Model run by stephane.hess using Apollo 0.2.8 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : ECL_preference_space_heteroskedasticity Model description : Error components logit model on Swiss route choice data, uncorrelated Lognormals in preference space, with heteroskedasticity term Model run at : 2022-10-08 17:40:39 Estimation method : bfgs Model diagnosis : successful convergence Number of individuals : 388 Number of rows in database : 3492 Number of modelled outcomes : 3492 Number of cores used : 4 Number of inter-individual draws : 500 (halton) LL(start) : -2253.78 LL at equal shares, LL(0) : -2420.47 LL at observed shares, LL(C) : -2420.39 LL(final) : -1442.21 Rho-squared vs equal shares : 0.4042 Adj.Rho-squared vs equal shares : 0.4004 Rho-squared vs observed shares : 0.4041 Adj.Rho-squared vs observed shares : 0.4004 AIC : 2902.41 BIC : 2957.84 Estimated parameters : 9 Time taken (hh:mm:ss) : 00:01:52.3 pre-estimation : 00:00:25.84 estimation : 00:00:40.76 post-estimation : 00:00:45.7 Iterations : 37 Min abs eigenvalue of Hessian : 33.35096 Unconstrained optimisation. These outputs have had the scaling used in estimation applied to them. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) mu_log_b_tt -1.9422 0.08984 -21.620 0.11691 -16.614 sigma_log_b_tt -0.4401 0.06696 -6.573 0.05720 -7.695 mu_log_b_tc -1.0198 0.14418 -7.073 0.18751 -5.438 sigma_log_b_tc -1.0464 0.09085 -11.517 0.08989 -11.641 mu_log_b_hw -2.8952 0.08712 -33.233 0.09154 -31.630 sigma_log_b_hw -0.8331 0.10184 -8.181 0.10107 -8.243 mu_log_b_ch 0.6675 0.07524 8.871 0.08285 8.057 sigma_log_b_ch -0.8122 0.10237 -7.934 0.11579 -7.014 sigma_hsk -0.5507 0.13089 -4.207 0.16850 -3.268 Overview of choices for MNL model component : alt1 alt2 Times available 3492.00 3492.00 Times chosen 1734.00 1758.00 Percentage chosen overall 49.66 50.34 Percentage chosen when available 49.66 50.34 Classical covariance matrix: mu_log_b_tt sigma_log_b_tt mu_log_b_tc sigma_log_b_tc mu_log_b_hw sigma_log_b_hw mu_log_b_tt 0.008070 0.001699 0.008546 0.002378 0.002312 -0.001255 sigma_log_b_tt 0.001699 0.004484 7.4837e-04 7.0879e-04 -3.8844e-04 -7.632e-05 mu_log_b_tc 0.008546 7.4837e-04 0.020789 0.007114 0.002897 -0.001563 sigma_log_b_tc 0.002378 7.0879e-04 0.007114 0.008255 -3.0035e-04 8.0369e-04 mu_log_b_hw 0.002312 -3.8844e-04 0.002897 -3.0035e-04 0.007589 0.002141 sigma_log_b_hw -0.001255 -7.632e-05 -0.001563 8.0369e-04 0.002141 0.010371 mu_log_b_ch 0.002583 -3.4307e-04 0.002366 -4.9350e-04 0.001621 -0.001371 sigma_log_b_ch -0.001597 -4.3924e-04 -0.001757 -5.4063e-04 -4.5771e-04 0.001690 sigma_hsk -0.002902 1.4103e-04 -0.001237 9.6144e-04 -0.002630 3.0515e-04 mu_log_b_ch sigma_log_b_ch sigma_hsk mu_log_b_tt 0.002583 -0.001597 -0.002902 sigma_log_b_tt -3.4307e-04 -4.3924e-04 1.4103e-04 mu_log_b_tc 0.002366 -0.001757 -0.001237 sigma_log_b_tc -4.9350e-04 -5.4063e-04 9.6144e-04 mu_log_b_hw 0.001621 -4.5771e-04 -0.002630 sigma_log_b_hw -0.001371 0.001690 3.0515e-04 mu_log_b_ch 0.005662 -1.1336e-04 -0.002909 sigma_log_b_ch -1.1336e-04 0.010479 1.4704e-04 sigma_hsk -0.002909 1.4704e-04 0.017132 Robust covariance matrix: mu_log_b_tt sigma_log_b_tt mu_log_b_tc sigma_log_b_tc mu_log_b_hw sigma_log_b_hw mu_log_b_tt 0.013667 0.002490 0.017368 0.004832 0.004332 -0.001673 sigma_log_b_tt 0.002490 0.003271 0.003217 0.002201 1.9436e-04 1.4741e-04 mu_log_b_tc 0.017368 0.003217 0.035162 0.009889 0.006151 -0.002997 sigma_log_b_tc 0.004832 0.002201 0.009889 0.008079 1.0956e-04 5.2746e-04 mu_log_b_hw 0.004332 1.9436e-04 0.006151 1.0956e-04 0.008379 0.001685 sigma_log_b_hw -0.001673 1.4741e-04 -0.002997 5.2746e-04 0.001685 0.010215 mu_log_b_ch 0.005203 1.8565e-04 0.006111 5.3755e-04 0.003264 -0.001381 sigma_log_b_ch -0.001996 -6.3448e-04 -0.002906 -0.001466 1.5437e-04 0.004047 sigma_hsk -0.003081 -4.886e-05 0.002357 0.002493 -0.001910 0.002285 mu_log_b_ch sigma_log_b_ch sigma_hsk mu_log_b_tt 0.005203 -0.001996 -0.003081 sigma_log_b_tt 1.8565e-04 -6.3448e-04 -4.886e-05 mu_log_b_tc 0.006111 -0.002906 0.002357 sigma_log_b_tc 5.3755e-04 -0.001466 0.002493 mu_log_b_hw 0.003264 1.5437e-04 -0.001910 sigma_log_b_hw -0.001381 0.004047 0.002285 mu_log_b_ch 0.006864 -2.2175e-04 -0.003468 sigma_log_b_ch -2.2175e-04 0.013408 7.2389e-04 sigma_hsk -0.003468 7.2389e-04 0.028392 Classical correlation matrix: mu_log_b_tt sigma_log_b_tt mu_log_b_tc sigma_log_b_tc mu_log_b_hw sigma_log_b_hw mu_log_b_tt 1.0000 0.28245 0.65976 0.29136 0.29539 -0.13715 sigma_log_b_tt 0.2824 1.00000 0.07751 0.11651 -0.06659 -0.01119 mu_log_b_tc 0.6598 0.07751 1.00000 0.54305 0.23065 -0.10642 sigma_log_b_tc 0.2914 0.11651 0.54305 1.00000 -0.03795 0.08686 mu_log_b_hw 0.2954 -0.06659 0.23065 -0.03795 1.00000 0.24127 sigma_log_b_hw -0.1372 -0.01119 -0.10642 0.08686 0.24127 1.00000 mu_log_b_ch 0.3822 -0.06809 0.21811 -0.07219 0.24722 -0.17897 sigma_log_b_ch -0.1737 -0.06408 -0.11907 -0.05813 -0.05133 0.16216 sigma_hsk -0.2468 0.01609 -0.06557 0.08085 -0.23068 0.02289 mu_log_b_ch sigma_log_b_ch sigma_hsk mu_log_b_tt 0.38219 -0.17368 -0.24678 sigma_log_b_tt -0.06809 -0.06408 0.01609 mu_log_b_tc 0.21811 -0.11907 -0.06557 sigma_log_b_tc -0.07219 -0.05813 0.08085 mu_log_b_hw 0.24722 -0.05133 -0.23068 sigma_log_b_hw -0.17897 0.16216 0.02289 mu_log_b_ch 1.00000 -0.01472 -0.29537 sigma_log_b_ch -0.01472 1.00000 0.01097 sigma_hsk -0.29537 0.01097 1.00000 Robust correlation matrix: mu_log_b_tt sigma_log_b_tt mu_log_b_tc sigma_log_b_tc mu_log_b_hw sigma_log_b_hw mu_log_b_tt 1.0000 0.372411 0.79230 0.45981 0.40484 -0.14158 sigma_log_b_tt 0.3724 1.000000 0.29992 0.42805 0.03712 0.02550 mu_log_b_tc 0.7923 0.299921 1.00000 0.58669 0.35836 -0.15816 sigma_log_b_tc 0.4598 0.428050 0.58669 1.00000 0.01332 0.05806 mu_log_b_hw 0.4048 0.037124 0.35836 0.01332 1.00000 0.18213 sigma_log_b_hw -0.1416 0.025500 -0.15816 0.05806 0.18213 1.00000 mu_log_b_ch 0.5372 0.039179 0.39339 0.07218 0.43038 -0.16491 sigma_log_b_ch -0.1474 -0.095803 -0.13384 -0.14083 0.01456 0.34585 sigma_hsk -0.1564 -0.005070 0.07461 0.16462 -0.12383 0.13418 mu_log_b_ch sigma_log_b_ch sigma_hsk mu_log_b_tt 0.53723 -0.14745 -0.156433 sigma_log_b_tt 0.03918 -0.09580 -0.005070 mu_log_b_tc 0.39339 -0.13384 0.074608 sigma_log_b_tc 0.07218 -0.14083 0.164621 mu_log_b_hw 0.43038 0.01456 -0.123831 sigma_log_b_hw -0.16491 0.34585 0.134177 mu_log_b_ch 1.00000 -0.02312 -0.248409 sigma_log_b_ch -0.02312 1.00000 0.037102 sigma_hsk -0.24841 0.03710 1.000000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 16178 0.2486126 15174 0.2656403 22580 0.2694539 21623 0.3165355 76862 0.3203901 16489 0.3269740 21922 0.3277797 23205 0.3413130 12534 0.3443340 15056 0.3574516 16617 0.3653125 22961 0.3752850 24627 0.3799142 14754 0.3832583 22820 0.3841577 17187 0.3930686 16184 0.3957191 20100 0.4058168 82613 0.4123299 15312 0.4262047 Changes in parameter estimates from starting values: Initial Estimate Difference mu_log_b_tt -3.00000 -1.9422 1.0578 sigma_log_b_tt -0.01000 -0.4401 -0.4301 mu_log_b_tc -3.00000 -1.0198 1.9802 sigma_log_b_tc -0.01000 -1.0464 -1.0364 mu_log_b_hw -3.00000 -2.8952 0.1048 sigma_log_b_hw -0.01000 -0.8331 -0.8231 mu_log_b_ch -3.00000 0.6675 3.6675 sigma_log_b_ch -0.01000 -0.8122 -0.8022 sigma_hsk 0.00000 -0.5507 -0.5507 Settings and functions used in model definition: apollo_control -------------- Value modelName "ECL_preference_space_heteroskedasticity" modelDescr "Error components logit model on Swiss route choice data, uncorrelated Lognormals in preference space, with heteroskedasticity term" indivID "ID" mixing "TRUE" nCores "4" outputDirectory "output/" debug "FALSE" workInLogs "FALSE" seed "13" 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 mu_log_b_tt 1.9422084 sigma_log_b_tt 0.4401318 mu_log_b_tc 1.0197788 sigma_log_b_tc 1.0464022 mu_log_b_hw 2.8952222 sigma_log_b_hw 0.8331070 mu_log_b_ch 0.6675030 sigma_log_b_ch 0.8121528 sigma_hsk 0.5506862 Scaling used in computing Hessian -------------- Value mu_log_b_tt 1.9422124 sigma_log_b_tt 0.4401319 mu_log_b_tc 1.0197780 sigma_log_b_tc 1.0464022 mu_log_b_hw 2.8952269 sigma_log_b_hw 0.8331068 mu_log_b_ch 0.6675032 sigma_log_b_ch 0.8121527 sigma_hsk 0.5506861 apollo_randCoeff ---------------- function(apollo_beta, apollo_inputs){ randcoeff = list() randcoeff[["b_tt"]] = -exp( mu_log_b_tt + sigma_log_b_tt * draws_tt ) randcoeff[["b_tc"]] = -exp( mu_log_b_tc + sigma_log_b_tc * draws_tc ) randcoeff[["b_hw"]] = -exp( mu_log_b_hw + sigma_log_b_hw * draws_hw ) randcoeff[["b_ch"]] = -exp( mu_log_b_ch + sigma_log_b_ch * draws_ch ) randcoeff[["hsk"]] = sigma_hsk * draws_hsk return(randcoeff) } apollo_probabilities -------------------- function(apollo_beta, apollo_inputs, functionality="estimate"){ ### Function initialisation: do not change the following three commands ### 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[["alt1"]] = b_tt * tt1 + b_tc * tc1 + b_hw * hw1 + b_ch * ch1 + hsk V[["alt2"]] = b_tt * tt2 + b_tc * tc2 + b_hw * hw2 + b_ch * ch2 ### Define settings for MNL model component mnl_settings = list( alternatives = c(alt1=1, alt2=2), avail = list(alt1=1, alt2=1), 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) ### Average across inter-individual draws P = apollo_avgInterDraws(P, apollo_inputs, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }