Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : FMNL Model description : Fractional MNL model on time use data Model run at : 2023-05-10 22:12:52 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -0.927452 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 : Not applicable Adj.Rho-squared vs equal shares : Not applicable 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) : 00:00:3.71 pre-estimation : 00:00:1.04 estimation : 00:00:1.15 initial estimation : 00:00:1 estimation after rescaling : 00:00:0.16 post-estimation : 00:00:1.51 Iterations : 26 initial estimation : 25 estimation after rescaling : 1 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_dropOff 1.4094 0.3326 4.2377 0.2644 5.3304 asc_work 3.4099 0.3030 11.2521 0.2288 14.9013 asc_school 0.1018 0.4113 0.2476 0.3249 0.3134 asc_shopping 1.6514 0.3255 5.0733 0.2343 7.0478 asc_privBusiness 1.5348 0.3287 4.6690 0.2277 6.7401 asc_petrol -1.1230 0.6018 -1.8660 0.5393 -2.0824 asc_leisure 2.4445 0.3108 7.8645 0.2313 10.5683 asc_vacation -1.5425 0.7104 -2.1714 0.4271 -3.6115 asc_exercise 2.0312 0.3171 6.4054 0.2602 7.8056 asc_home 5.1274 0.2990 17.1461 0.2244 22.8449 asc_travel 2.8119 0.3070 9.1596 0.2181 12.8910 asc_other 0.0000 NA NA NA NA Overview of choices for model component : dropOff work school shopping privBusiness petrol leisure vacation exercise Times available 2826.00 2826.00 2826 2826.00 2826.00 2826 2826.00 2826 2826.00 Observations with non-zero share 394.00 1139.00 85 783.00 535.00 66 883.00 21 420.00 Average share overall 0.02 0.12 0 0.02 0.02 0 0.05 0 0.03 Average share when available 0.02 0.12 0 0.02 0.02 0 0.05 0 0.03 home travel other Times available 2826.00 2826.00 2826 Observations with non-zero share 2770.00 2328.00 56 Average share overall 0.67 0.07 0 Average share when available 0.67 0.07 0 Classical covariance matrix: asc_dropOff asc_work asc_school asc_shopping asc_privBusiness asc_dropOff 0.11062 0.08890 0.08890 0.08890 0.08890 asc_work 0.08890 0.09184 0.08890 0.08890 0.08890 asc_school 0.08890 0.08890 0.16919 0.08890 0.08890 asc_shopping 0.08890 0.08890 0.08890 0.10595 0.08890 asc_privBusiness 0.08890 0.08890 0.08890 0.08890 0.10806 asc_petrol 0.08890 0.08890 0.08890 0.08890 0.08890 asc_leisure 0.08890 0.08890 0.08890 0.08890 0.08890 asc_vacation 0.08890 0.08890 0.08890 0.08890 0.08890 asc_exercise 0.08890 0.08890 0.08890 0.08890 0.08890 asc_home 0.08890 0.08890 0.08890 0.08890 0.08890 asc_travel 0.08890 0.08890 0.08890 0.08890 0.08890 asc_petrol asc_leisure asc_vacation asc_exercise asc_home asc_dropOff 0.08890 0.08890 0.08890 0.08890 0.08890 asc_work 0.08890 0.08890 0.08890 0.08890 0.08890 asc_school 0.08890 0.08890 0.08890 0.08890 0.08890 asc_shopping 0.08890 0.08890 0.08890 0.08890 0.08890 asc_privBusiness 0.08890 0.08890 0.08890 0.08890 0.08890 asc_petrol 0.36218 0.08890 0.08890 0.08890 0.08890 asc_leisure 0.08890 0.09661 0.08890 0.08890 0.08890 asc_vacation 0.08890 0.08890 0.50461 0.08890 0.08890 asc_exercise 0.08890 0.08890 0.08890 0.10056 0.08890 asc_home 0.08890 0.08890 0.08890 0.08890 0.08943 asc_travel 0.08890 0.08890 0.08890 0.08890 0.08890 asc_travel asc_dropOff 0.08890 asc_work 0.08890 asc_school 0.08890 asc_shopping 0.08890 asc_privBusiness 0.08890 asc_petrol 0.08890 asc_leisure 0.08890 asc_vacation 0.08890 asc_exercise 0.08890 asc_home 0.08890 asc_travel 0.09424 Robust covariance matrix: asc_dropOff asc_work asc_school asc_shopping asc_privBusiness asc_dropOff 0.06992 0.04837 0.04663 0.04573 0.04488 asc_work 0.04837 0.05237 0.04892 0.04757 0.04515 asc_school 0.04663 0.04892 0.10555 0.04723 0.04531 asc_shopping 0.04573 0.04757 0.04723 0.05490 0.04311 asc_privBusiness 0.04488 0.04515 0.04531 0.04311 0.05185 asc_petrol 0.05427 0.04496 0.04036 0.03819 0.03789 asc_leisure 0.04880 0.05052 0.05119 0.04811 0.04610 asc_vacation 0.04688 0.05040 0.04804 0.04673 0.04466 asc_exercise 0.05103 0.05152 0.05302 0.04838 0.04667 asc_home 0.04807 0.05023 0.04965 0.04722 0.04555 asc_travel 0.04698 0.04866 0.04770 0.04547 0.04387 asc_petrol asc_leisure asc_vacation asc_exercise asc_home asc_dropOff 0.05427 0.04880 0.04688 0.05103 0.04807 asc_work 0.04496 0.05052 0.05040 0.05152 0.05023 asc_school 0.04036 0.05119 0.04804 0.05302 0.04965 asc_shopping 0.03819 0.04811 0.04673 0.04838 0.04722 asc_privBusiness 0.03789 0.04610 0.04466 0.04667 0.04555 asc_petrol 0.29080 0.04193 0.04109 0.04486 0.04199 asc_leisure 0.04193 0.05350 0.05038 0.05150 0.05015 asc_vacation 0.04109 0.05038 0.18241 0.05030 0.05088 asc_exercise 0.04486 0.05150 0.05030 0.06772 0.05151 asc_home 0.04199 0.05015 0.05088 0.05151 0.05038 asc_travel 0.04141 0.04880 0.04951 0.05031 0.04816 asc_travel asc_dropOff 0.04698 asc_work 0.04866 asc_school 0.04770 asc_shopping 0.04547 asc_privBusiness 0.04387 asc_petrol 0.04141 asc_leisure 0.04880 asc_vacation 0.04951 asc_exercise 0.05031 asc_home 0.04816 asc_travel 0.04758 Classical correlation matrix: asc_dropOff asc_work asc_school asc_shopping asc_privBusiness asc_dropOff 1.0000 0.8820 0.6498 0.8212 0.8131 asc_work 0.8820 1.0000 0.7132 0.9012 0.8924 asc_school 0.6498 0.7132 1.0000 0.6640 0.6575 asc_shopping 0.8212 0.9012 0.6640 1.0000 0.8309 asc_privBusiness 0.8131 0.8924 0.6575 0.8309 1.0000 asc_petrol 0.4442 0.4875 0.3591 0.4538 0.4494 asc_leisure 0.8599 0.9438 0.6953 0.8787 0.8701 asc_vacation 0.3763 0.4130 0.3043 0.3845 0.3807 asc_exercise 0.8429 0.9251 0.6815 0.8613 0.8528 asc_home 0.8938 0.9810 0.7227 0.9133 0.9044 asc_travel 0.8707 0.9556 0.7040 0.8897 0.8809 asc_petrol asc_leisure asc_vacation asc_exercise asc_home asc_dropOff 0.4442 0.8599 0.3763 0.8429 0.8938 asc_work 0.4875 0.9438 0.4130 0.9251 0.9810 asc_school 0.3591 0.6953 0.3043 0.6815 0.7227 asc_shopping 0.4538 0.8787 0.3845 0.8613 0.9133 asc_privBusiness 0.4494 0.8701 0.3807 0.8528 0.9044 asc_petrol 1.0000 0.4753 0.2080 0.4658 0.4940 asc_leisure 0.4753 1.0000 0.4026 0.9019 0.9564 asc_vacation 0.2080 0.4026 1.0000 0.3946 0.4185 asc_exercise 0.4658 0.9019 0.3946 1.0000 0.9375 asc_home 0.4940 0.9564 0.4185 0.9375 1.0000 asc_travel 0.4812 0.9317 0.4077 0.9132 0.9684 asc_travel asc_dropOff 0.8707 asc_work 0.9556 asc_school 0.7040 asc_shopping 0.8897 asc_privBusiness 0.8809 asc_petrol 0.4812 asc_leisure 0.9317 asc_vacation 0.4077 asc_exercise 0.9132 asc_home 0.9684 asc_travel 1.0000 Robust correlation matrix: asc_dropOff asc_work asc_school asc_shopping asc_privBusiness asc_dropOff 1.0000 0.7994 0.5429 0.7382 0.7455 asc_work 0.7994 1.0000 0.6580 0.8872 0.8665 asc_school 0.5429 0.6580 1.0000 0.6204 0.6124 asc_shopping 0.7382 0.8872 0.6204 1.0000 0.8080 asc_privBusiness 0.7455 0.8665 0.6124 0.8080 1.0000 asc_petrol 0.3806 0.3643 0.2304 0.3023 0.3086 asc_leisure 0.7978 0.9545 0.6811 0.8877 0.8752 asc_vacation 0.4152 0.5156 0.3462 0.4669 0.4592 asc_exercise 0.7417 0.8651 0.6272 0.7935 0.7876 asc_home 0.8100 0.9779 0.6808 0.8979 0.8913 asc_travel 0.8146 0.9748 0.6732 0.8896 0.8833 asc_petrol asc_leisure asc_vacation asc_exercise asc_home asc_dropOff 0.3806 0.7978 0.4152 0.7417 0.8100 asc_work 0.3643 0.9545 0.5156 0.8651 0.9779 asc_school 0.2304 0.6811 0.3462 0.6272 0.6808 asc_shopping 0.3023 0.8877 0.4669 0.7935 0.8979 asc_privBusiness 0.3086 0.8752 0.4592 0.7876 0.8913 asc_petrol 1.0000 0.3362 0.1784 0.3196 0.3469 asc_leisure 0.3362 1.0000 0.5099 0.8556 0.9660 asc_vacation 0.1784 0.5099 1.0000 0.4526 0.5308 asc_exercise 0.3196 0.8556 0.4526 1.0000 0.8819 asc_home 0.3469 0.9660 0.5308 0.8819 1.0000 asc_travel 0.3520 0.9673 0.5314 0.8863 0.9837 asc_travel asc_dropOff 0.8146 asc_work 0.9748 asc_school 0.6732 asc_shopping 0.8896 asc_privBusiness 0.8833 asc_petrol 0.3520 asc_leisure 0.9673 asc_vacation 0.5314 asc_exercise 0.8863 asc_home 0.9837 asc_travel 1.0000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 3375723 0.01578851 2191235 0.05901841 7652039 0.06271657 2929853 0.07172675 2146576 0.07312284 1496531 0.07406810 2119561 0.08098049 4376416 0.08314333 9216479 0.08415630 9880000 0.08912148 3010000 0.08958131 5767103 0.10426927 2684804 0.10588728 1352278 0.10660640 8530000 0.10725205 8415029 0.10929981 9902059 0.11004236 8465193 0.11178612 5226574 0.11247077 56459 0.11648899 Changes in parameter estimates from starting values: Initial Estimate Difference asc_dropOff 0.000 1.4094 1.4094 asc_work 0.000 3.4099 3.4099 asc_school 0.000 0.1018 0.1018 asc_shopping 0.000 1.6514 1.6514 asc_privBusiness 0.000 1.5348 1.5348 asc_petrol 0.000 -1.1230 -1.1230 asc_leisure 0.000 2.4445 2.4445 asc_vacation 0.000 -1.5425 -1.5425 asc_exercise 0.000 2.0312 2.0312 asc_home 0.000 5.1274 5.1274 asc_travel 0.000 2.8119 2.8119 asc_other 0.000 0.0000 0.0000 Settings and functions used in model definition: apollo_control -------------- Value modelName "FMNL" modelDescr "Fractional MNL model on time use data" indivID "indivID" 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" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling in estimation --------------------- Value asc_dropOff 1.4094348 asc_work 3.4099337 asc_school 0.1018289 asc_shopping 1.6513614 asc_privBusiness 1.5347888 asc_petrol 1.1229682 asc_leisure 2.4444999 asc_vacation 1.5424633 asc_exercise 2.0312405 asc_home 5.1274154 asc_travel 2.8118870 Scaling used in computing Hessian --------------------------------- Value asc_dropOff 1.4094352 asc_work 3.4099277 asc_school 0.1018289 asc_shopping 1.6513618 asc_privBusiness 1.5347891 asc_petrol 1.1229683 asc_leisure 2.4444992 asc_vacation 1.5424630 asc_exercise 2.0312402 asc_home 5.1274387 asc_travel 2.8118850 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) }