Model run using Apollo for R, version 0.2.3 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : Apollo_example_26 Model description : HB model on mode choice SP data Model run at : 2021-02-06 10:45:30 Estimation method : Hierarchical Bayes Number of individuals : 500 Number of rows in database : 7000 Number of cores used : 1 Estimation carried out using RSGHB Burn-in iterations : 50000 Post burn-in iterations : 20000 LL(start) : -19242.48 LL(0) : -8196.021 Average post. LL post burn-in : -4636.72 Average post. RLH post burn-in : 0.5356 Time taken (hh:mm:ss) : 00:56:23.86 pre-estimation : 00:00:0.71 estimation : 00:56:21.37 post-estimation : 00:00:1.78 Chain convergence report (Geweke test) Fixed (non random) parameters (t-test value for Geweke test) asc_bus_shift_female asc_air_shift_female asc_rail_shift_female b_tt_shift_business b_cost_shift_business -1.0729 -3.1535 -4.2621 -3.2190 -3.0182 cost_income_elast -2.6077 Random parameters (t-test value for Geweke test) asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost b_wifi b_food 1.8123 2.4151 12.6135 -6.1113 -1.6534 -6.1139 5.0064 1.1071 -2.5394 -1.4560 -2.5948 Covariances of random parameters (t-test value for Geweke test) asc_bus_asc_bus asc_air_asc_bus asc_air_asc_air asc_rail_asc_bus asc_rail_asc_air 1.3107 -0.3005 -1.9281 -1.3488 -2.8553 asc_rail_asc_rail b_tt_car_asc_bus b_tt_car_asc_air b_tt_car_asc_rail b_tt_car_b_tt_car -0.2582 -1.3170 1.3435 1.0755 0.8645 b_tt_bus_asc_bus b_tt_bus_asc_air b_tt_bus_asc_rail b_tt_bus_b_tt_car b_tt_bus_b_tt_bus 0.6660 0.4189 0.9180 -1.3406 -0.6188 b_tt_air_asc_bus b_tt_air_asc_air b_tt_air_asc_rail b_tt_air_b_tt_car b_tt_air_b_tt_bus 1.3933 -0.5223 -6.1001 0.1119 2.3677 b_tt_air_b_tt_air b_tt_rail_asc_bus b_tt_rail_asc_air b_tt_rail_asc_rail b_tt_rail_b_tt_car 5.1807 -0.7215 -1.8321 0.7257 0.1620 b_tt_rail_b_tt_bus b_tt_rail_b_tt_air b_tt_rail_b_tt_rail b_access_asc_bus b_access_asc_air -0.7559 -1.9364 -2.2423 -1.7589 1.2759 b_access_asc_rail b_access_b_tt_car b_access_b_tt_bus b_access_b_tt_air b_access_b_tt_rail -0.1682 -0.0745 -1.0353 1.0033 -0.9298 b_access_b_access b_cost_asc_bus b_cost_asc_air b_cost_asc_rail b_cost_b_tt_car -0.9307 -0.4305 -0.3081 -1.1166 0.8605 b_cost_b_tt_bus b_cost_b_tt_air b_cost_b_tt_rail b_cost_b_access b_cost_b_cost 0.1873 1.1376 -0.7149 0.4699 -0.2681 b_wifi_asc_bus b_wifi_asc_air b_wifi_asc_rail b_wifi_b_tt_car b_wifi_b_tt_bus 1.6193 0.5093 -1.9798 -0.8592 3.0643 b_wifi_b_tt_air b_wifi_b_tt_rail b_wifi_b_access b_wifi_b_cost b_wifi_b_wifi 2.0773 -2.7490 -0.0423 0.9893 1.2312 b_food_asc_bus b_food_asc_air b_food_asc_rail b_food_b_tt_car b_food_b_tt_bus 0.8351 0.7000 -2.8618 -0.4221 1.5623 b_food_b_tt_air b_food_b_tt_rail b_food_b_access b_food_b_cost b_food_b_wifi 8.4964 -2.1035 0.1205 0.5697 1.5652 b_food_b_food 4.8418 Summary of parameter chains Non-random coefficients Mean SD asc_car 0.0000 NA asc_bus_shift_female 0.1802 0.0370 asc_air_shift_female 0.0838 0.0226 asc_rail_shift_female 0.0369 0.0548 b_tt_shift_business -0.0081 0.0007 b_cost_shift_business 0.0258 0.0035 cost_income_elast -0.6814 0.0211 b_no_frills 0.0000 NA Upper level model results for mean parameters for underlying Normals Mean SD asc_bus -0.4178 0.2244 asc_air -0.5740 0.1283 asc_rail -1.6767 0.1943 b_tt_car -4.6522 0.0532 b_tt_bus -4.0559 0.0438 b_tt_air -4.8226 0.1566 b_tt_rail -5.9695 0.1823 b_access -4.0497 0.1959 b_cost -2.6488 0.0335 b_wifi 0.9722 0.0596 b_food 0.3180 0.0954 Upper level model results for covariance matrix for underlying Normals (means across iterations) asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost b_wifi b_food asc_bus 0.2190 0.0117 0.0081 -0.0112 0.0264 0.0220 -0.0299 -0.0317 -0.0002 0.0133 0.0418 asc_air 0.0117 0.1550 0.0438 -0.0119 -0.0026 0.0323 -0.0162 0.0291 0.0144 0.0035 0.0174 asc_rail 0.0081 0.0438 0.1352 -0.0314 -0.0180 -0.0159 0.0122 -0.0126 -0.0057 -0.0026 -0.0008 b_tt_car -0.0112 -0.0119 -0.0314 0.0556 0.0110 -0.0017 0.0174 0.0257 0.0120 -0.0191 -0.0142 b_tt_bus 0.0264 -0.0026 -0.0180 0.0110 0.0508 0.0017 0.0069 -0.0033 0.0137 0.0022 -0.0009 b_tt_air 0.0220 0.0323 -0.0159 -0.0017 0.0017 0.1730 0.0029 -0.0247 -0.0039 0.0341 0.0482 b_tt_rail -0.0299 -0.0162 0.0122 0.0174 0.0069 0.0029 0.1763 0.0205 0.0029 -0.0044 -0.0198 b_access -0.0317 0.0291 -0.0126 0.0257 -0.0033 -0.0247 0.0205 0.1754 -0.0035 -0.0283 -0.0220 b_cost -0.0002 0.0144 -0.0057 0.0120 0.0137 -0.0039 0.0029 -0.0035 0.0469 0.0032 0.0096 b_wifi 0.0133 0.0035 -0.0026 -0.0191 0.0022 0.0341 -0.0044 -0.0283 0.0032 0.1630 0.0487 b_food 0.0418 0.0174 -0.0008 -0.0142 -0.0009 0.0482 -0.0198 -0.0220 0.0096 0.0487 0.2222 Upper level model results for covariance matrix for underlying Normals (SD across iterations) asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost b_wifi b_food asc_bus 0.0844 0.0545 0.0427 0.0235 0.0209 0.0660 0.0525 0.0579 0.0152 0.0502 0.0722 asc_air 0.0545 0.0490 0.0414 0.0232 0.0157 0.0494 0.0423 0.0481 0.0134 0.0407 0.0548 asc_rail 0.0427 0.0414 0.0437 0.0227 0.0156 0.0408 0.0370 0.0419 0.0119 0.0425 0.0484 b_tt_car 0.0235 0.0232 0.0227 0.0126 0.0080 0.0217 0.0187 0.0230 0.0064 0.0209 0.0213 b_tt_bus 0.0209 0.0157 0.0156 0.0080 0.0107 0.0169 0.0139 0.0183 0.0059 0.0139 0.0198 b_tt_air 0.0660 0.0494 0.0408 0.0217 0.0169 0.0555 0.0535 0.0473 0.0130 0.0456 0.0576 b_tt_rail 0.0525 0.0423 0.0370 0.0187 0.0139 0.0535 0.0619 0.0534 0.0140 0.0450 0.0570 b_access 0.0579 0.0481 0.0419 0.0230 0.0183 0.0473 0.0534 0.0708 0.0151 0.0489 0.0582 b_cost 0.0152 0.0134 0.0119 0.0064 0.0059 0.0130 0.0140 0.0151 0.0076 0.0120 0.0169 b_wifi 0.0502 0.0407 0.0425 0.0209 0.0139 0.0456 0.0450 0.0489 0.0120 0.0496 0.0564 b_food 0.0722 0.0548 0.0484 0.0213 0.0198 0.0576 0.0570 0.0582 0.0169 0.0564 0.0856 Summary of distributions of random coeffients (after distributional transforms) Mean SD asc_bus -0.4139 0.4678 asc_air -0.5741 0.3965 asc_rail -1.6766 0.3684 b_tt_car -0.0098 0.0023 b_tt_bus -0.0177 0.0041 b_tt_air -0.0087 0.0038 b_tt_rail -0.0028 0.0012 b_access -0.0191 0.0084 b_cost -0.0723 0.0159 b_wifi 0.9718 0.4012 b_food 0.3846 0.3699 Covariance matrix of random coeffients (after distributional transforms) asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost b_wifi b_food asc_bus 0.2188 0.0134 0.0104 1e-04 -5e-04 -2e-04 1e-04 6e-04 0.0001 0.0150 0.0318 asc_air 0.0134 0.1572 0.0451 1e-04 0e+00 -3e-04 0e+00 -5e-04 -0.0012 0.0030 0.0132 asc_rail 0.0104 0.0451 0.1357 3e-04 3e-04 1e-04 0e+00 2e-04 0.0004 -0.0010 -0.0006 b_tt_car 0.0001 0.0001 0.0003 0e+00 0e+00 0e+00 0e+00 0e+00 0.0000 0.0002 0.0001 b_tt_bus -0.0005 0.0000 0.0003 0e+00 0e+00 0e+00 0e+00 0e+00 0.0000 0.0000 0.0000 b_tt_air -0.0002 -0.0003 0.0001 0e+00 0e+00 0e+00 0e+00 0e+00 0.0000 -0.0003 -0.0003 b_tt_rail 0.0001 0.0000 0.0000 0e+00 0e+00 0e+00 0e+00 0e+00 0.0000 0.0000 0.0000 b_access 0.0006 -0.0005 0.0002 0e+00 0e+00 0e+00 0e+00 1e-04 0.0000 0.0006 0.0003 b_cost 0.0001 -0.0012 0.0004 0e+00 0e+00 0e+00 0e+00 0e+00 0.0003 -0.0002 -0.0005 b_wifi 0.0150 0.0030 -0.0010 2e-04 0e+00 -3e-04 0e+00 6e-04 -0.0002 0.1610 0.0383 b_food 0.0318 0.0132 -0.0006 1e-04 0e+00 -3e-04 0e+00 3e-04 -0.0005 0.0383 0.1368 Correlation matrix of random coeffients (after distributional transforms) asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost b_wifi b_food asc_bus 1.0000 0.0724 0.0602 0.1225 -0.2438 -0.1196 0.1471 0.1549 0.0133 0.0797 0.1837 asc_air 0.0724 1.0000 0.3087 0.1438 0.0131 -0.1900 0.0918 -0.1551 -0.1877 0.0188 0.0903 asc_rail 0.0602 0.3087 1.0000 0.3686 0.2025 0.0794 -0.0786 0.0719 0.0664 -0.0069 -0.0041 b_tt_car 0.1225 0.1438 0.3686 1.0000 0.1942 -0.0344 0.1516 0.2637 0.2297 0.1872 0.1049 b_tt_bus -0.2438 0.0131 0.2025 0.1942 1.0000 0.0240 0.0665 -0.0362 0.2810 -0.0267 -0.0035 b_tt_air -0.1196 -0.1900 0.0794 -0.0344 0.0240 1.0000 0.0091 -0.1431 -0.0357 -0.1947 -0.2245 b_tt_rail 0.1471 0.0918 -0.0786 0.1516 0.0665 0.0091 1.0000 0.1079 0.0168 0.0091 0.0776 b_access 0.1549 -0.1551 0.0719 0.2637 -0.0362 -0.1431 0.1079 1.0000 -0.0439 0.1678 0.0973 b_cost 0.0133 -0.1877 0.0664 0.2297 0.2810 -0.0357 0.0168 -0.0439 1.0000 -0.0387 -0.0899 b_wifi 0.0797 0.0188 -0.0069 0.1872 -0.0267 -0.1947 0.0091 0.1678 -0.0387 1.0000 0.2582 b_food 0.1837 0.0903 -0.0041 0.1049 -0.0035 -0.2245 0.0776 0.0973 -0.0899 0.2582 1.0000 Results for posterior means for random coefficients Mean SD asc_bus -0.4178 0.0404 asc_air -0.5741 0.0488 asc_rail -1.6765 0.0572 b_tt_car -0.0098 0.0008 b_tt_bus -0.0177 0.0014 b_tt_air -0.0089 0.0005 b_tt_rail -0.0028 0.0001 b_access -0.0193 0.0015 b_cost -0.0723 0.0056 b_wifi 0.9739 0.1251 b_food 0.3909 0.1046