Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : OP Model description : Ordered probit model fitted to attitudinal question in drug choice data Model run at : 2023-05-10 22:03:42 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -57.772519 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) : -1927.14 LL at equal shares, LL(0) : -1609.44 LL at observed shares, LL(C) : -1482.03 LL(final) : -1454.38 Rho-squared vs equal shares : 0.0963 Adj.Rho-squared vs equal shares : 0.092 Rho-squared vs observed shares : 0.0187 Adj.Rho-squared vs observed shares : 0.0166 AIC : 2922.77 BIC : 2957.12 Estimated parameters : 7 Time taken (hh:mm:ss) : 00:00:2.3 pre-estimation : 00:00:0.46 estimation : 00:00:1.02 initial estimation : 00:00:0.87 estimation after rescaling : 00:00:0.15 post-estimation : 00:00:0.82 Iterations : 19 initial estimation : 16 estimation after rescaling : 3 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) beta_reg_user -0.3957 0.07122 -5.556 0.07129 -5.550 beta_university -0.2694 0.06916 -3.895 0.06922 -3.892 beta_age_50 0.2105 0.06909 3.046 0.06915 3.044 tau_quality_1 -0.9639 0.06677 -14.437 0.06653 -14.489 tau_quality_2 -0.5048 0.06333 -7.971 0.06188 -8.158 tau_quality_3 0.5977 0.06361 9.396 0.06230 9.594 tau_quality_4 1.1509 0.07082 16.252 0.06970 16.511 Overview of choices for 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 beta_reg_user 0.005072 2.7792e-04 2.2222e-04 0.002180 0.002074 beta_university 2.7792e-04 0.004784 6.856e-05 0.002161 0.002073 beta_age_50 2.2222e-04 6.856e-05 0.004774 0.001859 0.001917 tau_quality_1 0.002180 0.002161 0.001859 0.004458 0.003636 tau_quality_2 0.002074 0.002073 0.001917 0.003636 0.004011 tau_quality_3 0.001773 0.001861 0.002062 0.002778 0.002923 tau_quality_4 0.001677 0.001817 0.002118 0.002603 0.002704 tau_quality_3 tau_quality_4 beta_reg_user 0.001773 0.001677 beta_university 0.001861 0.001817 beta_age_50 0.002062 0.002118 tau_quality_1 0.002778 0.002603 tau_quality_2 0.002923 0.002704 tau_quality_3 0.004047 0.003520 tau_quality_4 0.003520 0.005015 Robust covariance matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 beta_reg_user 0.005082 -5.385e-05 1.8573e-04 0.002074 0.001958 beta_university -5.385e-05 0.004791 -9.958e-05 0.002083 0.001900 beta_age_50 1.8573e-04 -9.958e-05 0.004782 0.001754 0.001803 tau_quality_1 0.002074 0.002083 0.001754 0.004426 0.003525 tau_quality_2 0.001958 0.001900 0.001803 0.003525 0.003829 tau_quality_3 0.001633 0.001600 0.002035 0.002647 0.002743 tau_quality_4 0.001378 0.001567 0.002132 0.002433 0.002494 tau_quality_3 tau_quality_4 beta_reg_user 0.001633 0.001378 beta_university 0.001600 0.001567 beta_age_50 0.002035 0.002132 tau_quality_1 0.002647 0.002433 tau_quality_2 0.002743 0.002494 tau_quality_3 0.003881 0.003347 tau_quality_4 0.003347 0.004859 Classical correlation matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 beta_reg_user 1.00000 0.05642 0.04516 0.4586 0.4599 beta_university 0.05642 1.00000 0.01435 0.4680 0.4734 beta_age_50 0.04516 0.01435 1.00000 0.4029 0.4380 tau_quality_1 0.45856 0.46802 0.40293 1.0000 0.8599 tau_quality_2 0.45989 0.47335 0.43800 0.8599 1.0000 tau_quality_3 0.39146 0.42299 0.46921 0.6540 0.7255 tau_quality_4 0.33258 0.37100 0.43283 0.5505 0.6028 tau_quality_3 tau_quality_4 beta_reg_user 0.3915 0.3326 beta_university 0.4230 0.3710 beta_age_50 0.4692 0.4328 tau_quality_1 0.6540 0.5505 tau_quality_2 0.7255 0.6028 tau_quality_3 1.0000 0.7815 tau_quality_4 0.7815 1.0000 Robust correlation matrix: beta_reg_user beta_university beta_age_50 tau_quality_1 tau_quality_2 beta_reg_user 1.00000 -0.01091 0.03768 0.4374 0.4438 beta_university -0.01091 1.00000 -0.02080 0.4524 0.4436 beta_age_50 0.03768 -0.02080 1.00000 0.3813 0.4214 tau_quality_1 0.43739 0.45244 0.38125 1.0000 0.8562 tau_quality_2 0.44377 0.44355 0.42137 0.8562 1.0000 tau_quality_3 0.36759 0.37102 0.47248 0.6387 0.7116 tau_quality_4 0.27730 0.32469 0.44235 0.5247 0.5782 tau_quality_3 tau_quality_4 beta_reg_user 0.3676 0.2773 beta_university 0.3710 0.3247 beta_age_50 0.4725 0.4424 tau_quality_1 0.6387 0.5247 tau_quality_2 0.7116 0.5782 tau_quality_3 1.0000 0.7708 tau_quality_4 0.7708 1.0000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 748 0.7145285 541 0.7471323 643 0.7471323 766 0.7471323 78 0.7560033 91 0.7560033 126 0.7560033 127 0.7560033 245 0.7560033 253 0.7560033 392 0.7560033 415 0.7560033 445 0.7560033 448 0.7560033 495 0.7560033 566 0.7560033 666 0.7560033 743 0.7560033 4 0.7649990 388 0.7649990 Changes in parameter estimates from starting values: Initial Estimate Difference beta_reg_user 0.000 -0.3957 -0.3957 beta_university 0.000 -0.2694 -0.2694 beta_age_50 0.000 0.2105 0.2105 tau_quality_1 -2.000 -0.9639 1.0361 tau_quality_2 -1.000 -0.5048 0.4952 tau_quality_3 1.000 0.5977 -0.4023 tau_quality_4 2.000 1.1509 -0.8491 Settings and functions used in model definition: apollo_control -------------- Value modelName "OP" modelDescr "Ordered probit model fitted to attitudinal question in drug choice data" indivID "ID" 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 second derivative of LL (using numDeriv) Scaling in estimation --------------------- Value beta_reg_user 0.3956805 beta_university 0.2694050 beta_age_50 0.2104927 tau_quality_1 0.9639049 tau_quality_2 0.5047912 tau_quality_3 0.5976940 tau_quality_4 1.1508553 Scaling used in computing Hessian --------------------------------- Value beta_reg_user 0.3956806 beta_university 0.2694051 beta_age_50 0.2104926 tau_quality_1 0.9639089 tau_quality_2 0.5047898 tau_quality_3 0.5976933 tau_quality_4 1.1508606 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 Probit model op_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_op(op_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) }