Model run by stephane.hess using Apollo 0.3.5 on R 4.4.0 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 : OL Model description : Ordered logit model fitted to attitudinal question in drug choice data Model run at : 2025-03-10 17:14:35.989956 Estimation method : bgw Model diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -19.866519 reciprocal of condition number : 0.0303475 Number of individuals : 1000 Number of rows in database : 10000 Number of modelled outcomes : 1000 Number of cores used : 1 Model without mixing LL(start) : -1523.56 LL at equal shares, LL(0) : -1609.44 LL at observed shares, LL(C) : -1482.03 LL(final) : -1452.86 Rho-squared vs equal shares : 0.0973 Adj.Rho-squared vs equal shares : 0.0929 Rho-squared vs observed shares : 0.0197 Adj.Rho-squared vs observed shares : 0.0177 AIC : 2919.72 BIC : 2954.08 Estimated parameters : 7 Time taken (hh:mm:ss) : 00:00:0.29 pre-estimation : 00:00:0.08 estimation : 00:00:0.05 post-estimation : 00:00:0.16 Iterations : 6 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) beta_reg_user -0.6812 0.1215 -5.606 0.1203 -5.662 beta_university -0.4776 0.1182 -4.042 0.1185 -4.032 beta_age_50 0.3731 0.1183 3.153 0.1185 3.149 tau_quality_1 -1.6098 0.1158 -13.905 0.1146 -14.043 tau_quality_2 -0.8387 0.1063 -7.889 0.1030 -8.145 tau_quality_3 0.9730 0.1074 9.061 0.1046 9.301 tau_quality_4 1.9779 0.1296 15.258 0.1274 15.528 Overview of choices for OL model component : 1 2 3 4 5 Times chosen 220 151.0 398.0 130 101.0 Percentage chosen overall 22 15.1 39.8 13 10.1 Classical covariance matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 tau_quality_3 tau_quality_4 beta_reg_user 0.014763 6.1563e-04 5.3550e-04 0.006627 0.006143 0.004797 0.004464 beta_university 6.1563e-04 0.013962 6.370e-06 0.006451 0.006051 0.005052 0.004865 beta_age_50 5.3550e-04 6.370e-06 0.014004 0.005096 0.005362 0.006108 0.006349 tau_quality_1 0.006627 0.006451 0.005096 0.013402 0.010608 0.007945 0.007553 tau_quality_2 0.006143 0.006051 0.005362 0.010608 0.011301 0.008203 0.007763 tau_quality_3 0.004797 0.005052 0.006108 0.007945 0.008203 0.011531 0.010543 tau_quality_4 0.004464 0.004865 0.006349 0.007553 0.007763 0.010543 0.016805 Robust covariance matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 tau_quality_3 tau_quality_4 beta_reg_user 0.014473 -3.9163e-04 3.6878e-04 0.006147 0.005703 0.004416 0.003710 beta_university -3.9163e-04 0.014035 -7.2730e-04 0.006158 0.005444 0.004136 0.004011 beta_age_50 3.6878e-04 -7.2730e-04 0.014044 0.004597 0.004821 0.005877 0.006201 tau_quality_1 0.006147 0.006158 0.004597 0.013141 0.010110 0.007409 0.006916 tau_quality_2 0.005703 0.005444 0.004821 0.010110 0.010603 0.007531 0.007011 tau_quality_3 0.004416 0.004136 0.005877 0.007409 0.007531 0.010944 0.009932 tau_quality_4 0.003710 0.004011 0.006201 0.006916 0.007011 0.009932 0.016225 Classical correlation matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 tau_quality_3 tau_quality_4 beta_reg_user 1.00000 0.04288 0.03724 0.4711 0.4756 0.3677 0.2834 beta_university 0.04288 1.00000 4.5558e-04 0.4716 0.4817 0.3982 0.3176 beta_age_50 0.03724 4.5558e-04 1.00000 0.3720 0.4263 0.4806 0.4139 tau_quality_1 0.47114 0.47161 0.37199 1.0000 0.8619 0.6391 0.5033 tau_quality_2 0.47561 0.48169 0.42626 0.8619 1.0000 0.7186 0.5633 tau_quality_3 0.36767 0.39819 0.48063 0.6391 0.7186 1.0000 0.7574 tau_quality_4 0.28338 0.31760 0.41387 0.5033 0.5633 0.7574 1.0000 Robust correlation matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 tau_quality_3 tau_quality_4 beta_reg_user 1.00000 -0.02748 0.02587 0.4457 0.4603 0.3509 0.2421 beta_university -0.02748 1.00000 -0.05180 0.4534 0.4462 0.3337 0.2658 beta_age_50 0.02587 -0.05180 1.00000 0.3384 0.3951 0.4741 0.4108 tau_quality_1 0.44572 0.45345 0.33843 1.0000 0.8565 0.6178 0.4736 tau_quality_2 0.46034 0.44624 0.39508 0.8565 1.0000 0.6992 0.5345 tau_quality_3 0.35091 0.33373 0.47410 0.6178 0.6992 1.0000 0.7453 tau_quality_4 0.24208 0.26581 0.41083 0.4736 0.5345 0.7453 1.0000 20 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 748 0.7276567 541 0.7539147 643 0.7539147 766 0.7539147 4 0.7601612 388 0.7601612 534 0.7601612 669 0.7601612 738 0.7601612 923 0.7601612 78 0.7613381 91 0.7613381 126 0.7613381 127 0.7613381 245 0.7613381 253 0.7613381 392 0.7613381 415 0.7613381 445 0.7613381 448 0.7613381 Changes in parameter estimates from starting values: Initial Estimate Difference beta_reg_user 0.000 -0.6812 -0.68116 beta_university 0.000 -0.4776 -0.47764 beta_age_50 0.000 0.3731 0.37315 tau_quality_1 -2.000 -1.6098 0.39022 tau_quality_2 -1.000 -0.8387 0.16131 tau_quality_3 1.000 0.9730 -0.02698 tau_quality_4 2.000 1.9779 -0.02205 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Ordered logit model fitted to attitudinal question in drug choice data" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "OL" 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 beta_reg_user 0.6811622 beta_university 0.4776440 beta_age_50 0.3731474 tau_quality_1 1.6097783 tau_quality_2 0.8386896 tau_quality_3 0.9730189 tau_quality_4 1.9779462 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() ### Calculate probabilities using Ordered Logit model ol_settings = list(outcomeOrdered = attitude_quality, utility = beta_reg_user*regular_user + beta_university*university_educated + beta_age_50*over_50, tau = list(tau_quality_1, tau_quality_2, tau_quality_3, tau_quality_4), rows = (task==1)) P[["model"]] = apollo_ol(ol_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) }