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 : OP Model description : Ordered probit model fitted to attitudinal question in drug choice data Model run at : 2025-09-19 11:47:08.141573 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -57.772511 reciprocal of condition number : 0.0315431 Number of individuals : 1000 Number of rows in database : 10000 Number of modelled outcomes : 0 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 : 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 : 2922.77 BIC : NA Estimated parameters : 7 Time taken (hh:mm:ss) : 00:00:0.75 pre-estimation : 00:00:0.12 estimation : 00:00:0.27 post-estimation : 00:00:0.36 Iterations : 8 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 OP 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 1.8574e-04 0.002074 0.001958 beta_university -5.385e-05 0.004791 -9.958e-05 0.002083 0.001900 beta_age_50 1.8574e-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 0.6029 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 0.6029 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 0.37101 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 most extreme outliers in terms of lowest average per choice prediction: ID Avg prob per choice 748 0.7145285 541 0.7471321 643 0.7471321 766 0.7471321 78 0.7560035 91 0.7560035 126 0.7560035 127 0.7560035 245 0.7560035 253 0.7560035 392 0.7560035 415 0.7560035 445 0.7560035 448 0.7560035 495 0.7560035 566 0.7560035 666 0.7560035 743 0.7560035 4 0.7649987 388 0.7649987 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "Ordered probit model fitted to attitudinal question in drug choice data" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "OP" 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 second derivative of LL (using numDeriv) Scaling used in computing Hessian --------------------------------- Value beta_reg_user 0.3956792 beta_university 0.2694064 beta_age_50 0.2104909 tau_quality_1 0.9639067 tau_quality_2 0.5047894 tau_quality_3 0.5976952 tau_quality_4 1.1508607 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) }