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 : MNL_iterative_coding Model description : MNL model using iterative coding for alternatives and attributes Model run at : 2025-09-19 11:36:51.939692 Estimation method : bgw Estimation diagnosis : Relative function convergence Optimisation diagnosis : Maximum found hessian properties : Negative definite maximum eigenvalue : -276.899952 reciprocal of condition number : 0.148796 Number of individuals : 2000 Number of rows in database : 2000 Number of modelled outcomes : 2000 Number of cores used : 1 Model without mixing LL(start) : -8488.9 LL at equal shares, LL(0) : -8488.9 LL at observed shares, LL(C) : -8439 LL(final) : -2403.2 Rho-squared vs equal shares : 0.7169 Adj.Rho-squared vs equal shares : 0.7157 Rho-squared vs observed shares : 0.7152 Adj.Rho-squared vs observed shares : 0.7258 AIC : 4826.39 BIC : 4882.4 Estimated parameters : 10 Time taken (hh:mm:ss) : 00:00:13.43 pre-estimation : 00:00:6.51 estimation : 00:00:0.92 post-estimation : 00:00:6 Iterations : 10 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) beta_1 1.0162 0.02974 34.17 0.02881 35.27 beta_2 -1.0203 0.02982 -34.22 0.02981 -34.23 beta_3 1.0394 0.03050 34.08 0.03064 33.93 beta_4 -1.0239 0.02966 -34.52 0.03042 -33.65 beta_5 0.9647 0.02936 32.86 0.02920 33.04 beta_6 -0.9560 0.02905 -32.91 0.03047 -31.38 beta_7 1.0383 0.03031 34.25 0.03011 34.49 beta_8 -0.9792 0.02923 -33.50 0.02963 -33.04 beta_9 1.0029 0.02939 34.12 0.03056 32.82 beta_10 -1.0131 0.02958 -34.25 0.02928 -34.61 Overview of choices for MNL model component : alt_1 alt_2 alt_3 alt_4 alt_5 alt_6 alt_7 Times available 1410.00 1419.00 1439.00 1401.00 1394.00 1382.00 1361.00 Times chosen 25.00 24.00 21.00 16.00 26.00 24.00 18.00 Percentage chosen overall 1.25 1.20 1.05 0.80 1.30 1.20 0.90 Percentage chosen when available 1.77 1.69 1.46 1.14 1.87 1.74 1.32 alt_8 alt_9 alt_10 alt_11 alt_12 alt_13 alt_14 Times available 1351.00 1384.00 1377.00 1437.00 1403.00 1425.00 1381.00 Times chosen 29.00 24.00 20.00 22.00 18.00 18.00 19.00 Percentage chosen overall 1.45 1.20 1.00 1.10 0.90 0.90 0.95 Percentage chosen when available 2.15 1.73 1.45 1.53 1.28 1.26 1.38 alt_15 alt_16 alt_17 alt_18 alt_19 alt_20 alt_21 Times available 1373.00 1411.00 1418.00 1416.00 1405.00 1390.00 1401.00 Times chosen 13.00 26.00 20.00 18.00 20.00 26.00 22.00 Percentage chosen overall 0.65 1.30 1.00 0.90 1.00 1.30 1.10 Percentage chosen when available 0.95 1.84 1.41 1.27 1.42 1.87 1.57 alt_22 alt_23 alt_24 alt_25 alt_26 alt_27 alt_28 Times available 1411.00 1400.00 1412.00 1364.00 1429.00 1405.00 1378.00 Times chosen 18.00 20.00 25.00 17.00 17.00 16.00 21.00 Percentage chosen overall 0.90 1.00 1.25 0.85 0.85 0.80 1.05 Percentage chosen when available 1.28 1.43 1.77 1.25 1.19 1.14 1.52 alt_29 alt_30 alt_31 alt_32 alt_33 alt_34 alt_35 Times available 1381.00 1376.00 1387.00 1381.00 1417.00 1391.00 1382.00 Times chosen 26.00 14.00 16.00 30.00 22.00 22.00 26.00 Percentage chosen overall 1.30 0.70 0.80 1.50 1.10 1.10 1.30 Percentage chosen when available 1.88 1.02 1.15 2.17 1.55 1.58 1.88 alt_36 alt_37 alt_38 alt_39 alt_40 alt_41 alt_42 Times available 1383.00 1374.00 1423.00 1387.00 1373.00 1437.00 1403.00 Times chosen 16.00 18.00 21.00 33.00 18.00 18.00 16.00 Percentage chosen overall 0.80 0.90 1.05 1.65 0.90 0.90 0.80 Percentage chosen when available 1.16 1.31 1.48 2.38 1.31 1.25 1.14 alt_43 alt_44 alt_45 alt_46 alt_47 alt_48 alt_49 Times available 1401.00 1387.00 1385.00 1395.00 1401.00 1398.00 1385.00 Times chosen 23.00 17.00 16.00 13.00 19.00 22.00 15.00 Percentage chosen overall 1.15 0.85 0.80 0.65 0.95 1.10 0.75 Percentage chosen when available 1.64 1.23 1.16 0.93 1.36 1.57 1.08 alt_50 alt_51 alt_52 alt_53 alt_54 alt_55 alt_56 Times available 1422.00 1366.00 1379.00 1362.00 1392.00 1411.00 1389.00 Times chosen 25.00 16.00 18.00 26.00 17.00 16.00 13.00 Percentage chosen overall 1.25 0.80 0.90 1.30 0.85 0.80 0.65 Percentage chosen when available 1.76 1.17 1.31 1.91 1.22 1.13 0.94 alt_57 alt_58 alt_59 alt_60 alt_61 alt_62 alt_63 alt_64 Times available 1365.00 1418.00 1352.00 1377.00 1418.00 1397.00 1414.0 1416.00 Times chosen 19.00 16.00 11.00 15.00 15.00 20.00 24.0 17.00 Percentage chosen overall 0.95 0.80 0.55 0.75 0.75 1.00 1.2 0.85 Percentage chosen when available 1.39 1.13 0.81 1.09 1.06 1.43 1.7 1.20 alt_65 alt_66 alt_67 alt_68 alt_69 alt_70 alt_71 alt_72 Times available 1414.0 1417.00 1369.00 1400.00 1387.00 1397.00 1403.00 1401.00 Times chosen 24.0 23.00 20.00 15.00 22.00 20.00 24.00 22.00 Percentage chosen overall 1.2 1.15 1.00 0.75 1.10 1.00 1.20 1.10 Percentage chosen when available 1.7 1.62 1.46 1.07 1.59 1.43 1.71 1.57 alt_73 alt_74 alt_75 alt_76 alt_77 alt_78 alt_79 Times available 1404.00 1420.00 1413.00 1394.00 1397.00 1377.00 1417.00 Times chosen 21.00 28.00 19.00 19.00 26.00 26.00 21.00 Percentage chosen overall 1.05 1.40 0.95 0.95 1.30 1.30 1.05 Percentage chosen when available 1.50 1.97 1.34 1.36 1.86 1.89 1.48 alt_80 alt_81 alt_82 alt_83 alt_84 alt_85 alt_86 alt_87 Times available 1388.00 1412.00 1416.00 1385.00 1395.0 1390.00 1451.00 1400.00 Times chosen 19.00 23.00 22.00 22.00 14.0 22.00 20.00 26.00 Percentage chosen overall 0.95 1.15 1.10 1.10 0.7 1.10 1.00 1.30 Percentage chosen when available 1.37 1.63 1.55 1.59 1.0 1.58 1.38 1.86 alt_88 alt_89 alt_90 alt_91 alt_92 alt_93 alt_94 Times available 1450.00 1380.00 1405.00 1384.00 1437.00 1369.00 1383.00 Times chosen 13.00 24.00 28.00 17.00 25.00 12.00 13.00 Percentage chosen overall 0.65 1.20 1.40 0.85 1.25 0.60 0.65 Percentage chosen when available 0.90 1.74 1.99 1.23 1.74 0.88 0.94 alt_95 alt_96 alt_97 alt_98 alt_99 alt_100 Times available 1381.00 1407.00 1419.00 1398.00 1398.0 1387.00 Times chosen 15.00 19.00 13.00 18.00 14.0 19.00 Percentage chosen overall 0.75 0.95 0.65 0.90 0.7 0.95 Percentage chosen when available 1.09 1.35 0.92 1.29 1.0 1.37 Classical covariance matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_1 8.8433e-04 -2.8835e-04 3.1359e-04 -2.9576e-04 2.8865e-04 -2.8625e-04 3.1352e-04 beta_2 -2.8835e-04 8.8902e-04 -3.0613e-04 3.0992e-04 -3.1409e-04 2.9761e-04 -3.1972e-04 beta_3 3.1359e-04 -3.0613e-04 9.3035e-04 -3.1459e-04 3.0407e-04 -3.0666e-04 3.3768e-04 beta_4 -2.9576e-04 3.0992e-04 -3.1459e-04 8.7965e-04 -2.8738e-04 2.8512e-04 -3.1795e-04 beta_5 2.8865e-04 -3.1409e-04 3.0407e-04 -2.8738e-04 8.6174e-04 -2.8375e-04 3.2582e-04 beta_6 -2.8625e-04 2.9761e-04 -3.0666e-04 2.8512e-04 -2.8375e-04 8.4363e-04 -3.0577e-04 beta_7 3.1352e-04 -3.1972e-04 3.3768e-04 -3.1795e-04 3.2582e-04 -3.0577e-04 9.1885e-04 beta_8 -3.0643e-04 3.0508e-04 -3.0980e-04 2.7908e-04 -2.9926e-04 2.7714e-04 -3.1238e-04 beta_9 3.0348e-04 -2.8497e-04 3.1187e-04 -3.0328e-04 2.9825e-04 -2.9657e-04 3.3187e-04 beta_10 -3.0450e-04 3.0338e-04 -3.1564e-04 2.9546e-04 -3.0063e-04 2.9895e-04 -3.1014e-04 beta_8 beta_9 beta_10 beta_1 -3.0643e-04 3.0348e-04 -3.0450e-04 beta_2 3.0508e-04 -2.8497e-04 3.0338e-04 beta_3 -3.0980e-04 3.1187e-04 -3.1564e-04 beta_4 2.7908e-04 -3.0328e-04 2.9546e-04 beta_5 -2.9926e-04 2.9825e-04 -3.0063e-04 beta_6 2.7714e-04 -2.9657e-04 2.9895e-04 beta_7 -3.1238e-04 3.3187e-04 -3.1014e-04 beta_8 8.5432e-04 -2.8951e-04 3.0435e-04 beta_9 -2.8951e-04 8.6378e-04 -2.9893e-04 beta_10 3.0435e-04 -2.9893e-04 8.7520e-04 Robust covariance matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_1 8.3019e-04 -2.4506e-04 3.2169e-04 -2.7958e-04 2.6594e-04 -2.8820e-04 2.8288e-04 beta_2 -2.4506e-04 8.8846e-04 -3.4646e-04 3.3935e-04 -3.0585e-04 2.9755e-04 -3.2382e-04 beta_3 3.2169e-04 -3.4646e-04 9.3868e-04 -3.4628e-04 2.9813e-04 -3.3738e-04 3.6538e-04 beta_4 -2.7958e-04 3.3935e-04 -3.4628e-04 9.2564e-04 -3.1803e-04 3.6692e-04 -3.7092e-04 beta_5 2.6594e-04 -3.0585e-04 2.9813e-04 -3.1803e-04 8.5236e-04 -3.0837e-04 3.3898e-04 beta_6 -2.8820e-04 2.9755e-04 -3.3738e-04 3.6692e-04 -3.0837e-04 9.2814e-04 -3.3549e-04 beta_7 2.8288e-04 -3.2382e-04 3.6538e-04 -3.7092e-04 3.3898e-04 -3.3549e-04 9.0650e-04 beta_8 -3.0906e-04 3.0526e-04 -3.5136e-04 3.0223e-04 -3.3752e-04 3.4322e-04 -3.3731e-04 beta_9 3.0924e-04 -3.1073e-04 3.3893e-04 -3.6680e-04 3.2665e-04 -3.6669e-04 3.6902e-04 beta_10 -2.5907e-04 3.0564e-04 -3.1378e-04 3.1290e-04 -2.6052e-04 3.0443e-04 -3.0691e-04 beta_8 beta_9 beta_10 beta_1 -3.0906e-04 3.0924e-04 -2.5907e-04 beta_2 3.0526e-04 -3.1073e-04 3.0564e-04 beta_3 -3.5136e-04 3.3893e-04 -3.1378e-04 beta_4 3.0223e-04 -3.6680e-04 3.1290e-04 beta_5 -3.3752e-04 3.2665e-04 -2.6052e-04 beta_6 3.4322e-04 -3.6669e-04 3.0443e-04 beta_7 -3.3731e-04 3.6902e-04 -3.0691e-04 beta_8 8.7822e-04 -3.1625e-04 3.1488e-04 beta_9 -3.1625e-04 9.3387e-04 -3.4027e-04 beta_10 3.1488e-04 -3.4027e-04 8.5705e-04 Classical correlation matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_1 1.0000 -0.3252 0.3457 -0.3353 0.3307 -0.3314 0.3478 beta_2 -0.3252 1.0000 -0.3366 0.3505 -0.3588 0.3436 -0.3537 beta_3 0.3457 -0.3366 1.0000 -0.3478 0.3396 -0.3461 0.3652 beta_4 -0.3353 0.3505 -0.3478 1.0000 -0.3301 0.3310 -0.3537 beta_5 0.3307 -0.3588 0.3396 -0.3301 1.0000 -0.3328 0.3662 beta_6 -0.3314 0.3436 -0.3461 0.3310 -0.3328 1.0000 -0.3473 beta_7 0.3478 -0.3537 0.3652 -0.3537 0.3662 -0.3473 1.0000 beta_8 -0.3526 0.3501 -0.3475 0.3219 -0.3488 0.3265 -0.3526 beta_9 0.3472 -0.3252 0.3479 -0.3479 0.3457 -0.3474 0.3725 beta_10 -0.3461 0.3439 -0.3498 0.3367 -0.3462 0.3479 -0.3459 beta_8 beta_9 beta_10 beta_1 -0.3526 0.3472 -0.3461 beta_2 0.3501 -0.3252 0.3439 beta_3 -0.3475 0.3479 -0.3498 beta_4 0.3219 -0.3479 0.3367 beta_5 -0.3488 0.3457 -0.3462 beta_6 0.3265 -0.3474 0.3479 beta_7 -0.3526 0.3725 -0.3459 beta_8 1.0000 -0.3370 0.3520 beta_9 -0.3370 1.0000 -0.3438 beta_10 0.3520 -0.3438 1.0000 Robust correlation matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_1 1.0000 -0.2853 0.3644 -0.3189 0.3161 -0.3283 0.3261 beta_2 -0.2853 1.0000 -0.3794 0.3742 -0.3515 0.3277 -0.3608 beta_3 0.3644 -0.3794 1.0000 -0.3715 0.3333 -0.3615 0.3961 beta_4 -0.3189 0.3742 -0.3715 1.0000 -0.3580 0.3959 -0.4049 beta_5 0.3161 -0.3515 0.3333 -0.3580 1.0000 -0.3467 0.3856 beta_6 -0.3283 0.3277 -0.3615 0.3959 -0.3467 1.0000 -0.3657 beta_7 0.3261 -0.3608 0.3961 -0.4049 0.3856 -0.3657 1.0000 beta_8 -0.3620 0.3456 -0.3870 0.3352 -0.3901 0.3802 -0.3780 beta_9 0.3512 -0.3411 0.3620 -0.3945 0.3661 -0.3939 0.4011 beta_10 -0.3071 0.3503 -0.3498 0.3513 -0.3048 0.3413 -0.3482 beta_8 beta_9 beta_10 beta_1 -0.3620 0.3512 -0.3071 beta_2 0.3456 -0.3411 0.3503 beta_3 -0.3870 0.3620 -0.3498 beta_4 0.3352 -0.3945 0.3513 beta_5 -0.3901 0.3661 -0.3048 beta_6 0.3802 -0.3939 0.3413 beta_7 -0.3780 0.4011 -0.3482 beta_8 1.0000 -0.3492 0.3629 beta_9 -0.3492 1.0000 -0.3803 beta_10 0.3629 -0.3803 1.0000 20 most extreme outliers in terms of lowest average per choice prediction: row Avg prob per choice 1034 2.077161e-05 1834 9.748525e-05 521 1.177273e-04 1611 2.760074e-04 493 4.552534e-04 379 4.919452e-04 951 8.381349e-04 1454 8.504092e-04 532 8.885780e-04 1033 9.621975e-04 447 1.108100e-03 1616 1.115511e-03 718 1.150762e-03 1849 1.209029e-03 1626 1.395271e-03 953 1.586373e-03 1925 2.006173e-03 1718 2.310324e-03 916 2.562021e-03 1272 2.982736e-03 Settings and functions used in model definition: apollo_control -------------- Value modelDescr "MNL model using iterative coding for alternatives and attributes" indivID "ID" outputDirectory "output/" debug "FALSE" modelName "MNL_iterative_coding" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" analyticHessian "FALSE" memorySaver "FALSE" panelData "FALSE" 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_1 1.0161769 beta_2 1.0203012 beta_3 1.0394071 beta_4 1.0238681 beta_5 0.9647193 beta_6 0.9559842 beta_7 1.0383468 beta_8 0.9792131 beta_9 1.0029348 beta_10 1.0130971 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 mnl_settings, order is irrelevant V = list() for(j in 1:apollo_inputs$J){ V[[paste0("alt_",j)]] = 0 for(k in 1:apollo_inputs$K) V[[paste0("alt_",j)]] = V[[paste0("alt_",j)]] + get(paste0("beta_",k))*get(paste0("x_",j,"_",k)) } ### Define settings for MNL model component mnl_settings = list( alternatives = setNames(1:apollo_inputs$J, names(V)), avail = setNames(apollo_inputs$database[,paste0("avail_",1:apollo_inputs$J)], names(V)), choiceVar = choice, utilities = V ) ### Compute probabilities using MNL model P[["model"]] = apollo_mnl(mnl_settings, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }