Model run using Apollo for R, version 0.2.6 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : MNL_SP Model description : Simple MNL model on mode choice SP data Model run at : 2021-11-04 13:04:25 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(C) : -6706.939 LL(final) : -5598.901 Rho-square (0) : 0.3169 Adj.Rho-square (0) : 0.3155 Rho-square (C) : 0.1652 Adj.Rho-square (C) : 0.1636 AIC : 11219.8 BIC : 11295.19 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:00:4.31 pre-estimation : 00:00:1.04 estimation : 00:00:1.18 post-estimation : 00:00:2.09 Iterations : 23 Min abs eigenvalue of Hessian : 3.296355 Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_car 0.000000 NA NA NA NA asc_bus 0.061909 0.538553 0.1150 0.533044 0.1161 asc_air 0.238310 0.340125 0.7007 0.329272 0.7237 asc_rail -1.481374 0.327325 -4.5257 0.309844 -4.7810 b_tt_car -0.011602 6.5322e-04 -17.7615 6.7831e-04 -17.1045 b_tt_bus -0.017367 0.001452 -11.9620 0.001464 -11.8603 b_tt_air -0.019484 0.002587 -7.5301 0.002475 -7.8718 b_tt_rail -0.006365 0.001704 -3.7350 0.001623 -3.9207 b_access -0.023193 0.002689 -8.6266 0.002645 -8.7678 b_cost -0.058756 0.001487 -39.5177 0.001660 -35.3948 b_no_frills 0.000000 NA NA NA NA b_wifi 0.937557 0.052981 17.6961 0.055184 16.9898 b_food 0.409558 0.052181 7.8489 0.052628 7.7821 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 b_wifi asc_bus 0.29004 0.033491 0.027795 9.467e-05 -7.1334e-04 -2.329e-05 1.913e-05 -4.894e-05 2.028e-05 -3.5989e-04 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 -0.002317 asc_rail 0.02780 0.049672 0.107142 1.3847e-04 4.386e-05 -2.902e-05 -4.2599e-04 -3.751e-05 -3.463e-05 -0.001517 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 -5.838e-06 b_tt_bus -7.1334e-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 -5.052e-06 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 -3.184e-06 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 -9.591e-06 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 6.306e-07 -4.147e-06 b_cost 2.028e-05 -8.220e-05 -3.463e-05 2.468e-07 2.528e-07 9.027e-07 5.224e-07 6.306e-07 2.211e-06 -1.845e-05 b_wifi -3.5989e-04 -0.002317 -0.001517 -5.838e-06 -5.052e-06 -3.184e-06 -9.591e-06 -4.147e-06 -1.845e-05 0.002807 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 0.001523 b_food asc_bus -2.1649e-04 asc_air -0.001440 asc_rail -0.001485 b_tt_car -3.034e-06 b_tt_bus -2.417e-06 b_tt_air -5.193e-06 b_tt_rail -4.345e-06 b_access -4.198e-06 b_cost -1.052e-05 b_wifi 0.001523 b_food 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 b_wifi asc_bus 0.284136 0.025233 0.020214 8.844e-05 -6.9983e-04 -3.251e-05 4.735e-05 7.429e-05 4.522e-05 -0.002793 asc_air 0.025233 0.108420 0.043448 1.3604e-04 6.657e-05 -5.2336e-04 5.960e-05 -4.9919e-04 -8.030e-07 -0.001849 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 -0.001278 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 -6.772e-06 b_tt_bus -6.9983e-04 6.657e-05 5.963e-05 1.752e-07 2.144e-06 9.818e-08 -1.633e-09 -4.737e-07 2.922e-07 4.308e-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 -1.392e-05 b_tt_rail 4.735e-05 5.960e-05 -3.5524e-04 6.102e-08 -1.633e-09 -3.109e-07 2.636e-06 -6.387e-07 4.481e-07 -1.386e-05 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 1.280e-06 b_cost 4.522e-05 -8.030e-07 2.027e-05 3.662e-07 2.922e-07 6.893e-07 4.481e-07 5.627e-07 2.756e-06 -1.152e-05 b_wifi -0.002793 -0.001849 -0.001278 -6.772e-06 4.308e-07 -1.392e-05 -1.386e-05 1.280e-06 -1.152e-05 0.003045 b_food 6.3581e-04 -0.001149 -0.001704 -4.808e-06 -6.389e-06 -1.586e-05 -5.822e-06 -6.565e-06 -1.244e-05 0.001591 b_food asc_bus 6.3581e-04 asc_air -0.001149 asc_rail -0.001704 b_tt_car -4.808e-06 b_tt_bus -6.389e-06 b_tt_air -1.586e-05 b_tt_rail -5.822e-06 b_access -6.565e-06 b_cost -1.244e-05 b_wifi 0.001591 b_food 0.002770 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 b_wifi asc_bus 1.000000 0.18284 0.15767 0.26911 -0.912311 -0.016717 0.02084 -0.03380 0.02533 -0.01261 asc_air 0.182838 1.00000 0.44617 0.59414 0.075414 -0.712320 0.02978 -0.57511 -0.16254 -0.12856 asc_rail 0.157674 0.44617 1.00000 0.64759 0.092298 -0.034268 -0.76369 -0.04262 -0.07115 -0.08749 b_tt_car 0.269105 0.59414 0.64759 1.00000 0.125271 -0.033533 -0.04482 -0.01046 0.25409 -0.16868 b_tt_bus -0.912311 0.07541 0.09230 0.12527 1.000000 -0.006203 -0.02019 -0.02503 0.11710 -0.06568 b_tt_air -0.016717 -0.71232 -0.03427 -0.03353 -0.006203 1.000000 -0.05688 0.33475 0.23465 -0.02323 b_tt_rail 0.020843 0.02978 -0.76369 -0.04482 -0.020189 -0.056882 1.00000 -0.12919 0.20618 -0.10622 b_access -0.033800 -0.57511 -0.04262 -0.01046 -0.025030 0.334752 -0.12919 1.00000 0.15776 -0.02911 b_cost 0.025333 -0.16254 -0.07115 0.25409 0.117095 0.234655 0.20618 0.15776 1.00000 -0.23420 b_wifi -0.012613 -0.12856 -0.08749 -0.16868 -0.065678 -0.023226 -0.10622 -0.02911 -0.23420 1.00000 b_food -0.007704 -0.08111 -0.08697 -0.08902 -0.031903 -0.038465 -0.04887 -0.02993 -0.13558 0.55090 b_food asc_bus -0.007704 asc_air -0.081109 asc_rail -0.086968 b_tt_car -0.089020 b_tt_bus -0.031903 b_tt_air -0.038465 b_tt_rail -0.048867 b_access -0.029926 b_cost -0.135577 b_wifi 0.550904 b_food 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 b_wifi asc_bus 1.00000 0.143763 0.12239 0.24460 -0.896599 -0.02464 0.05472 0.052687 0.051099 -0.094953 asc_air 0.14376 1.000000 0.42586 0.60907 0.138067 -0.64217 0.11149 -0.573112 -0.001469 -0.101744 asc_rail 0.12239 0.425862 1.00000 0.63265 0.131422 0.04240 -0.70623 -0.046291 0.039406 -0.074768 b_tt_car 0.24460 0.609073 0.63265 1.00000 0.176381 0.02880 0.05541 -0.041139 0.325260 -0.180911 b_tt_bus -0.89660 0.138067 0.13142 0.17638 1.000000 0.02709 -6.8686e-04 -0.122294 0.120223 0.005331 b_tt_air -0.02464 -0.642169 0.04240 0.02880 0.027090 1.00000 -0.07738 0.275910 0.167755 -0.101894 b_tt_rail 0.05472 0.111489 -0.70623 0.05541 -6.8686e-04 -0.07738 1.00000 -0.148728 0.166293 -0.154690 b_access 0.05269 -0.573112 -0.04629 -0.04114 -0.122294 0.27591 -0.14873 1.000000 0.128141 0.008766 b_cost 0.05110 -0.001469 0.03941 0.32526 0.120223 0.16776 0.16629 0.128141 1.000000 -0.125805 b_wifi -0.09495 -0.101744 -0.07477 -0.18091 0.005331 -0.10189 -0.15469 0.008766 -0.125805 1.000000 b_food 0.02266 -0.066283 -0.10451 -0.13468 -0.082911 -0.12178 -0.06814 -0.047158 -0.142360 0.547886 b_food asc_bus 0.02266 asc_air -0.06628 asc_rail -0.10451 b_tt_car -0.13468 b_tt_bus -0.08291 b_tt_air -0.12178 b_tt_rail -0.06814 b_access -0.04716 b_cost -0.14236 b_wifi 0.54789 b_food 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.1815939 272 0.2158490 457 0.2243956 82 0.2251271 151 0.2385041 263 0.2422008 186 0.2425682 196 0.2428436 278 0.2514737 77 0.2541716 147 0.2563695 146 0.2608279 276 0.2617125 293 0.2647152 25 0.2674984 400 0.2683083 369 0.2688840 309 0.2704936 304 0.2708662 446 0.2711951 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 -1.481374 -1.481374 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 "MNL_SP" modelDescr "Simple MNL model on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" Hessian routines attempted -------------- numerical jacobian of LL analytical gradient Scaling in estimation -------------- 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 Scaling used in computing Hessian -------------- Value asc_bus 0.061909275 asc_air 0.238310118 asc_rail 1.481374447 b_tt_car 0.011602241 b_tt_bus 0.017367131 b_tt_air 0.019483608 b_tt_rail 0.006364946 b_access 0.023193157 b_cost 0.058756167 b_wifi 0.937557365 b_food 0.409558377 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, utilities = 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) }