Model run using Apollo for R, version 0.2.3 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : Apollo_example_2 Model description : Simple MNL model on mode choice SP data Model run at : 2021-02-04 16:50:54 Estimation method : bfgs Model diagnosis : successful convergence 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) : -8196.021 LL(0) : -8196.021 LL(final) : -5598.901 Rho-square (0) : 0.3169 Adj.Rho-square (0) : 0.3155 AIC : 11219.8 BIC : 11295.19 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:01:33.61 pre-estimation : 00:00:1.79 estimation : 00:00:2.12 post-estimation : 00:01:29.71 Iterations : 21 Number of bootstrap repetitions : 30 Min abs eigenvalue of Hessian : 3.296311 Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) Bootstrap.s.e. Bootstrap.t.rat.(0) asc_car 0.000000 NA NA NA NA NA NA asc_bus 0.061909 0.538557 0.1150 0.533053 0.1161 0.588666 0.1052 asc_air 0.238310 0.340125 0.7007 0.329272 0.7237 0.319962 0.7448 asc_rail -1.481375 0.327325 -4.5257 0.309844 -4.7810 0.312033 -4.7475 b_tt_car -0.011602 6.5322e-04 -17.7615 6.7831e-04 -17.1045 6.1484e-04 -18.8704 b_tt_bus -0.017367 0.001452 -11.9620 0.001464 -11.8601 0.001592 -10.9071 b_tt_air -0.019484 0.002587 -7.5301 0.002475 -7.8718 0.002423 -8.0404 b_tt_rail -0.006365 0.001704 -3.7350 0.001623 -3.9207 0.001679 -3.7919 b_access -0.023193 0.002689 -8.6266 0.002645 -8.7678 0.002787 -8.3205 b_cost -0.058756 0.001487 -39.5176 0.001660 -35.3947 0.001729 -33.9838 b_no_frills 0.000000 NA NA NA NA NA NA b_wifi 0.937557 0.052981 17.6961 0.055184 16.9898 0.057860 16.2040 b_food 0.409558 0.052181 7.8489 0.052628 7.7821 0.055267 7.4105 Overview of choices for MNL 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 b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 0.29004 0.033491 0.027795 9.467e-05 -7.1335e-04 -2.329e-05 1.913e-05 -4.894e-05 2.029e-05 asc_air 0.03349 0.115685 0.049672 1.3200e-04 3.724e-05 -6.2688e-04 1.726e-05 -5.2591e-04 -8.220e-05 asc_rail 0.02779 0.049672 0.107142 1.3847e-04 4.386e-05 -2.902e-05 -4.2599e-04 -3.751e-05 -3.463e-05 b_tt_car 9.467e-05 1.3200e-04 1.3847e-04 4.267e-07 1.188e-07 -5.668e-08 -4.990e-08 -1.837e-08 2.468e-07 b_tt_bus -7.1335e-04 3.724e-05 4.386e-05 1.188e-07 2.108e-06 -2.330e-08 -4.995e-08 -9.770e-08 2.528e-07 b_tt_air -2.329e-05 -6.2688e-04 -2.902e-05 -5.668e-08 -2.330e-08 6.695e-06 -2.508e-07 2.329e-06 9.027e-07 b_tt_rail 1.913e-05 1.726e-05 -4.2599e-04 -4.990e-08 -4.995e-08 -2.508e-07 2.904e-06 -5.919e-07 5.224e-07 b_access -4.894e-05 -5.2591e-04 -3.751e-05 -1.837e-08 -9.770e-08 2.329e-06 -5.919e-07 7.228e-06 6.307e-07 b_cost 2.029e-05 -8.220e-05 -3.463e-05 2.468e-07 2.528e-07 9.027e-07 5.224e-07 6.307e-07 2.211e-06 b_wifi -3.5990e-04 -0.002317 -0.001517 -5.838e-06 -5.052e-06 -3.184e-06 -9.591e-06 -4.147e-06 -1.845e-05 b_food -2.1649e-04 -0.001440 -0.001485 -3.034e-06 -2.417e-06 -5.193e-06 -4.345e-06 -4.198e-06 -1.052e-05 b_wifi b_food asc_bus -3.5990e-04 -2.1649e-04 asc_air -0.002317 -0.001440 asc_rail -0.001517 -0.001485 b_tt_car -5.838e-06 -3.034e-06 b_tt_bus -5.052e-06 -2.417e-06 b_tt_air -3.184e-06 -5.193e-06 b_tt_rail -9.591e-06 -4.345e-06 b_access -4.147e-06 -4.198e-06 b_cost -1.845e-05 -1.052e-05 b_wifi 0.002807 0.001523 b_food 0.001523 0.002723 Robust covariance matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 0.284145 0.025232 0.020214 8.844e-05 -6.9986e-04 -3.251e-05 4.735e-05 7.429e-05 4.522e-05 asc_air 0.025232 0.108420 0.043448 1.3604e-04 6.657e-05 -5.2336e-04 5.960e-05 -4.9919e-04 -8.033e-07 asc_rail 0.020214 0.043448 0.096003 1.3297e-04 5.963e-05 3.252e-05 -3.5524e-04 -3.794e-05 2.027e-05 b_tt_car 8.844e-05 1.3604e-04 1.3297e-04 4.601e-07 1.752e-07 4.835e-08 6.102e-08 -7.382e-08 3.662e-07 b_tt_bus -6.9986e-04 6.657e-05 5.963e-05 1.752e-07 2.144e-06 9.818e-08 -1.632e-09 -4.737e-07 2.922e-07 b_tt_air -3.251e-05 -5.2336e-04 3.252e-05 4.835e-08 9.818e-08 6.126e-06 -3.109e-07 1.806e-06 6.893e-07 b_tt_rail 4.735e-05 5.960e-05 -3.5524e-04 6.102e-08 -1.632e-09 -3.109e-07 2.636e-06 -6.387e-07 4.481e-07 b_access 7.429e-05 -4.9919e-04 -3.794e-05 -7.382e-08 -4.737e-07 1.806e-06 -6.387e-07 6.997e-06 5.627e-07 b_cost 4.522e-05 -8.033e-07 2.027e-05 3.662e-07 2.922e-07 6.893e-07 4.481e-07 5.627e-07 2.756e-06 b_wifi -0.002793 -0.001849 -0.001278 -6.772e-06 4.308e-07 -1.392e-05 -1.386e-05 1.279e-06 -1.152e-05 b_food 6.3581e-04 -0.001149 -0.001704 -4.808e-06 -6.390e-06 -1.586e-05 -5.822e-06 -6.565e-06 -1.244e-05 b_wifi b_food asc_bus -0.002793 6.3581e-04 asc_air -0.001849 -0.001149 asc_rail -0.001278 -0.001704 b_tt_car -6.772e-06 -4.808e-06 b_tt_bus 4.308e-07 -6.390e-06 b_tt_air -1.392e-05 -1.586e-05 b_tt_rail -1.386e-05 -5.822e-06 b_access 1.279e-06 -6.565e-06 b_cost -1.152e-05 -1.244e-05 b_wifi 0.003045 0.001591 b_food 0.001591 0.002770 Bootstrap covariance matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 0.346528 0.052789 0.053723 1.3519e-04 -8.6519e-04 -3.6599e-04 -1.1193e-04 2.1009e-04 3.078e-05 asc_air 0.052789 0.102376 0.038581 1.2512e-04 -1.697e-05 -4.9535e-04 6.431e-05 -5.7131e-04 2.440e-05 asc_rail 0.053723 0.038581 0.097365 1.0459e-04 -6.603e-05 2.282e-05 -3.9192e-04 -6.443e-05 3.245e-05 b_tt_car 1.3519e-04 1.2512e-04 1.0459e-04 3.780e-07 -1.304e-08 -4.397e-08 1.057e-07 -2.130e-07 4.777e-07 b_tt_bus -8.6519e-04 -1.697e-05 -6.603e-05 -1.304e-08 2.535e-06 9.937e-07 5.542e-07 -9.996e-07 4.876e-07 b_tt_air -3.6599e-04 -4.9535e-04 2.282e-05 -4.397e-08 9.937e-07 5.872e-06 -1.897e-07 2.001e-06 6.692e-07 b_tt_rail -1.1193e-04 6.431e-05 -3.9192e-04 1.057e-07 5.542e-07 -1.897e-07 2.818e-06 -8.743e-07 6.306e-07 b_access 2.1009e-04 -5.7131e-04 -6.443e-05 -2.130e-07 -9.996e-07 2.001e-06 -8.743e-07 7.770e-06 5.034e-07 b_cost 3.078e-05 2.440e-05 3.245e-05 4.777e-07 4.876e-07 6.692e-07 6.306e-07 5.034e-07 2.989e-06 b_wifi -0.001568 -0.006775 -0.002976 -8.679e-06 -4.929e-06 1.479e-05 -1.198e-05 3.706e-05 -2.039e-05 b_food -0.003096 -0.004320 -0.002190 -1.264e-05 -6.281e-06 -1.351e-06 -1.694e-05 -1.690e-05 -2.983e-05 b_wifi b_food asc_bus -0.001568 -0.003096 asc_air -0.006775 -0.004320 asc_rail -0.002976 -0.002190 b_tt_car -8.679e-06 -1.264e-05 b_tt_bus -4.929e-06 -6.281e-06 b_tt_air 1.479e-05 -1.351e-06 b_tt_rail -1.198e-05 -1.694e-05 b_access 3.706e-05 -1.690e-05 b_cost -2.039e-05 -2.983e-05 b_wifi 0.003348 0.002145 b_food 0.002145 0.003054 Classical correlation matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 1.000000 0.18284 0.15767 0.26910 -0.912312 -0.016717 0.02084 -0.03380 0.02533 asc_air 0.182836 1.00000 0.44617 0.59414 0.075414 -0.712321 0.02978 -0.57511 -0.16254 asc_rail 0.157672 0.44617 1.00000 0.64759 0.092298 -0.034268 -0.76369 -0.04262 -0.07115 b_tt_car 0.269103 0.59414 0.64759 1.00000 0.125270 -0.033533 -0.04482 -0.01046 0.25409 b_tt_bus -0.912312 0.07541 0.09230 0.12527 1.000000 -0.006203 -0.02019 -0.02503 0.11709 b_tt_air -0.016717 -0.71232 -0.03427 -0.03353 -0.006203 1.000000 -0.05688 0.33475 0.23465 b_tt_rail 0.020842 0.02978 -0.76369 -0.04482 -0.020189 -0.056882 1.00000 -0.12919 0.20618 b_access -0.033799 -0.57511 -0.04262 -0.01046 -0.025030 0.334752 -0.12919 1.00000 0.15776 b_cost 0.025333 -0.16254 -0.07115 0.25409 0.117094 0.234655 0.20618 0.15776 1.00000 b_wifi -0.012613 -0.12856 -0.08749 -0.16868 -0.065677 -0.023226 -0.10622 -0.02911 -0.23420 b_food -0.007704 -0.08111 -0.08697 -0.08902 -0.031903 -0.038465 -0.04887 -0.02993 -0.13558 b_wifi b_food asc_bus -0.01261 -0.007704 asc_air -0.12856 -0.081109 asc_rail -0.08749 -0.086968 b_tt_car -0.16868 -0.089020 b_tt_bus -0.06568 -0.031903 b_tt_air -0.02323 -0.038465 b_tt_rail -0.10622 -0.048867 b_access -0.02911 -0.029926 b_cost -0.23420 -0.135577 b_wifi 1.00000 0.550904 b_food 0.55090 1.000000 Robust correlation matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 1.00000 0.143758 0.12239 0.24459 -0.896602 -0.02464 0.05472 0.052688 0.051100 asc_air 0.14376 1.000000 0.42586 0.60907 0.138066 -0.64217 0.11149 -0.573114 -0.001470 asc_rail 0.12239 0.425861 1.00000 0.63265 0.131421 0.04240 -0.70623 -0.046292 0.039407 b_tt_car 0.24459 0.609072 0.63265 1.00000 0.176380 0.02880 0.05541 -0.041138 0.325261 b_tt_bus -0.89660 0.138066 0.13142 0.17638 1.000000 0.02709 -6.8636e-04 -0.122293 0.120219 b_tt_air -0.02464 -0.642170 0.04240 0.02880 0.027089 1.00000 -0.07738 0.275911 0.167756 b_tt_rail 0.05472 0.111489 -0.70623 0.05541 -6.8636e-04 -0.07738 1.00000 -0.148728 0.166293 b_access 0.05269 -0.573114 -0.04629 -0.04114 -0.122293 0.27591 -0.14873 1.000000 0.128142 b_cost 0.05110 -0.001470 0.03941 0.32526 0.120219 0.16776 0.16629 0.128142 1.000000 b_wifi -0.09495 -0.101744 -0.07477 -0.18091 0.005332 -0.10189 -0.15469 0.008765 -0.125805 b_food 0.02266 -0.066284 -0.10451 -0.13468 -0.082910 -0.12178 -0.06814 -0.047158 -0.142360 b_wifi b_food asc_bus -0.094953 0.02266 asc_air -0.101744 -0.06628 asc_rail -0.074768 -0.10451 b_tt_car -0.180912 -0.13468 b_tt_bus 0.005332 -0.08291 b_tt_air -0.101894 -0.12178 b_tt_rail -0.154690 -0.06814 b_access 0.008765 -0.04716 b_cost -0.125805 -0.14236 b_wifi 1.000000 0.54789 b_food 0.547886 1.00000 Bootstrap correlation matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail b_access b_cost asc_bus 1.00000 0.28027 0.29247 0.37351 -0.92305 -0.25657 -0.11328 0.12803 0.03024 asc_air 0.28027 1.00000 0.38644 0.63604 -0.03331 -0.63888 0.11974 -0.64057 0.04410 asc_rail 0.29247 0.38644 1.00000 0.54514 -0.13289 0.03018 -0.74827 -0.07408 0.06015 b_tt_car 0.37351 0.63604 0.54514 1.00000 -0.01331 -0.02951 0.10242 -0.12429 0.44936 b_tt_bus -0.92305 -0.03331 -0.13289 -0.01331 1.00000 0.25755 0.20735 -0.22523 0.17713 b_tt_air -0.25657 -0.63888 0.03018 -0.02951 0.25755 1.00000 -0.04665 0.29625 0.15972 b_tt_rail -0.11328 0.11974 -0.74827 0.10242 0.20735 -0.04665 1.00000 -0.18685 0.21728 b_access 0.12803 -0.64057 -0.07408 -0.12429 -0.22523 0.29625 -0.18685 1.00000 0.10446 b_cost 0.03024 0.04410 0.06015 0.44936 0.17713 0.15972 0.21728 0.10446 1.00000 b_wifi -0.04604 -0.36594 -0.16481 -0.24398 -0.05351 0.10548 -0.12331 0.22976 -0.20381 b_food -0.09517 -0.24432 -0.12696 -0.37210 -0.07138 -0.01009 -0.18265 -0.10967 -0.31219 b_wifi b_food asc_bus -0.04604 -0.09517 asc_air -0.36594 -0.24432 asc_rail -0.16481 -0.12696 b_tt_car -0.24398 -0.37210 b_tt_bus -0.05351 -0.07138 b_tt_air 0.10548 -0.01009 b_tt_rail -0.12331 -0.18265 b_access 0.22976 -0.10967 b_cost -0.20381 -0.31219 b_wifi 1.00000 0.67074 b_food 0.67074 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.1815932 272 0.2158479 457 0.2243950 82 0.2251268 151 0.2385029 263 0.2422009 186 0.2425679 196 0.2428431 278 0.2514734 77 0.2541718 147 0.2563678 146 0.2608279 276 0.2617113 293 0.2647136 25 0.2674977 400 0.2683093 369 0.2688829 309 0.2704936 304 0.2708657 446 0.2711929 Changes in parameter estimates from starting values: Initial Estimate Difference asc_car 0.000 0.000000 0.000000 asc_bus 0.000 0.061909 0.061909 asc_air 0.000 0.238310 0.238310 asc_rail 0.000 -1.481375 -1.481375 b_tt_car 0.000 -0.011602 -0.011602 b_tt_bus 0.000 -0.017367 -0.017367 b_tt_air 0.000 -0.019484 -0.019484 b_tt_rail 0.000 -0.006365 -0.006365 b_access 0.000 -0.023193 -0.023193 b_cost 0.000 -0.058756 -0.058756 b_no_frills 0.000 0.000000 0.000000 b_wifi 0.000 0.937557 0.937557 b_food 0.000 0.409558 0.409558 Settings and functions used in model definition: apollo_control -------------- Value modelName "Apollo_example_2" modelDescr "Simple MNL model on mode choice SP data" indivID "ID" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" panelData "TRUE" analyticGrad "TRUE" Hessian routines attempted -------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian -------------- Value asc_bus 0.061909273 asc_air 0.238310133 asc_rail 1.481375385 b_tt_car 0.011602208 b_tt_bus 0.017367189 b_tt_air 0.019483602 b_tt_rail 0.006364949 b_access 0.023193160 b_cost 0.058756149 b_wifi 0.937557383 b_food 0.409558353 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() ### List of utilities: these must use the same names as in mnl_settings, order is irrelevant V = list() V[['car']] = asc_car + b_tt_car * time_car + b_cost * cost_car V[['bus']] = asc_bus + b_tt_bus * time_bus + b_access * access_bus + b_cost * cost_bus V[['air']] = asc_air + b_tt_air * time_air + b_access * access_air + b_cost * cost_air + b_no_frills * ( service_air == 1 ) + b_wifi * ( service_air == 2 ) + b_food * ( service_air == 3 ) V[['rail']] = asc_rail + b_tt_rail * time_rail + b_access * access_rail + b_cost * cost_rail + b_no_frills * ( service_rail == 1 ) + b_wifi * ( service_rail == 2 ) + b_food * ( service_rail == 3 ) ### Define settings for MNL model component mnl_settings = list( alternatives = c(car=1, bus=2, air=3, rail=4), avail = list(car=av_car, bus=av_bus, air=av_air, rail=av_rail), choiceVar = choice, V = V ) ### Compute probabilities using MNL model P[['model']] = apollo_mnl(mnl_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) }