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 : FMNL Model description : Fractional MNL model on time use data Model run at : 2025-09-19 11:52:10.486302 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -0.927153 reciprocal of condition number : 0.001199 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) : -7022.35 LL at equal shares, LL(0) : -7022.35 LL at observed shares, LL(C) : NA LL(final) : -3480.63 Rho-squared vs equal shares : 0.5043 Adj.Rho-squared vs equal shares : 0.5028 Rho-squared vs observed shares : Not applicable Adj.Rho-squared vs observed shares : Not applicable AIC : 6983.26 BIC : 7048.67 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:00:1.4 pre-estimation : 00:00:0.21 estimation : 00:00:0.49 post-estimation : 00:00:0.71 Iterations : 23 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_dropOff 1.4099 0.3326 4.2386 0.2645 5.3309 asc_work 3.4103 0.3031 11.2512 0.2289 14.8971 asc_school 0.1021 0.4114 0.2483 0.3250 0.3143 asc_shopping 1.6518 0.3256 5.0739 0.2344 7.0474 asc_privBusiness 1.5353 0.3288 4.6696 0.2278 6.7397 asc_petrol -1.1230 0.6020 -1.8657 0.5395 -2.0816 asc_leisure 2.4449 0.3109 7.8643 0.2314 10.5660 asc_vacation -1.5411 0.7101 -2.1703 0.4269 -3.6103 asc_exercise 2.0317 0.3172 6.4055 0.2603 7.8047 asc_home 5.1279 0.2991 17.1439 0.2245 22.8372 asc_travel 2.8123 0.3071 9.1591 0.2182 12.8874 asc_other 0.0000 NA NA NA NA Overview of choices for FMNL model component : dropOff work school shopping privBusiness petrol leisure Times available 2826.00 2826.00 2826 2826.00 2826.00 2826 2826.00 Observations with non-zero share 394.00 1139.00 85 783.00 535.00 66 883.00 Average share overall 0.02 0.12 0 0.02 0.02 0 0.05 Average share when available 0.02 0.12 0 0.02 0.02 0 0.05 vacation exercise home travel other Times available 2826 2826.00 2826.00 2826.00 2826 Observations with non-zero share 21 420.00 2770.00 2328.00 56 Average share overall 0 0.03 0.67 0.07 0 Average share when available 0 0.03 0.67 0.07 0 Classical covariance matrix: asc_dropOff asc_work asc_school asc_shopping asc_dropOff 0.11065 0.08894 0.08894 0.08894 asc_work 0.08894 0.09188 0.08894 0.08894 asc_school 0.08894 0.08894 0.16924 0.08894 asc_shopping 0.08894 0.08894 0.08894 0.10599 asc_privBusiness 0.08894 0.08894 0.08894 0.08894 asc_petrol 0.08894 0.08894 0.08894 0.08894 asc_leisure 0.08894 0.08894 0.08894 0.08894 asc_vacation 0.08894 0.08894 0.08894 0.08894 asc_exercise 0.08894 0.08894 0.08894 0.08894 asc_home 0.08894 0.08894 0.08894 0.08894 asc_travel 0.08894 0.08894 0.08894 0.08894 asc_privBusiness asc_petrol asc_leisure asc_vacation asc_dropOff 0.08894 0.08894 0.08894 0.08894 asc_work 0.08894 0.08894 0.08894 0.08894 asc_school 0.08894 0.08894 0.08894 0.08894 asc_shopping 0.08894 0.08894 0.08894 0.08894 asc_privBusiness 0.10809 0.08894 0.08894 0.08894 asc_petrol 0.08894 0.36235 0.08894 0.08894 asc_leisure 0.08894 0.08894 0.09665 0.08894 asc_vacation 0.08894 0.08894 0.08894 0.50427 asc_exercise 0.08894 0.08894 0.08894 0.08894 asc_home 0.08894 0.08894 0.08894 0.08894 asc_travel 0.08894 0.08894 0.08894 0.08894 asc_exercise asc_home asc_travel asc_dropOff 0.08894 0.08894 0.08894 asc_work 0.08894 0.08894 0.08894 asc_school 0.08894 0.08894 0.08894 asc_shopping 0.08894 0.08894 0.08894 asc_privBusiness 0.08894 0.08894 0.08894 asc_petrol 0.08894 0.08894 0.08894 asc_leisure 0.08894 0.08894 0.08894 asc_vacation 0.08894 0.08894 0.08894 asc_exercise 0.10060 0.08894 0.08894 asc_home 0.08894 0.08947 0.08894 asc_travel 0.08894 0.08894 0.09428 Robust covariance matrix: asc_dropOff asc_work asc_school asc_shopping asc_dropOff 0.06995 0.04841 0.04667 0.04578 asc_work 0.04841 0.05241 0.04896 0.04761 asc_school 0.04667 0.04896 0.10560 0.04727 asc_shopping 0.04578 0.04761 0.04727 0.05494 asc_privBusiness 0.04492 0.04519 0.04535 0.04315 asc_petrol 0.05431 0.04500 0.04039 0.03823 asc_leisure 0.04884 0.05057 0.05123 0.04815 asc_vacation 0.04693 0.05044 0.04808 0.04677 asc_exercise 0.05107 0.05156 0.05307 0.04842 asc_home 0.04811 0.05027 0.04969 0.04726 asc_travel 0.04703 0.04870 0.04775 0.04551 asc_privBusiness asc_petrol asc_leisure asc_vacation asc_dropOff 0.04492 0.05431 0.04884 0.04693 asc_work 0.04519 0.04500 0.05057 0.05044 asc_school 0.04535 0.04039 0.05123 0.04808 asc_shopping 0.04315 0.03823 0.04815 0.04677 asc_privBusiness 0.05189 0.03792 0.04614 0.04470 asc_petrol 0.03792 0.29108 0.04197 0.04113 asc_leisure 0.04614 0.04197 0.05354 0.05042 asc_vacation 0.04470 0.04113 0.05042 0.18222 asc_exercise 0.04671 0.04489 0.05154 0.05034 asc_home 0.04559 0.04202 0.05019 0.05093 asc_travel 0.04391 0.04144 0.04884 0.04955 asc_exercise asc_home asc_travel asc_dropOff 0.05107 0.04811 0.04703 asc_work 0.05156 0.05027 0.04870 asc_school 0.05307 0.04969 0.04775 asc_shopping 0.04842 0.04726 0.04551 asc_privBusiness 0.04671 0.04559 0.04391 asc_petrol 0.04489 0.04202 0.04144 asc_leisure 0.05154 0.05019 0.04884 asc_vacation 0.05034 0.05093 0.04955 asc_exercise 0.06776 0.05155 0.05035 asc_home 0.05155 0.05042 0.04820 asc_travel 0.05035 0.04820 0.04762 Classical correlation matrix: asc_dropOff asc_work asc_school asc_shopping asc_dropOff 1.0000 0.8821 0.6499 0.8213 asc_work 0.8821 1.0000 0.7132 0.9013 asc_school 0.6499 0.7132 1.0000 0.6641 asc_shopping 0.8213 0.9013 0.6641 1.0000 asc_privBusiness 0.8132 0.8925 0.6576 0.8309 asc_petrol 0.4442 0.4874 0.3591 0.4538 asc_leisure 0.8600 0.9438 0.6954 0.8787 asc_vacation 0.3765 0.4132 0.3044 0.3847 asc_exercise 0.8430 0.9251 0.6816 0.8613 asc_home 0.8939 0.9810 0.7228 0.9133 asc_travel 0.8708 0.9556 0.7041 0.8897 asc_privBusiness asc_petrol asc_leisure asc_vacation asc_dropOff 0.8132 0.4442 0.8600 0.3765 asc_work 0.8925 0.4874 0.9438 0.4132 asc_school 0.6576 0.3591 0.6954 0.3044 asc_shopping 0.8309 0.4538 0.8787 0.3847 asc_privBusiness 1.0000 0.4494 0.8701 0.3809 asc_petrol 0.4494 1.0000 0.4752 0.2081 asc_leisure 0.8701 0.4752 1.0000 0.4029 asc_vacation 0.3809 0.2081 0.4029 1.0000 asc_exercise 0.8529 0.4658 0.9020 0.3949 asc_home 0.9044 0.4940 0.9564 0.4187 asc_travel 0.8810 0.4812 0.9317 0.4079 asc_exercise asc_home asc_travel asc_dropOff 0.8430 0.8939 0.8708 asc_work 0.9251 0.9810 0.9556 asc_school 0.6816 0.7228 0.7041 asc_shopping 0.8613 0.9133 0.8897 asc_privBusiness 0.8529 0.9044 0.8810 asc_petrol 0.4658 0.4940 0.4812 asc_leisure 0.9020 0.9564 0.9317 asc_vacation 0.3949 0.4187 0.4079 asc_exercise 1.0000 0.9375 0.9132 asc_home 0.9375 1.0000 0.9684 asc_travel 0.9132 0.9684 1.0000 Robust correlation matrix: asc_dropOff asc_work asc_school asc_shopping asc_dropOff 1.0000 0.7996 0.5430 0.7384 asc_work 0.7996 1.0000 0.6582 0.8873 asc_school 0.5430 0.6582 1.0000 0.6206 asc_shopping 0.7384 0.8873 0.6206 1.0000 asc_privBusiness 0.7456 0.8666 0.6126 0.8082 asc_petrol 0.3806 0.3643 0.2304 0.3023 asc_leisure 0.7980 0.9546 0.6813 0.8877 asc_vacation 0.4156 0.5161 0.3466 0.4674 asc_exercise 0.7418 0.8652 0.6273 0.7936 asc_home 0.8101 0.9779 0.6810 0.8980 asc_travel 0.8148 0.9748 0.6733 0.8897 asc_privBusiness asc_petrol asc_leisure asc_vacation asc_dropOff 0.7456 0.3806 0.7980 0.4156 asc_work 0.8666 0.3643 0.9546 0.5161 asc_school 0.6126 0.2304 0.6813 0.3466 asc_shopping 0.8082 0.3023 0.8877 0.4674 asc_privBusiness 1.0000 0.3086 0.8753 0.4597 asc_petrol 0.3086 1.0000 0.3362 0.1786 asc_leisure 0.8753 0.3362 1.0000 0.5104 asc_vacation 0.4597 0.1786 0.5104 1.0000 asc_exercise 0.7877 0.3196 0.8557 0.4531 asc_home 0.8914 0.3469 0.9660 0.5313 asc_travel 0.8834 0.3520 0.9673 0.5319 asc_exercise asc_home asc_travel asc_dropOff 0.7418 0.8101 0.8148 asc_work 0.8652 0.9779 0.9748 asc_school 0.6273 0.6810 0.6733 asc_shopping 0.7936 0.8980 0.8897 asc_privBusiness 0.7877 0.8914 0.8834 asc_petrol 0.3196 0.3469 0.3520 asc_leisure 0.8557 0.9660 0.9673 asc_vacation 0.4531 0.5313 0.5319 asc_exercise 1.0000 0.8820 0.8864 asc_home 0.8820 1.0000 0.9837 asc_travel 0.8864 0.9837 1.0000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 3375723 0.01578864 2191235 0.05901098 7652039 0.06271484 2929853 0.07172681 2146576 0.07312397 1496531 0.07406910 2119561 0.08098043 4376416 0.08314347 9216479 0.08415818 9880000 0.08912257 3010000 0.08958300 5767103 0.10427215 2684804 0.10588989 1352278 0.10660330 8530000 0.10725024 8415029 0.10929684 9902059 0.11004369 8465193 0.11178851 5226574 0.11246656 56459 0.11649224 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Fractional MNL model on time use data" indivID "indivID" outputDirectory "output/" debug "FALSE" modelName "FMNL" 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_dropOff 1.4099415 asc_work 3.4103464 asc_school 0.1021322 asc_shopping 1.6518363 asc_privBusiness 1.5352621 asc_petrol 1.1230360 asc_leisure 2.4449236 asc_vacation 1.5411344 asc_exercise 2.0316635 asc_home 5.1278605 asc_travel 2.8123056 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 fmnl_settings, order is irrelevant V = list() V[["dropOff" ]] = asc_dropOff V[["work" ]] = asc_work V[["school" ]] = asc_school V[["shopping" ]] = asc_shopping V[["privBusiness"]] = asc_privBusiness V[["petrol" ]] = asc_petrol V[["leisure" ]] = asc_leisure V[["vacation" ]] = asc_vacation V[["exercise" ]] = asc_exercise V[["home" ]] = asc_home V[["travel" ]] = asc_travel V[["other" ]] = asc_other ### Define settings for MNL model component fmnl_settings = list( alternatives = c("dropOff", "work", "school", "shopping", "privBusiness", "petrol", "leisure", "vacation", "exercise", "home", "travel", "other"), choiceShares = list(dropOff = t_a01, work = t_a02, school = t_a03, shopping = t_a04, privBusiness = t_a05, petrol = t_a06, leisure = t_a07, vacation = t_a08, exercise = t_a09, home = t_a10, travel = t_a11, other = t_a12), utilities = V ) ### Compute probabilities using FMNL model P[["model"]] = apollo_fmnl(fmnl_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) }