Model run using Apollo for R, version 0.2.6 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : MDCEV_no_outside_good Model description : MDCEV model on time use data, alpha-gamma profile, no outside good and constants only in utilities Model run at : 2021-11-04 17:39:44 Estimation method : bfgs Model diagnosis : successful convergence Number of individuals : 447 Number of rows in database : 2826 Number of modelled outcomes : 2826 Number of cores used : 1 Model without mixing LL(start) : -36122.93 LL(0) : Not applicable LL(C) : Not applicable LL(final) : -24018.62 Rho-square (0) : Not applicable Adj.Rho-square (0) : Not applicable AIC : 48085.24 BIC : 48227.96 Estimated parameters : 24 Time taken (hh:mm:ss) : 00:00:30.79 pre-estimation : 00:00:0.63 estimation : 00:00:20.26 post-estimation : 00:00:9.9 Iterations : 91 Min abs eigenvalue of Hessian : 0.000487 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) alpha_base -14.68670 45.33382 -0.3240 0.05890 -249.3373 gamma_dropOff 0.45377 0.04495 10.0954 0.07941 5.7142 gamma_work 6.91952 0.39914 17.3361 0.30643 22.5813 gamma_school 3.12856 0.58316 5.3649 0.53842 5.8107 gamma_shopping 0.42558 0.02678 15.8890 0.03037 14.0142 gamma_privBusiness 0.61734 0.04987 12.3782 0.06650 9.2827 gamma_petrol 0.11693 0.02517 4.6448 0.03437 3.4017 gamma_leisure 1.82732 0.10868 16.8137 0.10582 17.2689 gamma_vacation 1.55884 0.59247 2.6311 0.43768 3.5616 gamma_exercise 2.87579 0.26228 10.9646 0.33648 8.5466 gamma_home 2.66404 0.23252 11.4571 0.40706 6.5445 gamma_travel 0.20166 0.01072 18.8168 0.01227 16.4361 gamma_other 1.66111 0.49189 3.3770 0.80138 2.0728 delta_dropOff -3.57836 0.08836 -40.4975 0.15790 -22.6624 delta_work -2.35205 0.07961 -29.5443 0.13405 -17.5463 delta_school -5.19983 0.13038 -39.8815 0.23359 -22.2604 delta_shopping -2.76149 0.08103 -34.0817 0.13923 -19.8344 delta_privBusiness -3.23577 0.08450 -38.2937 0.14438 -22.4108 delta_petrol -5.45225 0.14279 -38.1840 0.20658 -26.3929 delta_leisure -2.62775 0.08046 -32.6586 0.14134 -18.5918 delta_vacation -6.60975 0.22990 -28.7510 0.27378 -24.1424 delta_exercise -3.52951 0.08758 -40.3025 0.15579 -22.6561 delta_home 0.00000 NA NA NA NA delta_travel -0.07434 0.08621 -0.8623 0.14177 -0.5244 delta_other -5.62274 0.15198 -36.9957 0.20701 -27.1618 sig 1.00000 NA NA NA NA Overview of choices for MDCEV model component : dropOff work school shopping privBusiness Times available 2826.00 2826.00 2826.00 2826.0 2826.00 Observations in which chosen 394.00 1139.00 85.00 783.0 535.00 Average consumption when available 0.39 2.89 0.11 0.5 0.44 Average consumption when chosen 2.81 7.17 3.52 1.8 2.34 petrol leisure vacation exercise home Times available 2826.00 2826.00 2826.00 2826.00 2826.00 Observations in which chosen 66.00 883.00 21.00 420.00 2770.00 Average consumption when available 0.03 1.10 0.02 0.73 16.10 Average consumption when chosen 1.33 3.52 2.75 4.90 16.43 travel other Times available 2826.00 2826.00 Observations in which chosen 2328.00 56.00 Average consumption when available 1.59 0.10 Average consumption when chosen 1.93 4.82 Classical covariance matrix: alpha_base gamma_dropOff gamma_work alpha_base 2055.155116 -7.4514e-04 -0.007798 gamma_dropOff -7.4514e-04 0.002020 -4.279e-05 gamma_work -0.007798 -4.279e-05 0.159311 gamma_school -0.003389 -6.005e-06 -3.4634e-04 gamma_shopping -5.7148e-04 6.953e-08 -4.645e-05 gamma_privBusiness -9.1802e-04 -2.450e-07 -7.014e-05 gamma_petrol -1.5312e-04 -1.189e-08 -2.157e-06 gamma_leisure -0.002287 -2.112e-06 -5.0692e-04 gamma_vacation -0.001871 1.965e-07 1.772e-05 gamma_exercise -0.003766 -7.491e-06 -9.5946e-04 gamma_home -0.004672 -3.351e-05 -0.007948 gamma_travel -3.1586e-04 6.224e-07 3.951e-05 gamma_other -0.003218 -3.724e-06 -8.0724e-04 delta_dropOff 8.367e-05 -1.6397e-04 -0.002427 delta_work 6.089e-05 -8.446e-06 -0.006127 delta_school 7.040e-05 -9.641e-06 -0.002431 delta_shopping 7.113e-05 -1.015e-05 -0.002381 delta_privBusiness 7.993e-05 -9.866e-06 -0.002399 delta_petrol 7.191e-05 -9.723e-06 -0.002439 delta_leisure 6.456e-05 -9.721e-06 -0.002354 delta_vacation 7.106e-05 -9.693e-06 -0.002437 delta_exercise 7.685e-05 -9.599e-06 -0.002416 delta_travel -2.2342e-04 -1.352e-05 -0.002672 delta_other 7.368e-05 -9.678e-06 -0.002440 gamma_school gamma_shopping gamma_privBusiness alpha_base -0.003389 -5.7148e-04 -9.1802e-04 gamma_dropOff -6.005e-06 6.953e-08 -2.450e-07 gamma_work -3.4634e-04 -4.645e-05 -7.014e-05 gamma_school 0.340071 -3.500e-06 -1.311e-05 gamma_shopping -3.500e-06 7.1741e-04 1.755e-07 gamma_privBusiness -1.311e-05 1.755e-07 0.002487 gamma_petrol -4.655e-07 1.315e-08 -2.528e-08 gamma_leisure -9.247e-05 -1.293e-06 -4.573e-06 gamma_vacation 1.142e-05 -1.466e-06 -1.395e-06 gamma_exercise -2.1808e-04 -5.577e-06 -1.165e-05 gamma_home -0.001407 -1.518e-05 -6.417e-05 gamma_travel -2.327e-06 1.244e-06 8.631e-07 gamma_other -1.3424e-04 -1.931e-06 -7.614e-06 delta_dropOff -4.2001e-04 -4.242e-06 -1.898e-05 delta_work -4.1096e-04 -1.257e-06 -1.568e-05 delta_school -0.001309 -3.669e-06 -1.875e-05 delta_shopping -4.1894e-04 -1.5923e-04 -1.960e-05 delta_privBusiness -4.1985e-04 -4.185e-06 -2.2254e-04 delta_petrol -4.2041e-04 -3.926e-06 -1.875e-05 delta_leisure -4.1566e-04 -3.849e-06 -1.874e-05 delta_vacation -4.2045e-04 -3.753e-06 -1.877e-05 delta_exercise -4.1831e-04 -3.546e-06 -1.850e-05 delta_travel -4.1219e-04 -1.022e-05 -2.374e-05 delta_other -4.2053e-04 -3.729e-06 -1.890e-05 gamma_petrol gamma_leisure gamma_vacation alpha_base -1.5312e-04 -0.002287 -0.001871 gamma_dropOff -1.189e-08 -2.112e-06 1.965e-07 gamma_work -2.157e-06 -5.0692e-04 1.772e-05 gamma_school -4.655e-07 -9.247e-05 1.142e-05 gamma_shopping 1.315e-08 -1.293e-06 -1.466e-06 gamma_privBusiness -2.528e-08 -4.573e-06 -1.395e-06 gamma_petrol 6.3376e-04 -1.401e-07 1.361e-08 gamma_leisure -1.401e-07 0.011812 -7.296e-05 gamma_vacation 1.361e-08 -7.296e-05 0.351021 gamma_exercise -3.573e-07 -8.144e-05 -1.105e-05 gamma_home -1.989e-06 -5.3921e-04 -4.0004e-04 gamma_travel 2.238e-08 6.378e-06 -7.083e-07 gamma_other -6.632e-08 -5.723e-05 -1.8845e-04 delta_dropOff -6.099e-07 -1.6426e-04 -1.1988e-04 delta_work -5.274e-07 -1.4320e-04 -1.2006e-04 delta_school -5.908e-07 -1.6357e-04 -1.1982e-04 delta_shopping -6.756e-07 -1.6575e-04 -1.1956e-04 delta_privBusiness -5.961e-07 -1.6396e-04 -1.1966e-04 delta_petrol -3.687e-05 -1.6407e-04 -1.1984e-04 delta_leisure -6.044e-07 -9.0586e-04 -1.1593e-04 delta_vacation -5.953e-07 -1.6428e-04 -5.8781e-04 delta_exercise -5.919e-07 -1.6156e-04 -1.1985e-04 delta_travel -7.340e-07 -2.0487e-04 -1.1798e-04 delta_other -5.943e-07 -1.6373e-04 -1.1954e-04 gamma_exercise gamma_home gamma_travel alpha_base -0.003766 -0.004672 -3.1586e-04 gamma_dropOff -7.491e-06 -3.351e-05 6.224e-07 gamma_work -9.5946e-04 -0.007948 3.951e-05 gamma_school -2.1808e-04 -0.001407 -2.327e-06 gamma_shopping -5.577e-06 -1.518e-05 1.244e-06 gamma_privBusiness -1.165e-05 -6.417e-05 8.631e-07 gamma_petrol -3.573e-07 -1.989e-06 2.238e-08 gamma_leisure -8.144e-05 -5.3921e-04 6.378e-06 gamma_vacation -1.105e-05 -4.0004e-04 -7.083e-07 gamma_exercise 0.068791 -0.001391 1.037e-06 gamma_home -0.001391 0.054067 -2.149e-05 gamma_travel 1.037e-06 -2.149e-05 1.1486e-04 gamma_other -5.546e-05 -5.3006e-04 -1.166e-06 delta_dropOff -4.2105e-04 0.016216 -1.058e-05 delta_work -3.9537e-04 0.016389 -1.358e-05 delta_school -4.2035e-04 0.016190 -9.571e-06 delta_shopping -4.1900e-04 0.016198 -1.200e-05 delta_privBusiness -4.1879e-04 0.016207 -1.067e-05 delta_petrol -4.2085e-04 0.016193 -9.657e-06 delta_leisure -4.1478e-04 0.016259 -1.239e-05 delta_vacation -4.2077e-04 0.016190 -9.522e-06 delta_exercise -0.001414 0.016245 -1.028e-05 delta_travel -4.3241e-04 0.016297 -4.3677e-04 delta_other -4.2095e-04 0.016203 -9.571e-06 gamma_other delta_dropOff delta_work alpha_base -0.003218 8.367e-05 6.089e-05 gamma_dropOff -3.724e-06 -1.6397e-04 -8.446e-06 gamma_work -8.0724e-04 -0.002427 -0.006127 gamma_school -1.3424e-04 -4.2001e-04 -4.1096e-04 gamma_shopping -1.931e-06 -4.242e-06 -1.257e-06 gamma_privBusiness -7.614e-06 -1.898e-05 -1.568e-05 gamma_petrol -6.632e-08 -6.099e-07 -5.274e-07 gamma_leisure -5.723e-05 -1.6426e-04 -1.4320e-04 gamma_vacation -1.8845e-04 -1.1988e-04 -1.2006e-04 gamma_exercise -5.546e-05 -4.2105e-04 -3.9537e-04 gamma_home -5.3006e-04 0.016216 0.016389 gamma_travel -1.166e-06 -1.058e-05 -1.358e-05 gamma_other 0.241960 -1.5894e-04 -1.4051e-04 delta_dropOff -1.5894e-04 0.007807 0.005305 delta_work -1.4051e-04 0.005305 0.006338 delta_school -1.5874e-04 0.005241 0.005296 delta_shopping -1.5889e-04 0.005244 0.005294 delta_privBusiness -1.5895e-04 0.005247 0.005299 delta_petrol -1.5911e-04 0.005242 0.005298 delta_leisure -1.5657e-04 0.005264 0.005314 delta_vacation -1.5890e-04 0.005241 0.005297 delta_exercise -1.5853e-04 0.005259 0.005314 delta_travel -1.5574e-04 0.005298 0.005370 delta_other -6.7344e-04 0.005245 0.005301 delta_school delta_shopping delta_privBusiness alpha_base 7.040e-05 7.113e-05 7.993e-05 gamma_dropOff -9.641e-06 -1.015e-05 -9.866e-06 gamma_work -0.002431 -0.002381 -0.002399 gamma_school -0.001309 -4.1894e-04 -4.1985e-04 gamma_shopping -3.669e-06 -1.5923e-04 -4.185e-06 gamma_privBusiness -1.875e-05 -1.960e-05 -2.2254e-04 gamma_petrol -5.908e-07 -6.756e-07 -5.961e-07 gamma_leisure -1.6357e-04 -1.6575e-04 -1.6396e-04 gamma_vacation -1.1982e-04 -1.1956e-04 -1.1966e-04 gamma_exercise -4.2035e-04 -4.1900e-04 -4.1879e-04 gamma_home 0.016190 0.016198 0.016207 gamma_travel -9.571e-06 -1.200e-05 -1.067e-05 gamma_other -1.5874e-04 -1.5889e-04 -1.5895e-04 delta_dropOff 0.005241 0.005244 0.005247 delta_work 0.005296 0.005294 0.005299 delta_school 0.016999 0.005234 0.005238 delta_shopping 0.005234 0.006565 0.005241 delta_privBusiness 0.005238 0.005241 0.007140 delta_petrol 0.005233 0.005236 0.005239 delta_leisure 0.005255 0.005258 0.005261 delta_vacation 0.005232 0.005234 0.005238 delta_exercise 0.005250 0.005252 0.005256 delta_travel 0.005283 0.005298 0.005295 delta_other 0.005236 0.005239 0.005242 delta_petrol delta_leisure delta_vacation alpha_base 7.191e-05 6.456e-05 7.106e-05 gamma_dropOff -9.723e-06 -9.721e-06 -9.693e-06 gamma_work -0.002439 -0.002354 -0.002437 gamma_school -4.2041e-04 -4.1566e-04 -4.2045e-04 gamma_shopping -3.926e-06 -3.849e-06 -3.753e-06 gamma_privBusiness -1.875e-05 -1.874e-05 -1.877e-05 gamma_petrol -3.687e-05 -6.044e-07 -5.953e-07 gamma_leisure -1.6407e-04 -9.0586e-04 -1.6428e-04 gamma_vacation -1.1984e-04 -1.1593e-04 -5.8781e-04 gamma_exercise -4.2085e-04 -4.1478e-04 -4.2077e-04 gamma_home 0.016193 0.016259 0.016190 gamma_travel -9.657e-06 -1.239e-05 -9.522e-06 gamma_other -1.5911e-04 -1.5657e-04 -1.5890e-04 delta_dropOff 0.005242 0.005264 0.005241 delta_work 0.005298 0.005314 0.005297 delta_school 0.005233 0.005255 0.005232 delta_shopping 0.005236 0.005258 0.005234 delta_privBusiness 0.005239 0.005261 0.005238 delta_petrol 0.020389 0.005256 0.005233 delta_leisure 0.005256 0.006474 0.005255 delta_vacation 0.005233 0.005255 0.052852 delta_exercise 0.005252 0.005273 0.005250 delta_travel 0.005285 0.005324 0.005283 delta_other 0.005237 0.005260 0.005236 delta_exercise delta_travel delta_other alpha_base 7.685e-05 -2.2342e-04 7.368e-05 gamma_dropOff -9.599e-06 -1.352e-05 -9.678e-06 gamma_work -0.002416 -0.002672 -0.002440 gamma_school -4.1831e-04 -4.1219e-04 -4.2053e-04 gamma_shopping -3.546e-06 -1.022e-05 -3.729e-06 gamma_privBusiness -1.850e-05 -2.374e-05 -1.890e-05 gamma_petrol -5.919e-07 -7.340e-07 -5.943e-07 gamma_leisure -1.6156e-04 -2.0487e-04 -1.6373e-04 gamma_vacation -1.1985e-04 -1.1798e-04 -1.1954e-04 gamma_exercise -0.001414 -4.3241e-04 -4.2095e-04 gamma_home 0.016245 0.016297 0.016203 gamma_travel -1.028e-05 -4.3677e-04 -9.571e-06 gamma_other -1.5853e-04 -1.5574e-04 -6.7344e-04 delta_dropOff 0.005259 0.005298 0.005245 delta_work 0.005314 0.005370 0.005301 delta_school 0.005250 0.005283 0.005236 delta_shopping 0.005252 0.005298 0.005239 delta_privBusiness 0.005256 0.005295 0.005242 delta_petrol 0.005252 0.005285 0.005237 delta_leisure 0.005273 0.005324 0.005260 delta_vacation 0.005250 0.005283 0.005236 delta_exercise 0.007669 0.005306 0.005255 delta_travel 0.005306 0.007432 0.005288 delta_other 0.005255 0.005288 0.023099 Robust covariance matrix: alpha_base gamma_dropOff gamma_work alpha_base 0.003470 6.7630e-04 -0.003062 gamma_dropOff 6.7630e-04 0.006306 -0.002267 gamma_work -0.003062 -0.002267 0.093897 gamma_school -0.005233 -0.004751 0.028215 gamma_shopping 1.1454e-04 1.5046e-04 -7.3880e-04 gamma_privBusiness 3.8919e-04 9.230e-05 4.2990e-04 gamma_petrol 2.9886e-04 2.5027e-04 -7.1539e-04 gamma_leisure 3.5649e-04 1.6107e-04 0.002383 gamma_vacation 6.9703e-04 -2.8647e-04 -4.2053e-04 gamma_exercise 5.2407e-04 0.001235 -0.010660 gamma_home 0.011836 0.008396 -0.021863 gamma_travel 3.6926e-04 -1.138e-05 -4.2108e-04 gamma_other 0.005679 0.003482 -0.010878 delta_dropOff 0.003598 0.003600 -0.006121 delta_work 0.002689 0.002767 -0.013379 delta_school 0.003831 0.003306 -0.004096 delta_shopping 0.003462 0.003161 -0.007250 delta_privBusiness 0.003637 0.002865 -0.005561 delta_petrol 0.003811 0.003750 -0.008636 delta_leisure 0.003104 0.002839 -0.007462 delta_vacation 0.003196 0.002654 -0.001619 delta_exercise 0.003356 0.002893 -0.006385 delta_travel 0.001413 0.002977 -0.006509 delta_other 0.005029 0.002810 -0.010472 gamma_school gamma_shopping gamma_privBusiness alpha_base -0.005233 1.1454e-04 3.8919e-04 gamma_dropOff -0.004751 1.5046e-04 9.230e-05 gamma_work 0.028215 -7.3880e-04 4.2990e-04 gamma_school 0.289893 -6.1156e-04 8.3979e-04 gamma_shopping -6.1156e-04 9.2221e-04 1.1979e-04 gamma_privBusiness 8.3979e-04 1.1979e-04 0.004423 gamma_petrol -0.001915 6.252e-05 4.166e-05 gamma_leisure 0.003510 4.2834e-04 -2.1737e-04 gamma_vacation -0.004033 5.8380e-04 0.001493 gamma_exercise 0.004204 -1.6695e-04 -0.001308 gamma_home -0.033439 0.001353 9.1366e-04 gamma_travel -2.9323e-04 1.237e-05 7.463e-05 gamma_other 0.004637 0.002925 0.007089 delta_dropOff -0.014696 -3.184e-05 -1.1178e-04 delta_work -0.012321 5.1147e-04 -6.053e-06 delta_school 0.001109 8.4380e-04 9.1903e-04 delta_shopping -0.010757 1.7122e-04 6.001e-05 delta_privBusiness -0.010433 3.1493e-04 2.1331e-04 delta_petrol -0.015574 2.7661e-04 3.7023e-04 delta_leisure -0.010131 3.8726e-04 4.372e-05 delta_vacation -0.009758 5.6170e-04 -1.8522e-04 delta_exercise -0.009007 2.6193e-04 1.3262e-04 delta_travel -0.009160 3.0421e-04 -1.7388e-04 delta_other -0.009313 8.993e-05 6.4150e-04 gamma_petrol gamma_leisure gamma_vacation alpha_base 2.9886e-04 3.5649e-04 6.9703e-04 gamma_dropOff 2.5027e-04 1.6107e-04 -2.8647e-04 gamma_work -7.1539e-04 0.002383 -4.2053e-04 gamma_school -0.001915 0.003510 -0.004033 gamma_shopping 6.252e-05 4.2834e-04 5.8380e-04 gamma_privBusiness 4.166e-05 -2.1737e-04 0.001493 gamma_petrol 0.001182 1.2612e-04 3.864e-05 gamma_leisure 1.2612e-04 0.011197 4.451e-06 gamma_vacation 3.864e-05 4.451e-06 0.191564 gamma_exercise 8.6928e-04 -3.8981e-04 0.002443 gamma_home 0.002686 0.007042 -0.003861 gamma_travel -1.265e-05 -1.372e-05 1.9075e-04 gamma_other 0.001301 7.1739e-04 0.009566 delta_dropOff 9.0240e-04 0.001541 -0.001792 delta_work 0.001120 0.002177 -0.001157 delta_school 0.001128 0.002542 -0.008421 delta_shopping 7.2277e-04 0.001463 -0.002255 delta_privBusiness 8.5727e-04 0.001681 -0.002545 delta_petrol 0.002465 8.333e-05 -2.0749e-04 delta_leisure 8.3558e-04 7.9581e-04 -0.003399 delta_vacation 8.1244e-04 7.1844e-04 0.004133 delta_exercise 7.8842e-04 0.002107 -0.001450 delta_travel 0.001003 0.001992 -0.003252 delta_other 0.001329 0.002575 -0.001268 gamma_exercise gamma_home gamma_travel alpha_base 5.2407e-04 0.011836 3.6926e-04 gamma_dropOff 0.001235 0.008396 -1.138e-05 gamma_work -0.010660 -0.021863 -4.2108e-04 gamma_school 0.004204 -0.033439 -2.9323e-04 gamma_shopping -1.6695e-04 0.001353 1.237e-05 gamma_privBusiness -0.001308 9.1366e-04 7.463e-05 gamma_petrol 8.6928e-04 0.002686 -1.265e-05 gamma_leisure -3.8981e-04 0.007042 -1.372e-05 gamma_vacation 0.002443 -0.003861 1.9075e-04 gamma_exercise 0.113221 0.013850 1.5848e-04 gamma_home 0.013850 0.165701 4.6990e-04 gamma_travel 1.5848e-04 4.6990e-04 1.5054e-04 gamma_other 0.001060 0.054143 8.1655e-04 delta_dropOff 0.002556 0.054284 -1.1265e-04 delta_work 0.005621 0.050204 -2.099e-05 delta_school 0.010345 0.061929 -8.223e-05 delta_shopping 0.004146 0.052556 -6.517e-05 delta_privBusiness 0.003781 0.053099 -6.407e-05 delta_petrol 0.003596 0.055774 -1.0674e-04 delta_leisure 0.003951 0.053314 -5.069e-05 delta_vacation 0.005618 0.050716 2.4438e-04 delta_exercise 0.007322 0.053623 -7.508e-05 delta_travel 0.004861 0.049299 -6.3421e-04 delta_other 0.003420 0.060626 1.7094e-04 gamma_other delta_dropOff delta_work alpha_base 0.005679 0.003598 0.002689 gamma_dropOff 0.003482 0.003600 0.002767 gamma_work -0.010878 -0.006121 -0.013379 gamma_school 0.004637 -0.014696 -0.012321 gamma_shopping 0.002925 -3.184e-05 5.1147e-04 gamma_privBusiness 0.007089 -1.1178e-04 -6.053e-06 gamma_petrol 0.001301 9.0240e-04 0.001120 gamma_leisure 7.1739e-04 0.001541 0.002177 gamma_vacation 0.009566 -0.001792 -0.001157 gamma_exercise 0.001060 0.002556 0.005621 gamma_home 0.054143 0.054284 0.050204 gamma_travel 8.1655e-04 -1.1265e-04 -2.099e-05 gamma_other 0.642208 0.007240 0.015586 delta_dropOff 0.007240 0.024932 0.016913 delta_work 0.015586 0.016913 0.017969 delta_school 0.022266 0.020107 0.017635 delta_shopping 0.014310 0.018579 0.016160 delta_privBusiness 0.018236 0.018557 0.015999 delta_petrol 0.023504 0.020811 0.018405 delta_leisure 0.013787 0.018414 0.016671 delta_vacation 0.021520 0.015702 0.014625 delta_exercise 0.010671 0.018636 0.016483 delta_travel 0.011713 0.018522 0.016761 delta_other 0.024439 0.021817 0.019355 delta_school delta_shopping delta_privBusiness alpha_base 0.003831 0.003462 0.003637 gamma_dropOff 0.003306 0.003161 0.002865 gamma_work -0.004096 -0.007250 -0.005561 gamma_school 0.001109 -0.010757 -0.010433 gamma_shopping 8.4380e-04 1.7122e-04 3.1493e-04 gamma_privBusiness 9.1903e-04 6.001e-05 2.1331e-04 gamma_petrol 0.001128 7.2277e-04 8.5727e-04 gamma_leisure 0.002542 0.001463 0.001681 gamma_vacation -0.008421 -0.002255 -0.002545 gamma_exercise 0.010345 0.004146 0.003781 gamma_home 0.061929 0.052556 0.053099 gamma_travel -8.223e-05 -6.517e-05 -6.407e-05 gamma_other 0.022266 0.014310 0.018236 delta_dropOff 0.020107 0.018579 0.018557 delta_work 0.017635 0.016160 0.015999 delta_school 0.054565 0.019306 0.019911 delta_shopping 0.019306 0.019384 0.017587 delta_privBusiness 0.019911 0.017587 0.020847 delta_petrol 0.020217 0.019521 0.018540 delta_leisure 0.020501 0.017931 0.018149 delta_vacation 0.019535 0.016247 0.015916 delta_exercise 0.020909 0.017858 0.017955 delta_travel 0.019949 0.017448 0.017466 delta_other 0.021568 0.020323 0.020770 delta_petrol delta_leisure delta_vacation alpha_base 0.003811 0.003104 0.003196 gamma_dropOff 0.003750 0.002839 0.002654 gamma_work -0.008636 -0.007462 -0.001619 gamma_school -0.015574 -0.010131 -0.009758 gamma_shopping 2.7661e-04 3.8726e-04 5.6170e-04 gamma_privBusiness 3.7023e-04 4.372e-05 -1.8522e-04 gamma_petrol 0.002465 8.3558e-04 8.1244e-04 gamma_leisure 8.333e-05 7.9581e-04 7.1844e-04 gamma_vacation -2.0749e-04 -0.003399 0.004133 gamma_exercise 0.003596 0.003951 0.005618 gamma_home 0.055774 0.053314 0.050716 gamma_travel -1.0674e-04 -5.069e-05 2.4438e-04 gamma_other 0.023504 0.013787 0.021520 delta_dropOff 0.020811 0.018414 0.015702 delta_work 0.018405 0.016671 0.014625 delta_school 0.020217 0.020501 0.019535 delta_shopping 0.019521 0.017931 0.016247 delta_privBusiness 0.018540 0.018149 0.015916 delta_petrol 0.042675 0.019123 0.016746 delta_leisure 0.019123 0.019977 0.018385 delta_vacation 0.016746 0.018385 0.074956 delta_exercise 0.019168 0.017755 0.015218 delta_travel 0.019101 0.017873 0.015758 delta_other 0.023559 0.020282 0.018539 delta_exercise delta_travel delta_other alpha_base 0.003356 0.001413 0.005029 gamma_dropOff 0.002893 0.002977 0.002810 gamma_work -0.006385 -0.006509 -0.010472 gamma_school -0.009007 -0.009160 -0.009313 gamma_shopping 2.6193e-04 3.0421e-04 8.993e-05 gamma_privBusiness 1.3262e-04 -1.7388e-04 6.4150e-04 gamma_petrol 7.8842e-04 0.001003 0.001329 gamma_leisure 0.002107 0.001992 0.002575 gamma_vacation -0.001450 -0.003252 -0.001268 gamma_exercise 0.007322 0.004861 0.003420 gamma_home 0.053623 0.049299 0.060626 gamma_travel -7.508e-05 -6.3421e-04 1.7094e-04 gamma_other 0.010671 0.011713 0.024439 delta_dropOff 0.018636 0.018522 0.021817 delta_work 0.016483 0.016761 0.019355 delta_school 0.020909 0.019949 0.021568 delta_shopping 0.017858 0.017448 0.020323 delta_privBusiness 0.017955 0.017466 0.020770 delta_petrol 0.019168 0.019101 0.023559 delta_leisure 0.017755 0.017873 0.020282 delta_vacation 0.015218 0.015758 0.018539 delta_exercise 0.024269 0.018120 0.020045 delta_travel 0.018120 0.020097 0.019579 delta_other 0.020045 0.019579 0.042853 Classical correlation matrix: alpha_base gamma_dropOff gamma_work alpha_base 1.000 -3.6568e-04 -4.3094e-04 gamma_dropOff -3.6568e-04 1.000000 -0.002385 gamma_work -4.3094e-04 -0.002385 1.000000 gamma_school -1.2818e-04 -2.2910e-04 -0.001488 gamma_shopping -4.7064e-04 5.775e-05 -0.004345 gamma_privBusiness -4.0603e-04 -1.0929e-04 -0.003524 gamma_petrol -1.3417e-04 -1.051e-05 -2.1467e-04 gamma_leisure -4.6417e-04 -4.3240e-04 -0.011686 gamma_vacation -6.964e-05 7.377e-06 7.492e-05 gamma_exercise -3.1675e-04 -6.3544e-04 -0.009165 gamma_home -4.4323e-04 -0.003206 -0.085634 gamma_travel -6.5011e-04 0.001292 0.009235 gamma_other -1.4433e-04 -1.6844e-04 -0.004112 delta_dropOff 2.089e-05 -0.041286 -0.068825 delta_work 1.687e-05 -0.002360 -0.192831 delta_school 1.191e-05 -0.001645 -0.046722 delta_shopping 1.936e-05 -0.002786 -0.073618 delta_privBusiness 2.087e-05 -0.002598 -0.071128 delta_petrol 1.111e-05 -0.001515 -0.042802 delta_leisure 1.770e-05 -0.002688 -0.073312 delta_vacation 6.818e-06 -9.3802e-04 -0.026563 delta_exercise 1.936e-05 -0.002439 -0.069126 delta_travel -5.717e-05 -0.003490 -0.077664 delta_other 1.069e-05 -0.001417 -0.040220 gamma_school gamma_shopping gamma_privBusiness alpha_base -1.2818e-04 -4.7064e-04 -4.0603e-04 gamma_dropOff -2.2910e-04 5.775e-05 -1.0929e-04 gamma_work -0.001488 -0.004345 -0.003524 gamma_school 1.000000 -2.2407e-04 -4.5072e-04 gamma_shopping -2.2407e-04 1.000000 1.3135e-04 gamma_privBusiness -4.5072e-04 1.3135e-04 1.000000 gamma_petrol -3.171e-05 1.950e-05 -2.013e-05 gamma_leisure -0.001459 -4.4407e-04 -8.4366e-04 gamma_vacation 3.305e-05 -9.238e-05 -4.722e-05 gamma_exercise -0.001426 -7.9382e-04 -8.9047e-04 gamma_home -0.010374 -0.002437 -0.005533 gamma_travel -3.7238e-04 0.004334 0.001615 gamma_other -4.6797e-04 -1.4654e-04 -3.1036e-04 delta_dropOff -0.008151 -0.001793 -0.004307 delta_work -0.008852 -5.8943e-04 -0.003950 delta_school -0.017212 -0.001051 -0.002883 delta_shopping -0.008866 -0.073371 -0.004851 delta_privBusiness -0.008520 -0.001849 -0.052806 delta_petrol -0.005049 -0.001026 -0.002633 delta_leisure -0.008859 -0.001786 -0.004670 delta_vacation -0.003136 -6.0944e-04 -0.001637 delta_exercise -0.008191 -0.001512 -0.004235 delta_travel -0.008199 -0.004425 -0.005522 delta_other -0.004745 -9.1610e-04 -0.002494 gamma_petrol gamma_leisure gamma_vacation alpha_base -1.3417e-04 -4.6417e-04 -6.964e-05 gamma_dropOff -1.051e-05 -4.3240e-04 7.377e-06 gamma_work -2.1467e-04 -0.011686 7.492e-05 gamma_school -3.171e-05 -0.001459 3.305e-05 gamma_shopping 1.950e-05 -4.4407e-04 -9.238e-05 gamma_privBusiness -2.013e-05 -8.4366e-04 -4.722e-05 gamma_petrol 1.00000 -5.121e-05 9.124e-07 gamma_leisure -5.121e-05 1.000000 -0.001133 gamma_vacation 9.124e-07 -0.001133 1.000000 gamma_exercise -5.411e-05 -0.002857 -7.114e-05 gamma_home -3.3982e-04 -0.021337 -0.002904 gamma_travel 8.294e-05 0.005476 -1.1155e-04 gamma_other -5.356e-06 -0.001070 -6.4662e-04 delta_dropOff -2.7419e-04 -0.017105 -0.002290 delta_work -2.6315e-04 -0.016550 -0.002545 delta_school -1.7999e-04 -0.011543 -0.001551 delta_shopping -3.3123e-04 -0.018823 -0.002491 delta_privBusiness -2.8025e-04 -0.017854 -0.002390 delta_petrol -0.01026 -0.010573 -0.001417 delta_leisure -2.9839e-04 -0.103591 -0.002432 delta_vacation -1.0285e-04 -0.006575 -0.004316 delta_exercise -2.6849e-04 -0.016974 -0.002310 delta_travel -3.3821e-04 -0.021866 -0.002310 delta_other -1.5533e-04 -0.009912 -0.001328 gamma_exercise gamma_home gamma_travel alpha_base -3.1675e-04 -4.4323e-04 -6.5011e-04 gamma_dropOff -6.3544e-04 -0.003206 0.001292 gamma_work -0.009165 -0.085634 0.009235 gamma_school -0.001426 -0.010374 -3.7238e-04 gamma_shopping -7.9382e-04 -0.002437 0.004334 gamma_privBusiness -8.9047e-04 -0.005533 0.001615 gamma_petrol -5.411e-05 -3.3982e-04 8.294e-05 gamma_leisure -0.002857 -0.021337 0.005476 gamma_vacation -7.114e-05 -0.002904 -1.1155e-04 gamma_exercise 1.000000 -0.022812 3.6877e-04 gamma_home -0.022812 1.000000 -0.008625 gamma_travel 3.6877e-04 -0.008625 1.000000 gamma_other -4.2984e-04 -0.004634 -2.2119e-04 delta_dropOff -0.018168 0.789246 -0.011169 delta_work -0.018935 0.885375 -0.015918 delta_school -0.012292 0.534029 -0.006850 delta_shopping -0.019716 0.859742 -0.013818 delta_privBusiness -0.018897 0.824876 -0.011780 delta_petrol -0.011237 0.487730 -0.006310 delta_leisure -0.019655 0.869067 -0.014368 delta_vacation -0.006978 0.302863 -0.003865 delta_exercise -0.061576 0.797749 -0.010951 delta_travel -0.019123 0.812994 -0.472718 delta_other -0.010560 0.458506 -0.005876 gamma_other delta_dropOff delta_work alpha_base -1.4433e-04 2.089e-05 1.687e-05 gamma_dropOff -1.6844e-04 -0.041286 -0.002360 gamma_work -0.004112 -0.068825 -0.192831 gamma_school -4.6797e-04 -0.008151 -0.008852 gamma_shopping -1.4654e-04 -0.001793 -5.8943e-04 gamma_privBusiness -3.1036e-04 -0.004307 -0.003950 gamma_petrol -5.356e-06 -2.7419e-04 -2.6315e-04 gamma_leisure -0.001070 -0.017105 -0.016550 gamma_vacation -6.4662e-04 -0.002290 -0.002545 gamma_exercise -4.2984e-04 -0.018168 -0.018935 gamma_home -0.004634 0.789246 0.885375 gamma_travel -2.2119e-04 -0.011169 -0.015918 gamma_other 1.000000 -0.003657 -0.003588 delta_dropOff -0.003657 1.000000 0.754106 delta_work -0.003588 0.754106 1.000000 delta_school -0.002475 0.454882 0.510243 delta_shopping -0.003987 0.732444 0.820770 delta_privBusiness -0.003824 0.702704 0.787782 delta_petrol -0.002265 0.415474 0.466073 delta_leisure -0.003956 0.740417 0.829608 delta_vacation -0.001405 0.257987 0.289404 delta_exercise -0.003680 0.679640 0.762203 delta_travel -0.003673 0.695467 0.782359 delta_other -0.009008 0.390573 0.438147 delta_school delta_shopping delta_privBusiness alpha_base 1.191e-05 1.936e-05 2.087e-05 gamma_dropOff -0.001645 -0.002786 -0.002598 gamma_work -0.046722 -0.073618 -0.071128 gamma_school -0.017212 -0.008866 -0.008520 gamma_shopping -0.001051 -0.073371 -0.001849 gamma_privBusiness -0.002883 -0.004851 -0.052806 gamma_petrol -1.7999e-04 -3.3123e-04 -2.8025e-04 gamma_leisure -0.011543 -0.018823 -0.017854 gamma_vacation -0.001551 -0.002491 -0.002390 gamma_exercise -0.012292 -0.019716 -0.018897 gamma_home 0.534029 0.859742 0.824876 gamma_travel -0.006850 -0.013818 -0.011780 gamma_other -0.002475 -0.003987 -0.003824 delta_dropOff 0.454882 0.732444 0.702704 delta_work 0.510243 0.820770 0.787782 delta_school 1.000000 0.495429 0.475402 delta_shopping 0.495429 1.000000 0.765441 delta_privBusiness 0.475402 0.765441 1.000000 delta_petrol 0.281080 0.452555 0.434199 delta_leisure 0.500931 0.806527 0.773805 delta_vacation 0.174540 0.280992 0.269618 delta_exercise 0.459822 0.740210 0.710241 delta_travel 0.470013 0.758496 0.726857 delta_other 0.264242 0.425395 0.408195 delta_petrol delta_leisure delta_vacation alpha_base 1.111e-05 1.770e-05 6.818e-06 gamma_dropOff -0.001515 -0.002688 -9.3802e-04 gamma_work -0.042802 -0.073312 -0.026563 gamma_school -0.005049 -0.008859 -0.003136 gamma_shopping -0.001026 -0.001786 -6.0944e-04 gamma_privBusiness -0.002633 -0.004670 -0.001637 gamma_petrol -0.010256 -2.9839e-04 -1.0285e-04 gamma_leisure -0.010573 -0.103591 -0.006575 gamma_vacation -0.001417 -0.002432 -0.004316 gamma_exercise -0.011237 -0.019655 -0.006978 gamma_home 0.487730 0.869067 0.302863 gamma_travel -0.006310 -0.014368 -0.003865 gamma_other -0.002265 -0.003956 -0.001405 delta_dropOff 0.415474 0.740417 0.257987 delta_work 0.466073 0.829608 0.289404 delta_school 0.281080 0.500931 0.174540 delta_shopping 0.452555 0.806527 0.280992 delta_privBusiness 0.434199 0.773805 0.269618 delta_petrol 1.000000 0.457524 0.159413 delta_leisure 0.457524 1.000000 0.284112 delta_vacation 0.159413 0.284112 1.000000 delta_exercise 0.419967 0.748334 0.260782 delta_travel 0.429326 0.767495 0.266573 delta_other 0.241341 0.430106 0.149863 delta_exercise delta_travel delta_other alpha_base 1.936e-05 -5.717e-05 1.069e-05 gamma_dropOff -0.002439 -0.003490 -0.001417 gamma_work -0.069126 -0.077664 -0.040220 gamma_school -0.008191 -0.008199 -0.004745 gamma_shopping -0.001512 -0.004425 -9.1610e-04 gamma_privBusiness -0.004235 -0.005522 -0.002494 gamma_petrol -2.6849e-04 -3.3821e-04 -1.5533e-04 gamma_leisure -0.016974 -0.021866 -0.009912 gamma_vacation -0.002310 -0.002310 -0.001328 gamma_exercise -0.061576 -0.019123 -0.010560 gamma_home 0.797749 0.812994 0.458506 gamma_travel -0.010951 -0.472718 -0.005876 gamma_other -0.003680 -0.003673 -0.009008 delta_dropOff 0.679640 0.695467 0.390573 delta_work 0.762203 0.782359 0.438147 delta_school 0.459822 0.470013 0.264242 delta_shopping 0.740210 0.758496 0.425395 delta_privBusiness 0.710241 0.726857 0.408195 delta_petrol 0.419967 0.429326 0.241341 delta_leisure 0.748334 0.767495 0.430106 delta_vacation 0.260782 0.266573 0.149863 delta_exercise 1.000000 0.702774 0.394805 delta_travel 0.702774 1.000000 0.403583 delta_other 0.394805 0.403583 1.000000 Robust correlation matrix: alpha_base gamma_dropOff gamma_work alpha_base 1.00000 0.144583 -0.169624 gamma_dropOff 0.14458 1.000000 -0.093179 gamma_work -0.16962 -0.093179 1.000000 gamma_school -0.16499 -0.111122 0.171016 gamma_shopping 0.06403 0.062390 -0.079394 gamma_privBusiness 0.09935 0.017477 0.021096 gamma_petrol 0.14760 0.091682 -0.067918 gamma_leisure 0.05720 0.019168 0.073479 gamma_vacation 0.02704 -0.008242 -0.003136 gamma_exercise 0.02644 0.046204 -0.103389 gamma_home 0.49364 0.259726 -0.175275 gamma_travel 0.51093 -0.011677 -0.111998 gamma_other 0.12032 0.054722 -0.044298 delta_dropOff 0.38689 0.287076 -0.126502 delta_work 0.34060 0.259946 -0.325716 delta_school 0.27846 0.178215 -0.057222 delta_shopping 0.42209 0.285943 -0.169942 delta_privBusiness 0.42770 0.249832 -0.125687 delta_petrol 0.31321 0.228575 -0.136432 delta_leisure 0.37288 0.252962 -0.172302 delta_vacation 0.19817 0.122067 -0.019297 delta_exercise 0.36577 0.233826 -0.133750 delta_travel 0.16917 0.264456 -0.149837 delta_other 0.41247 0.170963 -0.165094 gamma_school gamma_shopping gamma_privBusiness alpha_base -0.164994 0.064032 0.099352 gamma_dropOff -0.111122 0.062390 0.017477 gamma_work 0.171016 -0.079394 0.021096 gamma_school 1.000000 -0.037403 0.023453 gamma_shopping -0.037403 1.000000 0.059315 gamma_privBusiness 0.023453 0.059315 1.000000 gamma_petrol -0.103472 0.059890 0.018226 gamma_leisure 0.061612 0.133297 -0.030889 gamma_vacation -0.017115 0.043923 0.051306 gamma_exercise 0.023204 -0.016338 -0.058457 gamma_home -0.152571 0.109427 0.033750 gamma_travel -0.044388 0.033198 0.091459 gamma_other 0.010746 0.120208 0.133008 delta_dropOff -0.172863 -0.006640 -0.010645 delta_work -0.170717 0.125644 -6.7894e-04 delta_school 0.008815 0.118951 0.059159 delta_shopping -0.143494 0.040496 0.006481 delta_privBusiness -0.134200 0.071827 0.022214 delta_petrol -0.140021 0.044093 0.026948 delta_leisure -0.133126 0.090224 0.004651 delta_vacation -0.066195 0.067559 -0.010173 delta_exercise -0.107383 0.055365 0.012801 delta_travel -0.120008 0.070663 -0.018443 delta_other -0.083557 0.014306 0.046597 gamma_petrol gamma_leisure gamma_vacation alpha_base 0.147604 0.057196 0.027037 gamma_dropOff 0.091682 0.019168 -0.008242 gamma_work -0.067918 0.073479 -0.003136 gamma_school -0.103472 0.061612 -0.017115 gamma_shopping 0.059890 0.133297 0.043923 gamma_privBusiness 0.018226 -0.030889 0.051306 gamma_petrol 1.000000 0.034672 0.002568 gamma_leisure 0.034672 1.000000 9.611e-05 gamma_vacation 0.002568 9.611e-05 1.000000 gamma_exercise 0.075155 -0.010948 0.016588 gamma_home 0.191940 0.163487 -0.021672 gamma_travel -0.029986 -0.010566 0.035520 gamma_other 0.047222 0.008460 0.027272 delta_dropOff 0.166259 0.092246 -0.025934 delta_work 0.243072 0.153470 -0.019723 delta_school 0.140449 0.102834 -0.082362 delta_shopping 0.151022 0.099325 -0.036997 delta_privBusiness 0.172728 0.110019 -0.040266 delta_petrol 0.347102 0.003812 -0.002295 delta_leisure 0.171984 0.053210 -0.054940 delta_vacation 0.086328 0.024799 0.034495 delta_exercise 0.147228 0.127829 -0.021264 delta_travel 0.205829 0.132790 -0.052409 delta_other 0.186728 0.117531 -0.013998 gamma_exercise gamma_home gamma_travel alpha_base 0.026441 0.49364 0.51093 gamma_dropOff 0.046204 0.25973 -0.01168 gamma_work -0.103389 -0.17528 -0.11200 gamma_school 0.023204 -0.15257 -0.04439 gamma_shopping -0.016338 0.10943 0.03320 gamma_privBusiness -0.058457 0.03375 0.09146 gamma_petrol 0.075155 0.19194 -0.02999 gamma_leisure -0.010948 0.16349 -0.01057 gamma_vacation 0.016588 -0.02167 0.03552 gamma_exercise 1.000000 0.10111 0.03839 gamma_home 0.101115 1.00000 0.09408 gamma_travel 0.038386 0.09408 1.00000 gamma_other 0.003930 0.16597 0.08304 delta_dropOff 0.048112 0.84456 -0.05815 delta_work 0.124631 0.92006 -0.01276 delta_school 0.131623 0.65129 -0.02869 delta_shopping 0.088505 0.92733 -0.03815 delta_privBusiness 0.077828 0.90344 -0.03617 delta_petrol 0.051734 0.66326 -0.04211 delta_leisure 0.083070 0.92665 -0.02923 delta_vacation 0.060989 0.45507 0.07275 delta_exercise 0.139677 0.84558 -0.03928 delta_travel 0.101904 0.85429 -0.36462 delta_other 0.049106 0.71946 0.06730 gamma_other delta_dropOff delta_work alpha_base 0.120319 0.386889 0.34060 gamma_dropOff 0.054722 0.287076 0.25995 gamma_work -0.044298 -0.126502 -0.32572 gamma_school 0.010746 -0.172863 -0.17072 gamma_shopping 0.120208 -0.006640 0.12564 gamma_privBusiness 0.133008 -0.010645 -6.7894e-04 gamma_petrol 0.047222 0.166259 0.24307 gamma_leisure 0.008460 0.092246 0.15347 gamma_vacation 0.027272 -0.025934 -0.01972 gamma_exercise 0.003930 0.048112 0.12463 gamma_home 0.165974 0.844565 0.92006 gamma_travel 0.083045 -0.058145 -0.01276 gamma_other 1.000000 0.057216 0.14509 delta_dropOff 0.057216 1.000000 0.79904 delta_work 0.145092 0.799044 1.00000 delta_school 0.118947 0.545152 0.56320 delta_shopping 0.128258 0.845100 0.86589 delta_privBusiness 0.157608 0.813978 0.82662 delta_petrol 0.141974 0.638006 0.66463 delta_leisure 0.121720 0.825086 0.87990 delta_vacation 0.098083 0.363214 0.39850 delta_exercise 0.085474 0.757605 0.78931 delta_travel 0.103099 0.827424 0.88202 delta_other 0.147317 0.667448 0.69749 delta_school delta_shopping delta_privBusiness alpha_base 0.278460 0.422088 0.42770 gamma_dropOff 0.178215 0.285943 0.24983 gamma_work -0.057222 -0.169942 -0.12569 gamma_school 0.008815 -0.143494 -0.13420 gamma_shopping 0.118951 0.040496 0.07183 gamma_privBusiness 0.059159 0.006481 0.02221 gamma_petrol 0.140449 0.151022 0.17273 gamma_leisure 0.102834 0.099325 0.11002 gamma_vacation -0.082362 -0.036997 -0.04027 gamma_exercise 0.131623 0.088505 0.07783 gamma_home 0.651291 0.927330 0.90344 gamma_travel -0.028689 -0.038147 -0.03617 gamma_other 0.118947 0.128258 0.15761 delta_dropOff 0.545152 0.845100 0.81398 delta_work 0.563204 0.865890 0.82662 delta_school 1.000000 0.593635 0.59035 delta_shopping 0.593635 1.000000 0.87486 delta_privBusiness 0.590354 0.874863 1.00000 delta_petrol 0.418962 0.678704 0.62159 delta_leisure 0.620936 0.911199 0.88935 delta_vacation 0.305460 0.426234 0.40264 delta_exercise 0.574578 0.823341 0.79823 delta_travel 0.602407 0.884001 0.85332 delta_other 0.446025 0.705144 0.69490 delta_petrol delta_leisure delta_vacation alpha_base 0.313210 0.372884 0.19817 gamma_dropOff 0.228575 0.252962 0.12207 gamma_work -0.136432 -0.172302 -0.01930 gamma_school -0.140021 -0.133126 -0.06619 gamma_shopping 0.044093 0.090224 0.06756 gamma_privBusiness 0.026948 0.004651 -0.01017 gamma_petrol 0.347102 0.171984 0.08633 gamma_leisure 0.003812 0.053210 0.02480 gamma_vacation -0.002295 -0.054940 0.03449 gamma_exercise 0.051734 0.083070 0.06099 gamma_home 0.663260 0.926648 0.45507 gamma_travel -0.042111 -0.029231 0.07275 gamma_other 0.141974 0.121720 0.09808 delta_dropOff 0.638006 0.825086 0.36321 delta_work 0.664629 0.879902 0.39850 delta_school 0.418962 0.620936 0.30546 delta_shopping 0.678704 0.911199 0.42623 delta_privBusiness 0.621587 0.889348 0.40264 delta_petrol 1.000000 0.654950 0.29608 delta_leisure 0.654950 1.000000 0.47512 delta_vacation 0.296084 0.475119 1.00000 delta_exercise 0.595613 0.806344 0.35680 delta_travel 0.652241 0.891980 0.40601 delta_other 0.550901 0.693212 0.32712 delta_exercise delta_travel delta_other alpha_base 0.36577 0.16917 0.41247 gamma_dropOff 0.23383 0.26446 0.17096 gamma_work -0.13375 -0.14984 -0.16509 gamma_school -0.10738 -0.12001 -0.08356 gamma_shopping 0.05536 0.07066 0.01431 gamma_privBusiness 0.01280 -0.01844 0.04660 gamma_petrol 0.14723 0.20583 0.18673 gamma_leisure 0.12783 0.13279 0.11753 gamma_vacation -0.02126 -0.05241 -0.01400 gamma_exercise 0.13968 0.10190 0.04911 gamma_home 0.84558 0.85429 0.71946 gamma_travel -0.03928 -0.36462 0.06730 gamma_other 0.08547 0.10310 0.14732 delta_dropOff 0.75761 0.82742 0.66745 delta_work 0.78931 0.88202 0.69749 delta_school 0.57458 0.60241 0.44602 delta_shopping 0.82334 0.88400 0.70514 delta_privBusiness 0.79823 0.85332 0.69490 delta_petrol 0.59561 0.65224 0.55090 delta_leisure 0.80634 0.89198 0.69321 delta_vacation 0.35680 0.40601 0.32712 delta_exercise 1.00000 0.82045 0.62156 delta_travel 0.82045 1.00000 0.66715 delta_other 0.62156 0.66715 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 3375723 1.788132e-09 7652039 4.106724e-08 6292582 4.390068e-08 1226238 6.551171e-08 6873173 1.040644e-07 2684804 1.497519e-07 2191235 2.442603e-07 3051038 2.605943e-07 8530000 2.828529e-07 2146576 3.516958e-07 5804392 4.033760e-07 9216479 4.701231e-07 4376416 6.485365e-07 1482825 8.088769e-07 9902059 9.757484e-07 9545640 9.938237e-07 7177352 1.138460e-06 1496531 1.202539e-06 6526613 1.205564e-06 8465193 1.219903e-06 Changes in parameter estimates from starting values: Initial Estimate Difference alpha_base 0.000 -14.68670 -14.68670 gamma_dropOff 1.000 0.45377 -0.54623 gamma_work 1.000 6.91952 5.91952 gamma_school 1.000 3.12856 2.12856 gamma_shopping 1.000 0.42558 -0.57442 gamma_privBusiness 1.000 0.61734 -0.38266 gamma_petrol 1.000 0.11693 -0.88307 gamma_leisure 1.000 1.82732 0.82732 gamma_vacation 1.000 1.55884 0.55884 gamma_exercise 1.000 2.87579 1.87579 gamma_home 1.000 2.66404 1.66404 gamma_travel 1.000 0.20166 -0.79834 gamma_other 1.000 1.66111 0.66111 delta_dropOff 0.000 -3.57836 -3.57836 delta_work 0.000 -2.35205 -2.35205 delta_school 0.000 -5.19983 -5.19983 delta_shopping 0.000 -2.76149 -2.76149 delta_privBusiness 0.000 -3.23577 -3.23577 delta_petrol 0.000 -5.45225 -5.45225 delta_leisure 0.000 -2.62775 -2.62775 delta_vacation 0.000 -6.60975 -6.60975 delta_exercise 0.000 -3.52951 -3.52951 delta_home 0.000 0.00000 0.00000 delta_travel 0.000 -0.07434 -0.07434 delta_other 0.000 -5.62274 -5.62274 sig 1.000 1.00000 0.00000 Settings and functions used in model definition: apollo_control -------------- Value modelName "MDCEV_no_outside_good" modelDescr "MDCEV model on time use data, alpha-gamma profile, no outside good and constants only in utilities" indivID "indivID" 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" Hessian routines attempted -------------- numerical second derivative of LL (using numDeriv) Scaling in estimation -------------- Value alpha_base 14.68666891 gamma_dropOff 0.45377219 gamma_work 6.91948875 gamma_school 3.12852855 gamma_shopping 0.42558135 gamma_privBusiness 0.61733885 gamma_petrol 0.11693032 gamma_leisure 1.82732691 gamma_vacation 1.55884785 gamma_exercise 2.87578939 gamma_home 2.66403601 gamma_travel 0.20166381 gamma_other 1.66110821 delta_dropOff 3.57834129 delta_work 2.35204904 delta_school 5.19981348 delta_shopping 2.76149256 delta_privBusiness 3.23576012 delta_petrol 5.45222251 delta_leisure 2.62774687 delta_vacation 6.60975651 delta_exercise 3.52952679 delta_travel 0.07434369 delta_other 5.62269439 Scaling used in computing Hessian -------------- Value alpha_base 14.68670251 gamma_dropOff 0.45377257 gamma_work 6.91951517 gamma_school 3.12855514 gamma_shopping 0.42558132 gamma_privBusiness 0.61733879 gamma_petrol 0.11693031 gamma_leisure 1.82732348 gamma_vacation 1.55884392 gamma_exercise 2.87579044 gamma_home 2.66403732 gamma_travel 0.20166402 gamma_other 1.66110833 delta_dropOff 3.57835865 delta_work 2.35204847 delta_school 5.19982856 delta_shopping 2.76149172 delta_privBusiness 3.23576789 delta_petrol 5.45225159 delta_leisure 2.62774629 delta_vacation 6.60975209 delta_exercise 3.52951309 delta_travel 0.07434367 delta_other 5.62274364 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() ### Define individual alternatives alternatives = c("dropOff", "work", "school", "shopping", "privBusiness", "petrol", "leisure", "vacation", "exercise", "home", "travel", "other") ### Define availabilities avail = list(dropOff = 1, work = 1, school = 1, shopping = 1, privBusiness = 1, petrol = 1, leisure = 1, vacation = 1, exercise = 1, home = 1, travel = 1, other = 1) ### Define continuous consumption for individual alternatives continuousChoice = list(dropOff = t_a01/60, work = t_a02/60, school = t_a03/60, shopping = t_a04/60, privBusiness = t_a05/60, petrol = t_a06/60, leisure = t_a07/60, vacation = t_a08/60, exercise = t_a09/60, home = t_a10/60, travel = t_a11/60, other = t_a12/60) ### Define utilities for individual alternatives V = list() V[["dropOff" ]] = delta_dropOff V[["work" ]] = delta_work V[["school" ]] = delta_school V[["shopping"]] = delta_shopping V[["privBusiness"]] = delta_privBusiness V[["petrol" ]] = delta_petrol V[["leisure" ]] = delta_leisure V[["vacation"]] = delta_vacation V[["exercise"]] = delta_exercise V[["home" ]] = delta_home V[["travel" ]] = delta_travel V[["other" ]] = delta_other ### Define alpha parameters alpha = list(dropOff = 1 /(1 + exp(-alpha_base)), work = 1 /(1 + exp(-alpha_base)), school = 1 /(1 + exp(-alpha_base)), shopping = 1 /(1 + exp(-alpha_base)), privBusiness = 1 /(1 + exp(-alpha_base)), petrol = 1 /(1 + exp(-alpha_base)), leisure = 1 /(1 + exp(-alpha_base)), vacation = 1 /(1 + exp(-alpha_base)), exercise = 1 /(1 + exp(-alpha_base)), home = 1 /(1 + exp(-alpha_base)), travel = 1 /(1 + exp(-alpha_base)), other = 1 /(1 + exp(-alpha_base))) ### Define gamma parameters gamma = list(dropOff = gamma_dropOff, work = gamma_work, school = gamma_school, shopping = gamma_shopping, privBusiness = gamma_privBusiness, petrol = gamma_petrol, leisure = gamma_leisure, vacation = gamma_vacation, exercise = gamma_exercise, home = gamma_home, travel = gamma_travel, other = gamma_other) ### Define costs for individual alternatives cost = list(dropOff = 1, work = 1, school = 1, shopping = 1, privBusiness = 1, petrol = 1, leisure = 1, vacation = 1, exercise = 1, home = 1, travel = 1, other = 1) ### Define budget budget = budget/60 ### Define settings for MDCEV model mdcev_settings <- list(alternatives = alternatives, avail = avail, continuousChoice = continuousChoice, utilities = V, alpha = alpha, gamma = gamma, sigma = sig, cost = cost, budget = budget) ### Compute probabilities using MDCEV model P[["model"]] = apollo_mdcev(mdcev_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) }