Model run by stephane.hess using Apollo 0.3.6 on R 4.5.1 for Darwin. Please acknowledge the use of Apollo by citing Hess & Palma (2019) DOI 10.1016/j.jocm.2019.100170 www.ApolloChoiceModelling.com Model name : RRM Model description : Simple RRM model on mode choice SP data Model run at : 2025-09-19 11:41:38.550259 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -15.188985 reciprocal of condition number : 4.08944e-08 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) : -8196.02 LL at equal shares, LL(0) : -8196.02 LL at observed shares, LL(C) : -6706.94 LL(final) : -5737.51 Rho-squared vs equal shares : 0.3 Adj.Rho-squared vs equal shares : 0.2986 Rho-squared vs observed shares : 0.1445 Adj.Rho-squared vs observed shares : 0.1433 AIC : 11497.03 BIC : 11572.42 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:00:3.46 pre-estimation : 00:00:1.56 estimation : 00:00:0.52 post-estimation : 00:00:1.38 Iterations : 10 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 -1.217492 0.215509 -5.649 0.344364 -3.535 asc_air 0.891768 0.188027 4.743 0.267078 3.339 asc_rail 0.777407 0.144309 5.387 0.199215 3.902 b_tt_car -0.004508 2.5522e-04 -17.662 2.8536e-04 -15.797 b_tt_bus -0.005473 3.5380e-04 -15.470 5.2326e-04 -10.460 b_tt_air -0.010535 0.001346 -7.828 0.001590 -6.627 b_tt_rail -0.009138 6.0385e-04 -15.133 6.6345e-04 -13.773 b_access -0.008612 0.001155 -7.456 0.001366 -6.304 b_cost -0.027575 6.9581e-04 -39.630 8.6724e-04 -31.796 b_no_frills 0.000000 NA NA NA NA b_wifi 0.553115 0.033377 16.572 0.035096 15.760 b_food 0.218282 0.030366 7.188 0.030485 7.160 mu_rrm 1.000000 NA NA NA NA Overview of choices for RRM model component RRM: 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 asc_bus 0.04644 0.01688 0.01316 8.730e-06 -5.771e-05 -5.854e-05 -2.624e-05 asc_air 0.01688 0.03535 0.01240 1.109e-05 -1.248e-05 -1.4976e-04 -5.023e-06 asc_rail 0.01316 0.01240 0.02082 1.326e-05 -7.628e-06 -5.102e-06 -4.642e-05 b_tt_car 8.730e-06 1.109e-05 1.326e-05 6.514e-08 4.215e-08 1.354e-07 8.148e-08 b_tt_bus -5.771e-05 -1.248e-05 -7.628e-06 4.215e-08 1.252e-07 2.094e-07 1.128e-07 b_tt_air -5.854e-05 -1.4976e-04 -5.102e-06 1.354e-07 2.094e-07 1.811e-06 2.789e-07 b_tt_rail -2.624e-05 -5.023e-06 -4.642e-05 8.148e-08 1.128e-07 2.789e-07 3.646e-07 b_access -3.057e-05 -1.1217e-04 -2.308e-05 3.485e-08 3.112e-08 1.319e-07 3.318e-08 b_cost 7.484e-07 -3.583e-05 -1.513e-05 5.625e-08 5.443e-08 2.471e-07 1.356e-07 b_wifi -2.2993e-04 -3.2092e-04 -1.8156e-04 -1.332e-06 -9.334e-07 -4.945e-06 -4.804e-06 b_food -1.5662e-04 -3.1866e-04 -3.0234e-04 -4.989e-07 -2.652e-07 -2.950e-06 -2.593e-06 b_access b_cost b_wifi b_food asc_bus -3.057e-05 7.484e-07 -2.2993e-04 -1.5662e-04 asc_air -1.1217e-04 -3.583e-05 -3.2092e-04 -3.1866e-04 asc_rail -2.308e-05 -1.513e-05 -1.8156e-04 -3.0234e-04 b_tt_car 3.485e-08 5.625e-08 -1.332e-06 -4.989e-07 b_tt_bus 3.112e-08 5.443e-08 -9.334e-07 -2.652e-07 b_tt_air 1.319e-07 2.471e-07 -4.945e-06 -2.950e-06 b_tt_rail 3.318e-08 1.356e-07 -4.804e-06 -2.593e-06 b_access 1.334e-06 9.828e-08 -3.600e-06 -2.359e-06 b_cost 9.828e-08 4.841e-07 -5.937e-06 -2.952e-06 b_wifi -3.600e-06 -5.937e-06 0.001114 5.4078e-04 b_food -2.359e-06 -2.952e-06 5.4078e-04 9.2210e-04 Robust covariance matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail asc_bus 0.11859 0.021629 0.026030 1.322e-05 -1.5382e-04 -1.0839e-04 -7.200e-05 asc_air 0.02163 0.071331 0.024975 2.334e-05 -1.000e-05 -2.7329e-04 -4.873e-06 asc_rail 0.02603 0.024975 0.039687 2.882e-05 -1.398e-05 -9.890e-06 -7.433e-05 b_tt_car 1.322e-05 2.334e-05 2.882e-05 8.143e-08 5.235e-08 1.556e-07 6.757e-08 b_tt_bus -1.5382e-04 -1.000e-05 -1.398e-05 5.235e-08 2.738e-07 3.173e-07 1.773e-07 b_tt_air -1.0839e-04 -2.7329e-04 -9.890e-06 1.556e-07 3.173e-07 2.527e-06 2.864e-07 b_tt_rail -7.200e-05 -4.873e-06 -7.433e-05 6.757e-08 1.773e-07 2.864e-07 4.402e-07 b_access 4.902e-05 -2.4477e-04 -4.393e-05 -2.487e-08 -1.336e-07 5.469e-07 -9.287e-08 b_cost 3.386e-05 -5.320e-05 -2.354e-06 6.185e-08 8.511e-09 3.896e-07 7.119e-08 b_wifi -5.5366e-04 -0.001083 -0.001130 -2.359e-06 -1.578e-06 -6.617e-06 -3.879e-06 b_food -2.6069e-04 -6.5393e-04 -6.6351e-04 -1.196e-06 -6.984e-07 -5.325e-06 -2.791e-06 b_access b_cost b_wifi b_food asc_bus 4.902e-05 3.386e-05 -5.5366e-04 -2.6069e-04 asc_air -2.4477e-04 -5.320e-05 -0.001083 -6.5393e-04 asc_rail -4.393e-05 -2.354e-06 -0.001130 -6.6351e-04 b_tt_car -2.487e-08 6.185e-08 -2.359e-06 -1.196e-06 b_tt_bus -1.336e-07 8.511e-09 -1.578e-06 -6.984e-07 b_tt_air 5.469e-07 3.896e-07 -6.617e-06 -5.325e-06 b_tt_rail -9.287e-08 7.119e-08 -3.879e-06 -2.791e-06 b_access 1.866e-06 2.796e-07 1.300e-06 -8.198e-07 b_cost 2.796e-07 7.521e-07 -2.513e-06 -2.650e-06 b_wifi 1.300e-06 -2.513e-06 0.001232 5.7882e-04 b_food -8.198e-07 -2.650e-06 5.7882e-04 9.2936e-04 Classical correlation matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail asc_bus 1.000000 0.41659 0.42308 0.15872 -0.75684 -0.20186 -0.20165 asc_air 0.416592 1.00000 0.45705 0.23110 -0.18761 -0.59186 -0.04424 asc_rail 0.423079 0.45705 1.00000 0.36015 -0.14941 -0.02627 -0.53274 b_tt_car 0.158720 0.23110 0.36015 1.00000 0.46676 0.39410 0.52871 b_tt_bus -0.756843 -0.18761 -0.14941 0.46676 1.00000 0.43971 0.52783 b_tt_air -0.201864 -0.59186 -0.02627 0.39410 0.43971 1.00000 0.34325 b_tt_rail -0.201653 -0.04424 -0.53274 0.52871 0.52783 0.34325 1.00000 b_access -0.122795 -0.51650 -0.13844 0.11823 0.07617 0.08487 0.04758 b_cost 0.004991 -0.27385 -0.15072 0.31675 0.22111 0.26384 0.32280 b_wifi -0.031966 -0.05114 -0.03769 -0.15641 -0.07904 -0.11010 -0.23837 b_food -0.023933 -0.05581 -0.06900 -0.06437 -0.02469 -0.07219 -0.14142 b_access b_cost b_wifi b_food asc_bus -0.12280 0.004991 -0.03197 -0.02393 asc_air -0.51650 -0.273846 -0.05114 -0.05581 asc_rail -0.13844 -0.150723 -0.03769 -0.06900 b_tt_car 0.11823 0.316746 -0.15641 -0.06437 b_tt_bus 0.07617 0.221106 -0.07904 -0.02469 b_tt_air 0.08487 0.263837 -0.11010 -0.07219 b_tt_rail 0.04758 0.322802 -0.23837 -0.14142 b_access 1.00000 0.122284 -0.09337 -0.06725 b_cost 0.12228 1.000000 -0.25563 -0.13972 b_wifi -0.09337 -0.255629 1.00000 0.53356 b_food -0.06725 -0.139723 0.53356 1.00000 Robust correlation matrix: asc_bus asc_air asc_rail b_tt_car b_tt_bus b_tt_air b_tt_rail asc_bus 1.00000 0.23517 0.37943 0.13448 -0.85366 -0.19798 -0.31514 asc_air 0.23517 1.00000 0.46940 0.30619 -0.07156 -0.64366 -0.02750 asc_rail 0.37943 0.46940 1.00000 0.50702 -0.13412 -0.03123 -0.56241 b_tt_car 0.13448 0.30619 0.50702 1.00000 0.35062 0.34306 0.35689 b_tt_bus -0.85366 -0.07156 -0.13412 0.35062 1.00000 0.38139 0.51071 b_tt_air -0.19798 -0.64366 -0.03123 0.34306 0.38139 1.00000 0.27153 b_tt_rail -0.31514 -0.02750 -0.56241 0.35689 0.51071 0.27153 1.00000 b_access 0.10420 -0.67085 -0.16140 -0.06380 -0.18696 0.25183 -0.10247 b_cost 0.11337 -0.22970 -0.01362 0.24994 0.01876 0.28256 0.12373 b_wifi -0.04581 -0.11557 -0.16164 -0.23557 -0.08591 -0.11859 -0.16657 b_food -0.02483 -0.08032 -0.10925 -0.13753 -0.04378 -0.10988 -0.13799 b_access b_cost b_wifi b_food asc_bus 0.10420 0.11337 -0.04581 -0.02483 asc_air -0.67085 -0.22970 -0.11557 -0.08032 asc_rail -0.16140 -0.01362 -0.16164 -0.10925 b_tt_car -0.06380 0.24994 -0.23557 -0.13753 b_tt_bus -0.18696 0.01876 -0.08591 -0.04378 b_tt_air 0.25183 0.28256 -0.11859 -0.10988 b_tt_rail -0.10247 0.12373 -0.16657 -0.13799 b_access 1.00000 0.23602 0.02711 -0.01968 b_cost 0.23602 1.00000 -0.08257 -0.10023 b_wifi 0.02711 -0.08257 1.00000 0.54100 b_food -0.01968 -0.10023 0.54100 1.00000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 464 0.1817104 82 0.1943940 272 0.2073515 77 0.2242633 151 0.2290597 196 0.2303482 117 0.2307162 446 0.2372442 263 0.2417295 309 0.2431873 74 0.2489777 409 0.2528800 369 0.2530325 475 0.2532456 186 0.2550097 25 0.2554608 447 0.2559146 493 0.2579021 276 0.2587376 304 0.2627919 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Simple RRM model on mode choice SP data" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "RRM" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling used in computing Hessian --------------------------------- Value asc_bus 1.217492214 asc_air 0.891768081 asc_rail 0.777407049 b_tt_car 0.004507727 b_tt_bus 0.005473141 b_tt_air 0.010535190 b_tt_rail 0.009137818 b_access 0.008612201 b_cost 0.027574674 b_wifi 0.553114560 b_food 0.218281997 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 RRM settings rrm_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, rum_inputs = list(car = asc_car, bus = asc_bus, air = asc_air, rail = asc_rail), regret_inputs = list( time=list(x=list(time_car, time_bus, time_air, time_rail), b=list(b_tt_car,b_tt_bus,b_tt_air,b_tt_rail)), cost=list(x=list(cost_car, cost_bus, cost_air, cost_rail), b=list(b_cost)), access=list(x=list(0, access_bus, access_air, access_rail), b=list(b_access)), frills=list(x=list(0, 0, b_no_frills * ( service_air == 1 ) + b_wifi * ( service_air == 2 ) + b_food * ( service_air == 3 ), b_no_frills * ( service_rail == 1 ) + b_wifi * ( service_rail == 2 ) + b_food * ( service_rail == 3 )), b=1)), regret_scale = list(mu_rrm) ) ### Compute probabilities using RRM model P[["model"]] = apollo_rrm(rrm_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) }