019584 5.272540 1.9003 6.527116 1.5351 asc_air_shift_female 3.103229 2.529298 1.2269 2.583027 1.2014 asc_rail_shift_female 2.132244 2.025831 1.0525 2.082198 1.0240 b_tt_car -0.001632 4.0890e-04 -3.9902 5.1510e-04 -3.1676 b_tt_bus -0.002936 7.2859e-04 -4.0293 9.1145e-04 -3.2209 b_tt_air -0.003192 7.3440e-04 -4.3466 7.9184e-04 -4.0313 b_tt_rail -0.001692 4.0505e-04 -4.1777 4.3548e-04 -3.8859 b_tt_shift_business -0.001114 2.6254e-04 -4.2415 2.8387e-04 -3.9228 b_acc -0.003526 8.7661e-04 -4.0228 0.001036 -3.4025 b_cost -0.011915 0.002902 -4.1061 0.003616 -3.2946 b_cost_shift_business 0.005345 0.001434 3.7277 0.001771 3.0190 cost_income_elast -0.667426 0.034514 -19.3377 0.037441 -17.8261 b_no_frills 0.000000 NA NA NA NA b_wifi 0.155282 0.036675 4.2340 0.045113 3.4421 b_food 0.063239 0.016866 3.7495 0.020405 3.0992 p_error_sd 1.000000 NA NA NA NA p_timesteps 5.892891 0.452804 13.0142 0.564065 10.4472 p_phi1 1.199010 0.570488 2.1017 0.716327 1.6738 p_phi2 -5.286590 0.413694 -12.7790 0.432406 -12.2260 Overview of choices for DFT 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 79.294873 21.750098 -9.844969 17.052066 asc_air 21.750098 32.947864 10.543145 15.844841 asc_rail -9.844969 10.543145 23.642312 1.608991 asc_bus_shift_female 17.052066 15.844841 1.608991 27.799675 asc_air_shift_female 4.821709 -1.091730 -3.487944 -1.392015 asc_rail_shift_female 2.979501 -1.099529 -3.437814 -2.245722 b_tt_car 0.002532 0.001362 -5.9514e-04 0.001181 b_tt_bus 0.003956 0.002391 -0.001096 0.002033 b_tt_air 0.003764 9.5816e-04 -0.001719 0.001567 b_tt_rail 0.001876 4.7350e-04 -0.001369 6.3701e-04 b_tt_shift_business 0.001384 5.8357e-04 -5.6674e-04 6.1704e-04 b_acc 0.004749 0.002098 -0.001381 0.002341 b_cost 0.016368 0.009752 -0.004272 0.008121 b_cost_shift_business -0.007296 -0.004844 0.001838 -0.003714 cost_income_elast -0.033785 -0.017268 -0.026709 -0.017057 b_wifi -0.205844 -0.114532 0.054597 -0.100748 b_food -0.084162 -0.048205 0.020512 -0.041856 p_timesteps 2.675876 1.488807 -0.683618 1.316963 p_phi1 2.970190 1.960379 -0.690182 1.699787 p_phi2 -1.620528 -0.801650 0.980287 -0.744456 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 4.821709 2.979501 0.002532 0.003956 asc_air -1.091730 -1.099529 0.001362 0.002391 asc_rail -3.487944 -3.437814 -5.9514e-04 -0.001096 asc_bus_shift_female -1.392015 -2.245722 0.001181 0.002033 asc_air_shift_female 6.397346 3.851673 2.6309e-04 4.8519e-04 asc_rail_shift_female 3.851673 4.103991 1.5901e-04 2.9843e-04 b_tt_car 2.6309e-04 1.5901e-04 1.672e-07 2.935e-07 b_tt_bus 4.8519e-04 2.9843e-04 2.935e-07 5.308e-07 b_tt_air 4.4760e-04 3.0011e-04 2.670e-07 4.711e-07 b_tt_rail 2.3416e-04 1.6691e-04 1.366e-07 2.361e-07 b_tt_shift_business 1.9105e-04 1.2754e-04 9.374e-08 1.690e-07 b_acc 5.4965e-04 3.4012e-04 3.326e-07 5.910e-07 b_cost 0.001962 0.001216 1.165e-06 2.103e-06 b_cost_shift_business -9.3079e-04 -5.8540e-04 -5.539e-07 -1.006e-06 cost_income_elast 0.010984 0.009733 8.923e-07 2.571e-06 b_wifi -0.024402 -0.015215 -1.436e-05 -2.589e-05 b_food -0.009959 -0.006253 -5.921e-06 -1.068e-05 p_timesteps 0.306219 0.186608 1.8096e-04 3.2690e-04 p_phi1 0.436127 0.272309 2.1409e-04 3.8892e-04 p_phi2 -0.302185 -0.216263 -1.4832e-04 -2.7407e-04 b_tt_air b_tt_rail b_tt_shift_business b_acc asc_bus 0.003764 0.001876 0.001384 0.004749 asc_air 9.5816e-04 4.7350e-04 5.8357e-04 0.002098 asc_rail -0.001719 -0.001369 -5.6674e-04 -0.001381 asc_bus_shift_female 0.001567 6.3701e-04 6.1704e-04 0.002341 asc_air_shift_female 4.4760e-04 2.3416e-04 1.9105e-04 5.4965e-04 asc_rail_shift_female 3.0011e-04 1.6691e-04 1.2754e-04 3.4012e-04 b_tt_car 2.670e-07 1.366e-07 9.374e-08 3.326e-07 b_tt_bus 4.711e-07 2.361e-07 1.690e-07 5.910e-07 b_tt_air 5.393e-07 2.597e-07 1.598e-07 5.300e-07 b_tt_rail 2.597e-07 1.641e-07 8.296e-08 2.664e-07 b_tt_shift_business 1.598e-07 8.296e-08 6.893e-08 1.998e-07 b_acc 5.300e-07 2.664e-07 1.998e-07 7.684e-07 b_cost 1.838e-06 9.250e-07 6.741e-07 2.334e-06 b_cost_shift_business -8.651e-07 -4.341e-07 -2.968e-07 -1.091e-06 cost_income_elast 3.417e-06 1.532e-06 1.667e-06 3.152e-06 b_wifi -2.328e-05 -1.158e-05 -8.513e-06 -2.929e-05 b_food -9.684e-06 -4.795e-06 -3.487e-06 -1.212e-05 p_timesteps 2.8817e-04 1.4091e-04 1.0691e-04 3.6736e-04 p_phi1 3.2681e-04 1.5695e-04 1.3005e-04 4.3576e-04 p_phi2 -2.6342e-04 -1.4064e-04 -9.705e-05 -3.0834e-04 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.016368 -0.007296 -0.033785 -0.205844 asc_air 0.009752 -0.004844 -0.017268 -0.114532 asc_rail -0.004272 0.001838 -0.026709 0.054597 asc_bus_shift_female 0.008121 -0.003714 -0.017057 -0.100748 asc_air_shift_female 0.001962 -9.3079e-04 0.010984 -0.024402 asc_rail_shift_female 0.001216 -5.8540e-04 0.009733 -0.015215 b_tt_car 1.165e-06 -5.539e-07 8.923e-07 -1.436e-05 b_tt_bus 2.103e-06 -1.006e-06 2.571e-06 -2.589e-05 b_tt_air 1.838e-06 -8.651e-07 3.417e-06 -2.328e-05 b_tt_rail 9.250e-07 -4.341e-07 1.532e-06 -1.158e-05 b_tt_shift_business 6.741e-07 -2.968e-07 1.667e-06 -8.513e-06 b_acc 2.334e-06 -1.091e-06 3.152e-06 -2.929e-05 b_cost 8.420e-06 -4.044e-06 7.891e-06 -1.0344e-04 b_cost_shift_business -4.044e-06 2.056e-06 -4.843e-06 4.896e-05 cost_income_elast 7.891e-06 -4.843e-06 0.001191 -1.2068e-04 b_wifi -1.0344e-04 4.896e-05 -1.2068e-04 0.001345 b_food -4.284e-05 2.029e-05 -4.242e-05 5.6211e-04 p_timesteps 0.001302 -6.1776e-04 0.001559 -0.016143 p_phi1 0.001552 -7.3529e-04 0.003046 -0.019155 p_phi2 -0.001093 5.2452e-04 -0.003703 0.013599 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.084162 2.675876 2.970190 -1.620528 asc_air -0.048205 1.488807 1.960379 -0.801650 asc_rail 0.020512 -0.683618 -0.690182 0.980287 asc_bus_shift_female -0.041856 1.316963 1.699787 -0.744456 asc_air_shift_female -0.009959 0.306219 0.436127 -0.302185 asc_rail_shift_female -0.006253 0.186608 0.272309 -0.216263 b_tt_car -5.921e-06 1.8096e-04 2.1409e-04 -1.4832e-04 b_tt_bus -1.068e-05 3.2690e-04 3.8892e-04 -2.7407e-04 b_tt_air -9.684e-06 2.8817e-04 3.2681e-04 -2.6342e-04 b_tt_rail -4.795e-06 1.4091e-04 1.5695e-04 -1.4064e-04 b_tt_shift_business -3.487e-06 1.0691e-04 1.3005e-04 -9.705e-05 b_acc -1.212e-05 3.6736e-04 4.3576e-04 -3.0834e-04 b_cost -4.284e-05 0.001302 0.001552 -0.001093 b_cost_shift_business 2.029e-05 -6.1776e-04 -7.3529e-04 5.2452e-04 cost_income_elast -4.242e-05 0.001559 0.003046 -0.003703 b_wifi 5.6211e-04 -0.016143 -0.019155 0.013599 b_food 2.8447e-04 -0.006664 -0.007924 0.005614 p_timesteps -0.006664 0.205031 0.242701 -0.169063 p_phi1 -0.007924 0.242701 0.325456 -0.196742 p_phi2 0.005614 -0.169063 -0.196742 0.171142 Robust covariance matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 112.778660 57.052356 0.547602 36.836316 asc_air 57.052356 64.071285 21.189089 36.401237 asc_rail 0.547602 21.189089 30.439709 10.222734 asc_bus_shift_female 36.836316 36.401237 10.222734 42.603247 asc_air_shift_female 7.226788 1.302540 -3.514943 -0.470313 asc_rail_shift_female 2.691415 -1.008324 -3.732625 -2.544454 b_tt_car 0.004313 0.003119 -6.577e-05 0.002294 b_tt_bus 0.007089 0.005448 -1.5726e-04 0.003967 b_tt_air 0.005278 0.002723 -0.001080 0.002771 b_tt_rail 0.002517 9.9404e-04 -0.001431 9.6053e-04 b_tt_shift_business 0.001997 0.001287 -3.1591e-04 0.001004 b_acc 0.007750 0.005225 -3.8356e-04 0.004201 b_cost 0.028812 0.021921 -4.8175e-04 0.015724 b_cost_shift_business -0.013458 -0.010729 5.311e-06 -0.007503 cost_income_elast -0.150101 -0.084900 -0.009899 -0.063747 b_wifi -0.354736 -0.262560 0.007003 -0.192203 b_food -0.148624 -0.110630 9.6207e-04 -0.078221 p_timesteps 4.612937 3.420850 -0.052283 2.497100 p_phi1 5.373499 4.461288 0.273399 3.171653 p_phi2 -2.338721 -1.559595 0.754765 -1.181193 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 7.226788 2.691415 0.004313 0.007089 asc_air 1.302540 -1.008324 0.003119 0.005448 asc_rail -3.514943 -3.732625 -6.577e-05 -1.5726e-04 asc_bus_shift_female -0.470313 -2.544454 0.002294 0.003967 asc_air_shift_female 6.672030 4.202564 3.8348e-04 6.9598e-04 asc_rail_shift_female 4.202564 4.335548 1.7215e-04 3.2133e-04 b_tt_car 3.8348e-04 1.7215e-04 2.653e-07 4.652e-07 b_tt_bus 6.9598e-04 3.2133e-04 4.652e-07 8.307e-07 b_tt_air 5.6717e-04 3.1920e-04 3.622e-07 6.377e-07 b_tt_rail 3.2131e-04 2.0983e-04 1.722e-07 2.980e-07 b_tt_shift_business 2.6053e-04 1.4645e-04 1.300e-07 2.332e-07 b_acc 7.6954e-04 3.7428e-04 5.071e-07 8.985e-07 b_cost 0.002800 0.001299 1.842e-06 3.284e-06 b_cost_shift_business -0.001297 -5.8860e-04 -8.845e-07 -1.581e-06 cost_income_elast 0.009228 0.012372 -4.229e-06 -6.256e-06 b_wifi -0.036681 -0.017542 -2.254e-05 -4.021e-05 b_food -0.016317 -0.008084 -9.452e-06 -1.685e-05 p_timesteps 0.444075 0.199775 2.8635e-04 5.1094e-04 p_phi1 0.602555 0.278993 3.4779e-04 6.2301e-04 p_phi2 -0.396668 -0.259311 -1.9051e-04 -3.4858e-04 b_tt_air b_tt_rail b_tt_shift_business b_acc asc_bus 0.005278 0.002517 0.001997 0.007750 asc_air 0.002723 9.9404e-04 0.001287 0.005225 asc_rail -0.001080 -0.001431 -3.1591e-04 -3.8356e-04 asc_bus_shift_female 0.002771 9.6053e-04 0.001004 0.004201 asc_air_shift_female 5.6717e-04 3.2131e-04 2.6053e-04 7.6954e-04 asc_rail_shift_female 3.1920e-04 2.0983e-04 1.4645e-04 3.7428e-04 b_tt_car 3.622e-07 1.722e-07 1.300e-07 5.071e-07 b_tt_bus 6.377e-07 2.980e-07 2.332e-07 8.985e-07 b_tt_air 6.270e-07 2.907e-07 1.913e-07 7.040e-07 b_tt_rail 2.907e-07 1.896e-07 9.351e-08 3.298e-07 b_tt_shift_business 1.913e-07 9.351e-08 8.058e-08 2.638e-07 b_acc 7.040e-07 3.298e-07 2.638e-07 1.074e-06 b_cost 2.485e-06 1.162e-06 9.272e-07 3.546e-06 b_cost_shift_business -1.183e-06 -5.508e-07 -4.276e-07 -1.690e-06 cost_income_elast -2.828e-06 -2.341e-06 -9.101e-07 -5.917e-06 b_wifi -3.121e-05 -1.438e-05 -1.158e-05 -4.369e-05 b_food -1.326e-05 -6.050e-06 -4.833e-06 -1.833e-05 p_timesteps 3.8773e-04 1.7656e-04 1.4609e-04 5.5397e-04 p_phi1 4.5787e-04 1.9577e-04 1.8130e-04 6.7029e-04 p_phi2 -2.9949e-04 -1.5470e-04 -1.1209e-04 -3.8722e-04 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.028812 -0.013458 -0.150101 -0.354736 asc_air 0.021921 -0.010729 -0.084900 -0.262560 asc_rail -4.8175e-04 5.311e-06 -0.009899 0.007003 asc_bus_shift_female 0.015724 -0.007503 -0.063747 -0.192203 asc_air_shift_female 0.002800 -0.001297 0.009228 -0.036681 asc_rail_shift_female 0.001299 -5.8860e-04 0.012372 -0.017542 b_tt_car 1.842e-06 -8.845e-07 -4.229e-06 -2.254e-05 b_tt_bus 3.284e-06 -1.581e-06 -6.256e-06 -4.021e-05 b_tt_air 2.485e-06 -1.183e-06 -2.828e-06 -3.121e-05 b_tt_rail 1.162e-06 -5.508e-07 -2.341e-06 -1.438e-05 b_tt_shift_business 9.272e-07 -4.276e-07 -9.101e-07 -1.158e-05 b_acc 3.546e-06 -1.690e-06 -5.917e-06 -4.369e-05 b_cost 1.308e-05 -6.310e-06 -2.716e-05 -1.5992e-04 b_cost_shift_business -6.310e-06 3.135e-06 1.132e-05 7.652e-05 cost_income_elast -2.716e-05 1.132e-05 0.001402 3.0126e-04 b_wifi -1.5992e-04 7.652e-05 3.0126e-04 0.002035 b_food -6.713e-05 3.213e-05 1.1595e-04 8.5777e-04 p_timesteps 0.002029 -9.7147e-04 -0.004119 -0.024931 p_phi1 0.002480 -0.001189 -0.003202 -0.030521 p_phi2 -0.001382 6.6427e-04 -5.0418e-04 0.017128 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.148624 4.612937 5.373499 -2.338721 asc_air -0.110630 3.420850 4.461288 -1.559595 asc_rail 9.6207e-04 -0.052283 0.273399 0.754765 asc_bus_shift_female -0.078221 2.497100 3.171653 -1.181193 asc_air_shift_female -0.016317 0.444075 0.602555 -0.396668 asc_rail_shift_female -0.008084 0.199775 0.278993 -0.259311 b_tt_car -9.452e-06 2.8635e-04 3.4779e-04 -1.9051e-04 b_tt_bus -1.685e-05 5.1094e-04 6.2301e-04 -3.4858e-04 b_tt_air -1.326e-05 3.8773e-04 4.5787e-04 -2.9949e-04 b_tt_rail -6.050e-06 1.7656e-04 1.9577e-04 -1.5470e-04 b_tt_shift_business -4.833e-06 1.4609e-04 1.8130e-04 -1.1209e-04 b_acc -1.833e-05 5.5397e-04 6.7029e-04 -3.8722e-04 b_cost -6.713e-05 0.002029 0.002480 -0.001382 b_cost_shift_business 3.213e-05 -9.7147e-04 -0.001189 6.6427e-04 cost_income_elast 1.1595e-04 -0.004119 -0.003202 -5.0418e-04 b_wifi 8.5777e-04 -0.024931 -0.030521 0.017128 b_food 4.1637e-04 -0.010439 -0.012859 0.007151 p_timesteps -0.010439 0.318169 0.387504 -0.213773 p_phi1 -0.012859 0.387504 0.513125 -0.256572 p_phi2 0.007151 -0.213773 -0.256572 0.186975 Classical correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.0000 0.42552 -0.22738 0.36319 asc_air 0.4255 1.00000 0.37776 0.52355 asc_rail -0.2274 0.37776 1.00000 0.06276 asc_bus_shift_female 0.3632 0.52355 0.06276 1.00000 asc_air_shift_female 0.2141 -0.07520 -0.28361 -0.10438 asc_rail_shift_female 0.1652 -0.09456 -0.34901 -0.21025 b_tt_car 0.6954 0.58024 -0.29933 0.54761 b_tt_bus 0.6097 0.57177 -0.30923 0.52915 b_tt_air 0.5756 0.22730 -0.48135 0.40463 b_tt_rail 0.5201 0.20365 -0.69495 0.29828 b_tt_shift_business 0.5920 0.38724 -0.44395 0.44575 b_acc 0.6084 0.41700 -0.32411 0.50656 b_cost 0.6335 0.58553 -0.30276 0.53084 b_cost_shift_business -0.5714 -0.58858 0.26367 -0.49122 cost_income_elast -0.1099 -0.08716 -0.15915 -0.09373 b_wifi -0.6303 -0.54406 0.30617 -0.52102 b_food -0.5604 -0.49792 0.25012 -0.47068 p_timesteps 0.6636 0.57282 -0.31050 0.55163 p_phi1 0.5847 0.59866 -0.24881 0.56510 p_phi2 -0.4399 -0.33759 0.48734 -0.34130 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.21408 0.16516 0.69539 0.6097 asc_air -0.07520 -0.09456 0.58024 0.5718 asc_rail -0.28361 -0.34901 -0.29933 -0.3092 asc_bus_shift_female -0.10438 -0.21025 0.54761 0.5292 asc_air_shift_female 1.00000 0.75170 0.25438 0.2633 asc_rail_shift_female 0.75170 1.00000 0.19195 0.2022 b_tt_car 0.25438 0.19195 1.00000 0.9852 b_tt_bus 0.26329 0.20219 0.98520 1.0000 b_tt_air 0.24097 0.20172 0.88922 0.8804 b_tt_rail 0.22856 0.20341 0.82460 0.7999 b_tt_shift_business 0.28771 0.23979 0.87319 0.8832 b_acc 0.24790 0.19153 0.92789 0.9254 b_cost 0.26738 0.20680 0.98190 0.9946 b_cost_shift_business -0.25664 -0.20152 -0.94471 -0.9632 cost_income_elast 0.12583 0.13920 0.06323 0.1022 b_wifi -0.26307 -0.20479 -0.95776 -0.9690 b_food -0.23345 -0.18300 -0.85861 -0.8694 p_timesteps 0.26738 0.20343 0.97733 0.9909 p_phi1 0.30225 0.23562 0.91775 0.9357 p_phi2 -0.28880 -0.25805 -0.87680 -0.9093 b_tt_air b_tt_rail b_tt_shift_business b_acc asc_bus 0.5756 0.5201 0.5920 0.6084 asc_air 0.2273 0.2037 0.3872 0.4170 asc_rail -0.4814 -0.6949 -0.4440 -0.3241 asc_bus_shift_female 0.4046 0.2983 0.4458 0.5066 asc_air_shift_female 0.2410 0.2286 0.2877 0.2479 asc_rail_shift_female 0.2017 0.2034 0.2398 0.1915 b_tt_car 0.8892 0.8246 0.8732 0.9279 b_tt_bus 0.8804 0.7999 0.8832 0.9254 b_tt_air 1.0000 0.8731 0.8287 0.8233 b_tt_rail 0.8731 1.0000 0.7801 0.7503 b_tt_shift_business 0.8287 0.7801 1.0000 0.8682 b_acc 0.8233 0.7503 0.8682 1.0000 b_cost 0.8623 0.7870 0.8849 0.9175 b_cost_shift_business -0.8215 -0.7474 -0.7883 -0.8683 cost_income_elast 0.1348 0.1096 0.1839 0.1042 b_wifi -0.8645 -0.7798 -0.8841 -0.9112 b_food -0.7818 -0.7018 -0.7876 -0.8197 p_timesteps 0.8666 0.7683 0.8993 0.9255 p_phi1 0.7800 0.6792 0.8683 0.8714 p_phi2 -0.8670 -0.8393 -0.8936 -0.8502 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.63348 -0.57136 -0.10992 -0.63030 asc_air 0.58553 -0.58858 -0.08716 -0.54406 asc_rail -0.30276 0.26367 -0.15915 0.30617 asc_bus_shift_female 0.53084 -0.49122 -0.09373 -0.52102 asc_air_shift_female 0.26738 -0.25664 0.12583 -0.26307 asc_rail_shift_female 0.20680 -0.20152 0.13920 -0.20479 b_tt_car 0.98190 -0.94471 0.06323 -0.95776 b_tt_bus 0.99464 -0.96318 0.10225 -0.96903 b_tt_air 0.86233 -0.82147 0.13483 -0.86449 b_tt_rail 0.78699 -0.74736 0.10959 -0.77985 b_tt_shift_business 0.88491 -0.78830 0.18393 -0.88410 b_acc 0.91749 -0.86830 0.10418 -0.91120 b_cost 1.00000 -0.97184 0.07880 -0.97204 b_cost_shift_business -0.97184 1.00000 -0.09785 0.93104 cost_income_elast 0.07880 -0.09785 1.00000 -0.09534 b_wifi -0.97204 0.93104 -0.09534 1.00000 b_food -0.87544 0.83901 -0.07287 0.90875 p_timesteps 0.99127 -0.95145 0.09975 -0.97212 p_phi1 0.93740 -0.89885 0.15469 -0.91550 p_phi2 -0.91032 0.88423 -0.25936 0.89631 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.56037 0.66364 0.5847 -0.4399 asc_air -0.49792 0.57282 0.5987 -0.3376 asc_rail 0.25012 -0.31050 -0.2488 0.4873 asc_bus_shift_female -0.47068 0.55163 0.5651 -0.3413 asc_air_shift_female -0.23345 0.26738 0.3023 -0.2888 asc_rail_shift_female -0.18300 0.20343 0.2356 -0.2580 b_tt_car -0.85861 0.97733 0.9178 -0.8768 b_tt_bus -0.86939 0.99090 0.9357 -0.9093 b_tt_air -0.78183 0.86657 0.7800 -0.8670 b_tt_rail -0.70184 0.76830 0.6792 -0.8393 b_tt_shift_business -0.78755 0.89928 0.8683 -0.8936 b_acc -0.81968 0.92551 0.8714 -0.8502 b_cost -0.87544 0.99127 0.9374 -0.9103 b_cost_shift_business 0.83901 -0.95145 -0.8989 0.8842 cost_income_elast -0.07287 0.09975 0.1547 -0.2594 b_wifi 0.90875 -0.97212 -0.9155 0.8963 b_food 1.00000 -0.87262 -0.8235 0.8045 p_timesteps -0.87262 1.00000 0.9395 -0.9025 p_phi1 -0.82349 0.93954 1.0000 -0.8336 p_phi2 0.80453 -0.90253 -0.8336 1.0000 Robust correlation matrix: asc_bus asc_air asc_rail asc_bus_shift_female asc_bus 1.000000 0.67116 0.009346 0.53142 asc_air 0.671164 1.00000 0.479800 0.69673 asc_rail 0.009346 0.47980 1.000000 0.28387 asc_bus_shift_female 0.531424 0.69673 0.283874 1.00000 asc_air_shift_female 0.263453 0.06300 -0.246643 -0.02790 asc_rail_shift_female 0.121715 -0.06050 -0.324917 -0.18722 b_tt_car 0.788517 0.75654 -0.023143 0.68230 b_tt_bus 0.732389 0.74668 -0.031273 0.66686 b_tt_air 0.627607 0.42956 -0.247266 0.53621 b_tt_rail 0.544260 0.28517 -0.595712 0.33793 b_tt_shift_business 0.662459 0.56639 -0.201704 0.54179 b_acc 0.704104 0.62984 -0.067079 0.62095 b_cost 0.750214 0.75728 -0.024145 0.66613 b_cost_shift_business -0.715729 -0.75707 5.4368e-04 -0.64921 cost_income_elast -0.377506 -0.28329 -0.047923 -0.26085 b_wifi -0.740438 -0.72710 0.028136 -0.65273 b_food -0.685862 -0.67733 0.008546 -0.58730 p_timesteps 0.770079 0.75766 -0.016800 0.67824 p_phi1 0.706370 0.77807 0.069177 0.67835 p_phi2 -0.509300 -0.45060 0.316374 -0.41851 asc_air_shift_female asc_rail_shift_female b_tt_car b_tt_bus asc_bus 0.26345 0.12172 0.78852 0.73239 asc_air 0.06300 -0.06050 0.75654 0.74668 asc_rail -0.24664 -0.32492 -0.02314 -0.03127 asc_bus_shift_female -0.02790 -0.18722 0.68230 0.66686 asc_air_shift_female 1.00000 0.78138 0.28822 0.29562 asc_rail_shift_female 0.78138 1.00000 0.16051 0.16931 b_tt_car 0.28822 0.16051 1.00000 0.99092 b_tt_bus 0.29562 0.16931 0.99092 1.00000 b_tt_air 0.27730 0.19360 0.88790 0.88353 b_tt_rail 0.28565 0.23141 0.76785 0.75082 b_tt_shift_business 0.35530 0.24776 0.88901 0.90138 b_acc 0.28746 0.17344 0.94984 0.95117 b_cost 0.29979 0.17254 0.98858 0.99636 b_cost_shift_business -0.28361 -0.15966 -0.96985 -0.97943 cost_income_elast 0.09542 0.15869 -0.21928 -0.18333 b_wifi -0.31478 -0.18675 -0.96995 -0.97786 b_food -0.30959 -0.19026 -0.89926 -0.90575 p_timesteps 0.30479 0.17009 0.98554 0.99381 p_phi1 0.32565 0.18705 0.94258 0.95423 p_phi2 -0.35515 -0.28801 -0.85532 -0.88445 b_tt_air b_tt_rail b_tt_shift_business b_acc asc_bus 0.62761 0.5443 0.66246 0.70410 asc_air 0.42956 0.2852 0.56639 0.62984 asc_rail -0.24727 -0.5957 -0.20170 -0.06708 asc_bus_shift_female 0.53621 0.3379 0.54179 0.62095 asc_air_shift_female 0.27730 0.2856 0.35530 0.28746 asc_rail_shift_female 0.19360 0.2314 0.24776 0.17344 b_tt_car 0.88790 0.7678 0.88901 0.94984 b_tt_bus 0.88353 0.7508 0.90138 0.95117 b_tt_air 1.00000 0.8429 0.85121 0.85785 b_tt_rail 0.84289 1.0000 0.75645 0.73083 b_tt_shift_business 0.85121 0.7565 1.00000 0.89674 b_acc 0.85785 0.7308 0.89674 1.00000 b_cost 0.86783 0.7379 0.90316 0.94615 b_cost_shift_business -0.84392 -0.7143 -0.85070 -0.92096 cost_income_elast -0.09538 -0.1436 -0.08563 -0.15249 b_wifi -0.87379 -0.7320 -0.90443 -0.93437 b_food -0.82050 -0.6808 -0.83429 -0.86656 p_timesteps 0.86809 0.7188 0.91235 0.94760 p_phi1 0.80721 0.6276 0.89156 0.90286 p_phi2 -0.87468 -0.8215 -0.91319 -0.86404 b_cost b_cost_shift_business cost_income_elast b_wifi asc_bus 0.75021 -0.7157 -0.37751 -0.74044 asc_air 0.75728 -0.7571 -0.28329 -0.72710 asc_rail -0.02414 5.4368e-04 -0.04792 0.02814 asc_bus_shift_female 0.66613 -0.6492 -0.26085 -0.65273 asc_air_shift_female 0.29979 -0.2836 0.09542 -0.31478 asc_rail_shift_female 0.17254 -0.1597 0.15869 -0.18675 b_tt_car 0.98858 -0.9698 -0.21928 -0.96995 b_tt_bus 0.99636 -0.9794 -0.18333 -0.97786 b_tt_air 0.86783 -0.8439 -0.09538 -0.87379 b_tt_rail 0.73786 -0.7143 -0.14358 -0.73195 b_tt_shift_business 0.90316 -0.8507 -0.08563 -0.90443 b_acc 0.94615 -0.9210 -0.15249 -0.93437 b_cost 1.00000 -0.9856 -0.20059 -0.98019 b_cost_shift_business -0.98555 1.0000 0.17071 0.95803 cost_income_elast -0.20059 0.1707 1.00000 0.17836 b_wifi -0.98019 0.9580 0.17836 1.00000 b_food -0.90967 0.8892 0.15178 0.93181 p_timesteps 0.99469 -0.9727 -0.19502 -0.97972 p_phi1 0.95737 -0.9378 -0.11937 -0.94445 p_phi2 -0.88378 0.8677 -0.03114 0.87806 b_food p_timesteps p_phi1 p_phi2 asc_bus -0.685862 0.77008 0.70637 -0.50930 asc_air -0.677332 0.75766 0.77807 -0.45060 asc_rail 0.008546 -0.01680 0.06918 0.31637 asc_bus_shift_female -0.587305 0.67824 0.67835 -0.41851 asc_air_shift_female -0.309588 0.30479 0.32565 -0.35515 asc_rail_shift_female -0.190263 0.17009 0.18705 -0.28801 b_tt_car -0.899256 0.98554 0.94258 -0.85532 b_tt_bus -0.905751 0.99381 0.95423 -0.88445 b_tt_air -0.820495 0.86809 0.80721 -0.87468 b_tt_rail -0.680836 0.71877 0.62757 -0.82154 b_tt_shift_business -0.834288 0.91235 0.89156 -0.91319 b_acc -0.866556 0.94760 0.90286 -0.86404 b_cost -0.909674 0.99469 0.95737 -0.88378 b_cost_shift_business 0.889208 -0.97274 -0.93778 0.86767 cost_income_elast 0.151776 -0.19502 -0.11937 -0.03114 b_wifi 0.931813 -0.97972 -0.94445 0.87806 b_food 1.000000 -0.90694 -0.87972 0.81043 p_timesteps -0.906936 1.00000 0.95904 -0.87646 p_phi1 -0.879725 0.95904 1.00000 -0.82834 p_phi2 0.810427 -0.87646 -0.82834 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 400 0.2378026 464 0.2521165 146 0.2568278 293 0.2614134 186 0.2704741 276 0.2781852 317 0.2828261 467 0.2892039 263 0.2923654 370 0.2940515 181 0.2940872 183 0.2956372 161 0.2984975 441 0.3008122 367 0.3028885 259 0.3037961 133 0.3069040 434 0.3118567 307 0.3129866 379 0.3149290 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.00000 0.000000 0.000000 asc_bus 0.00000 23.185539 23.185539 asc_air 0.00000 4.416363 4.416363 asc_rail 0.00000 -16.567332 -16.567332 asc_bus_shift_female 0.00000 10.019584 10.019584 asc_air_shift_female 0.00000 3.103229 3.103229 asc_rail_shift_female 0.00000 2.132244 2.132244 b_tt_car -0.01000 -0.001632 0.008368 b_tt_bus -0.01000 -0.002936 0.007064 b_tt_air -0.01000 -0.003192 0.006808 b_tt_rail -0.01000 -0.001692 0.008308 b_tt_shift_business 0.00000 -0.001114 -0.001114 b_acc -0.01000 -0.003526 0.006474 b_cost -0.01000 -0.011915 -0.001915 b_cost_shift_business 0.00000 0.005345 0.005345 cost_income_elast 0.00000 -0.667426 -0.667426 b_no_frills 0.00000 0.000000 0.000000 b_wifi -0.01000 0.155282 0.165282 b_food -0.01000 0.063239 0.073239 p_error_sd 1.00000 1.000000 0.000000 p_timesteps 1.00000 5.892891 4.892891 p_phi1 -2.00000 1.199010 3.199010 p_phi2 -2.00000 -5.286590 -3.286590 Settings and functions used in model definition: apollo_control -------------- Value modelName "DFT_mode_choice" modelDescr "DFT model on mode choice SP data" indivID "ID" nCores "4" outputDirectory "output/" debug "FALSE" 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 18.582237183 asc_air 1.729810048 asc_rail 13.524007475 asc_bus_shift_female 4.224180853 asc_air_shift_female 2.990592999 asc_rail_shift_female 2.407758044 b_tt_car 0.002184544 b_tt_bus 0.003954637 b_tt_air 0.004088523 b_tt_rail 0.002202872 b_tt_shift_business 0.001452776 b_acc 0.004651481 b_cost 0.015854416 b_cost_shift_business 0.007194870 cost_income_elast 0.671954779 b_wifi 0.203082990 b_food 0.082598017 p_timesteps 5.358491664 p_phi1 0.510152439 p_phi2 4.856064880 Scaling used in computing Hessian --------------------------------- Value asc_bus 23.185539121 asc_air 4.416363066 asc_rail 16.567332279 asc_bus_shift_female 10.019584099 asc_air_shift_female 3.103228686 asc_rail_shift_female 2.132243618 b_tt_car 0.001631613 b_tt_bus 0.002935700 b_tt_air 0.003192129 b_tt_rail 0.001692211 b_tt_shift_business 0.001113574 b_acc 0.003526373 b_cost 0.011914707 b_cost_shift_business 0.005345177 cost_income_elast 0.667426419 b_wifi 0.155281790 b_food 0.063239156 p_timesteps 5.892891180 p_phi1 1.199009871 p_phi2 5.286589950 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 attribute values attrValues = list() attrValues[["car"]] = list(time=time_car , access=0 , cost=cost_car , wifi=0 , food=0 ) attrValues[["bus"]] = list(time=time_bus , access=access_bus , cost=cost_bus , wifi=0 , food=0 ) attrValues[["air"]] = list(time=time_air , access=access_air , cost=cost_air , wifi=1*(service_air == 2), food=1*(service_air == 3)) attrValues[["rail"]] = list(time=time_rail, access=access_rail, cost=cost_rail, wifi=1*(service_rail == 2), food=1*(service_rail == 3)) ### List of initial preference values altStart = list() altStart[["car"]] = asc_car altStart[["bus"]] = asc_bus_value altStart[["air"]] = asc_air_value altStart[["rail"]] = asc_rail_value ### List of attribute scaling factors attrScalings = list(time = list(car = b_tt_car_value, bus = b_tt_bus_value, air = b_tt_air_value, rail = b_tt_rail_value), access = b_acc, cost = b_cost_value, wifi = b_wifi, food = b_food) ### List of process parameters procPars = list( error_sd = p_error_sd, timesteps = 1+exp(p_timesteps), phi1 = exp(p_phi1), phi2 = exp(p_phi2)/(1+exp(p_phi2)) ) ### Define settings for DFT model component dft_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, attrValues = attrValues, altStart = altStart, attrWeights = 1, ### Using scaling factors, so attrWeights must be set to 1. attrScalings = attrScalings, procPars = procPars ) ### Compute choice probabilities using DFT model P[["model"]] = apollo_dft(dft_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) }