Model run by stephane.hess using Apollo 0.2.9 on R 4.0.5 for Darwin. www.ApolloChoiceModelling.com Model name : MNL_iterative_coding Model description : MNL model using iterative coding for alternatives and attributes Model run at : 2023-05-10 19:50:34 Estimation method : bfgs Model diagnosis : successful convergence Optimisation diagnosis : Maximum found hessian properties : Negative definitive maximum eigenvalue : -276.859111 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) : 00:00:46.96 pre-estimation : 00:00:21.31 estimation : 00:00:6.67 initial estimation : 00:00:5.65 estimation after rescaling : 00:00:1.02 post-estimation : 00:00:18.98 Iterations : 32 initial estimation : 29 estimation after rescaling : 3 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) beta_1 1.0162 0.02974 34.17 0.02882 35.26 beta_2 -1.0204 0.02982 -34.22 0.02982 -34.22 beta_3 1.0395 0.03050 34.08 0.03065 33.92 beta_4 -1.0239 0.02966 -34.52 0.03043 -33.64 beta_5 0.9648 0.02936 32.86 0.02920 33.03 beta_6 -0.9560 0.02905 -32.91 0.03048 -31.37 beta_7 1.0384 0.03031 34.25 0.03012 34.48 beta_8 -0.9793 0.02923 -33.50 0.02964 -33.03 beta_9 1.0030 0.02939 34.13 0.03057 32.81 beta_10 -1.0131 0.02958 -34.25 0.02929 -34.60 Overview of choices for MNL model component : alt_1 alt_2 alt_3 alt_4 alt_5 alt_6 alt_7 alt_8 alt_9 alt_10 Times available 1410.00 1419.00 1439.00 1401.00 1394.00 1382.00 1361.00 1351.00 1384.00 1377.00 Times chosen 25.00 24.00 21.00 16.00 26.00 24.00 18.00 29.00 24.00 20.00 Percentage chosen overall 1.25 1.20 1.05 0.80 1.30 1.20 0.90 1.45 1.20 1.00 Percentage chosen when available 1.77 1.69 1.46 1.14 1.87 1.74 1.32 2.15 1.73 1.45 alt_11 alt_12 alt_13 alt_14 alt_15 alt_16 alt_17 alt_18 alt_19 alt_20 Times available 1437.00 1403.00 1425.00 1381.00 1373.00 1411.00 1418.00 1416.00 1405.00 1390.00 Times chosen 22.00 18.00 18.00 19.00 13.00 26.00 20.00 18.00 20.00 26.00 Percentage chosen overall 1.10 0.90 0.90 0.95 0.65 1.30 1.00 0.90 1.00 1.30 Percentage chosen when available 1.53 1.28 1.26 1.38 0.95 1.84 1.41 1.27 1.42 1.87 alt_21 alt_22 alt_23 alt_24 alt_25 alt_26 alt_27 alt_28 alt_29 alt_30 Times available 1401.00 1411.00 1400.00 1412.00 1364.00 1429.00 1405.00 1378.00 1381.00 1376.00 Times chosen 22.00 18.00 20.00 25.00 17.00 17.00 16.00 21.00 26.00 14.00 Percentage chosen overall 1.10 0.90 1.00 1.25 0.85 0.85 0.80 1.05 1.30 0.70 Percentage chosen when available 1.57 1.28 1.43 1.77 1.25 1.19 1.14 1.52 1.88 1.02 alt_31 alt_32 alt_33 alt_34 alt_35 alt_36 alt_37 alt_38 alt_39 alt_40 Times available 1387.00 1381.00 1417.00 1391.00 1382.00 1383.00 1374.00 1423.00 1387.00 1373.00 Times chosen 16.00 30.00 22.00 22.00 26.00 16.00 18.00 21.00 33.00 18.00 Percentage chosen overall 0.80 1.50 1.10 1.10 1.30 0.80 0.90 1.05 1.65 0.90 Percentage chosen when available 1.15 2.17 1.55 1.58 1.88 1.16 1.31 1.48 2.38 1.31 alt_41 alt_42 alt_43 alt_44 alt_45 alt_46 alt_47 alt_48 alt_49 alt_50 Times available 1437.00 1403.00 1401.00 1387.00 1385.00 1395.00 1401.00 1398.00 1385.00 1422.00 Times chosen 18.00 16.00 23.00 17.00 16.00 13.00 19.00 22.00 15.00 25.00 Percentage chosen overall 0.90 0.80 1.15 0.85 0.80 0.65 0.95 1.10 0.75 1.25 Percentage chosen when available 1.25 1.14 1.64 1.23 1.16 0.93 1.36 1.57 1.08 1.76 alt_51 alt_52 alt_53 alt_54 alt_55 alt_56 alt_57 alt_58 alt_59 alt_60 Times available 1366.00 1379.00 1362.00 1392.00 1411.00 1389.00 1365.00 1418.00 1352.00 1377.00 Times chosen 16.00 18.00 26.00 17.00 16.00 13.00 19.00 16.00 11.00 15.00 Percentage chosen overall 0.80 0.90 1.30 0.85 0.80 0.65 0.95 0.80 0.55 0.75 Percentage chosen when available 1.17 1.31 1.91 1.22 1.13 0.94 1.39 1.13 0.81 1.09 alt_61 alt_62 alt_63 alt_64 alt_65 alt_66 alt_67 alt_68 alt_69 alt_70 Times available 1418.00 1397.00 1414.0 1416.00 1414.0 1417.00 1369.00 1400.00 1387.00 1397.00 Times chosen 15.00 20.00 24.0 17.00 24.0 23.00 20.00 15.00 22.00 20.00 Percentage chosen overall 0.75 1.00 1.2 0.85 1.2 1.15 1.00 0.75 1.10 1.00 Percentage chosen when available 1.06 1.43 1.7 1.20 1.7 1.62 1.46 1.07 1.59 1.43 alt_71 alt_72 alt_73 alt_74 alt_75 alt_76 alt_77 alt_78 alt_79 alt_80 Times available 1403.00 1401.00 1404.00 1420.00 1413.00 1394.00 1397.00 1377.00 1417.00 1388.00 Times chosen 24.00 22.00 21.00 28.00 19.00 19.00 26.00 26.00 21.00 19.00 Percentage chosen overall 1.20 1.10 1.05 1.40 0.95 0.95 1.30 1.30 1.05 0.95 Percentage chosen when available 1.71 1.57 1.50 1.97 1.34 1.36 1.86 1.89 1.48 1.37 alt_81 alt_82 alt_83 alt_84 alt_85 alt_86 alt_87 alt_88 alt_89 alt_90 Times available 1412.00 1416.00 1385.00 1395.0 1390.00 1451.00 1400.00 1450.00 1380.00 1405.00 Times chosen 23.00 22.00 22.00 14.0 22.00 20.00 26.00 13.00 24.00 28.00 Percentage chosen overall 1.15 1.10 1.10 0.7 1.10 1.00 1.30 0.65 1.20 1.40 Percentage chosen when available 1.63 1.55 1.59 1.0 1.58 1.38 1.86 0.90 1.74 1.99 alt_91 alt_92 alt_93 alt_94 alt_95 alt_96 alt_97 alt_98 alt_99 alt_100 Times available 1384.00 1437.00 1369.00 1383.00 1381.00 1407.00 1419.00 1398.00 1398.0 1387.00 Times chosen 17.00 25.00 12.00 13.00 15.00 19.00 13.00 18.00 14.0 19.00 Percentage chosen overall 0.85 1.25 0.60 0.65 0.75 0.95 0.65 0.90 0.7 0.95 Percentage chosen when available 1.23 1.74 0.88 0.94 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_8 beta_9 beta_1 8.8440e-04 -2.8840e-04 3.1364e-04 -2.9580e-04 2.8869e-04 -2.8630e-04 3.1357e-04 -3.0648e-04 3.0354e-04 beta_2 -2.8840e-04 8.8912e-04 -3.0620e-04 3.0996e-04 -3.1414e-04 2.9766e-04 -3.1978e-04 3.0514e-04 -2.8504e-04 beta_3 3.1364e-04 -3.0620e-04 9.3045e-04 -3.1464e-04 3.0412e-04 -3.0672e-04 3.3774e-04 -3.0985e-04 3.1194e-04 beta_4 -2.9580e-04 3.0996e-04 -3.1464e-04 8.7968e-04 -2.8742e-04 2.8515e-04 -3.1799e-04 2.7912e-04 -3.0333e-04 beta_5 2.8869e-04 -3.1414e-04 3.0412e-04 -2.8742e-04 8.6180e-04 -2.8379e-04 3.2586e-04 -2.9931e-04 2.9831e-04 beta_6 -2.8630e-04 2.9766e-04 -3.0672e-04 2.8515e-04 -2.8379e-04 8.4370e-04 -3.0582e-04 2.7719e-04 -2.9663e-04 beta_7 3.1357e-04 -3.1978e-04 3.3774e-04 -3.1799e-04 3.2586e-04 -3.0582e-04 9.1892e-04 -3.1242e-04 3.3193e-04 beta_8 -3.0648e-04 3.0514e-04 -3.0985e-04 2.7912e-04 -2.9931e-04 2.7719e-04 -3.1242e-04 8.5439e-04 -2.8957e-04 beta_9 3.0354e-04 -2.8504e-04 3.1194e-04 -3.0333e-04 2.9831e-04 -2.9663e-04 3.3193e-04 -2.8957e-04 8.6388e-04 beta_10 -3.0455e-04 3.0343e-04 -3.1570e-04 2.9550e-04 -3.0068e-04 2.9900e-04 -3.1019e-04 3.0439e-04 -2.9898e-04 beta_10 beta_1 -3.0455e-04 beta_2 3.0343e-04 beta_3 -3.1570e-04 beta_4 2.9550e-04 beta_5 -3.0068e-04 beta_6 2.9900e-04 beta_7 -3.1019e-04 beta_8 3.0439e-04 beta_9 -2.9898e-04 beta_10 8.7526e-04 Robust covariance matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_8 beta_9 beta_1 8.3074e-04 -2.4529e-04 3.2196e-04 -2.7979e-04 2.6616e-04 -2.8844e-04 2.8312e-04 -3.0932e-04 3.0952e-04 beta_2 -2.4529e-04 8.8911e-04 -3.4677e-04 3.3962e-04 -3.0611e-04 2.9781e-04 -3.2410e-04 3.0553e-04 -3.1103e-04 beta_3 3.2196e-04 -3.4677e-04 9.3935e-04 -3.4655e-04 2.9839e-04 -3.3767e-04 3.6569e-04 -3.5166e-04 3.3924e-04 beta_4 -2.7979e-04 3.3962e-04 -3.4655e-04 9.2618e-04 -3.1826e-04 3.6718e-04 -3.7119e-04 3.0246e-04 -3.6710e-04 beta_5 2.6616e-04 -3.0611e-04 2.9839e-04 -3.1826e-04 8.5291e-04 -3.0862e-04 3.3924e-04 -3.3778e-04 3.2693e-04 beta_6 -2.8844e-04 2.9781e-04 -3.3767e-04 3.6718e-04 -3.0862e-04 9.2876e-04 -3.3576e-04 3.4350e-04 -3.6700e-04 beta_7 2.8312e-04 -3.2410e-04 3.6569e-04 -3.7119e-04 3.3924e-04 -3.3576e-04 9.0710e-04 -3.3758e-04 3.6934e-04 beta_8 -3.0932e-04 3.0553e-04 -3.5166e-04 3.0246e-04 -3.3778e-04 3.4350e-04 -3.3758e-04 8.7881e-04 -3.1654e-04 beta_9 3.0952e-04 -3.1103e-04 3.3924e-04 -3.6710e-04 3.2693e-04 -3.6700e-04 3.6934e-04 -3.1654e-04 9.3457e-04 beta_10 -2.5928e-04 3.0591e-04 -3.1405e-04 3.1313e-04 -2.6073e-04 3.0468e-04 -3.0716e-04 3.1513e-04 -3.4057e-04 beta_10 beta_1 -2.5928e-04 beta_2 3.0591e-04 beta_3 -3.1405e-04 beta_4 3.1313e-04 beta_5 -2.6073e-04 beta_6 3.0468e-04 beta_7 -3.0716e-04 beta_8 3.1513e-04 beta_9 -3.4057e-04 beta_10 8.5761e-04 Classical correlation matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_8 beta_9 beta_1 1.0000 -0.3252 0.3458 -0.3354 0.3307 -0.3314 0.3478 -0.3526 0.3473 beta_2 -0.3252 1.0000 -0.3366 0.3505 -0.3589 0.3437 -0.3538 0.3501 -0.3252 beta_3 0.3458 -0.3366 1.0000 -0.3478 0.3396 -0.3462 0.3653 -0.3475 0.3479 beta_4 -0.3354 0.3505 -0.3478 1.0000 -0.3301 0.3310 -0.3537 0.3220 -0.3480 beta_5 0.3307 -0.3589 0.3396 -0.3301 1.0000 -0.3328 0.3662 -0.3488 0.3457 beta_6 -0.3314 0.3437 -0.3462 0.3310 -0.3328 1.0000 -0.3473 0.3265 -0.3474 beta_7 0.3478 -0.3538 0.3653 -0.3537 0.3662 -0.3473 1.0000 -0.3526 0.3725 beta_8 -0.3526 0.3501 -0.3475 0.3220 -0.3488 0.3265 -0.3526 1.0000 -0.3371 beta_9 0.3473 -0.3252 0.3479 -0.3480 0.3457 -0.3474 0.3725 -0.3371 1.0000 beta_10 -0.3461 0.3440 -0.3498 0.3368 -0.3462 0.3479 -0.3459 0.3520 -0.3438 beta_10 beta_1 -0.3461 beta_2 0.3440 beta_3 -0.3498 beta_4 0.3368 beta_5 -0.3462 beta_6 0.3479 beta_7 -0.3459 beta_8 0.3520 beta_9 -0.3438 beta_10 1.0000 Robust correlation matrix: beta_1 beta_2 beta_3 beta_4 beta_5 beta_6 beta_7 beta_8 beta_9 beta_1 1.0000 -0.2854 0.3645 -0.3190 0.3162 -0.3284 0.3261 -0.3620 0.3513 beta_2 -0.2854 1.0000 -0.3795 0.3743 -0.3515 0.3277 -0.3609 0.3456 -0.3412 beta_3 0.3645 -0.3795 1.0000 -0.3715 0.3334 -0.3615 0.3962 -0.3870 0.3621 beta_4 -0.3190 0.3743 -0.3715 1.0000 -0.3581 0.3959 -0.4050 0.3353 -0.3946 beta_5 0.3162 -0.3515 0.3334 -0.3581 1.0000 -0.3468 0.3857 -0.3902 0.3662 beta_6 -0.3284 0.3277 -0.3615 0.3959 -0.3468 1.0000 -0.3658 0.3802 -0.3939 beta_7 0.3261 -0.3609 0.3962 -0.4050 0.3857 -0.3658 1.0000 -0.3781 0.4011 beta_8 -0.3620 0.3456 -0.3870 0.3353 -0.3902 0.3802 -0.3781 1.0000 -0.3493 beta_9 0.3513 -0.3412 0.3621 -0.3946 0.3662 -0.3939 0.4011 -0.3493 1.0000 beta_10 -0.3072 0.3503 -0.3499 0.3513 -0.3049 0.3414 -0.3482 0.3630 -0.3804 beta_10 beta_1 -0.3072 beta_2 0.3503 beta_3 -0.3499 beta_4 0.3513 beta_5 -0.3049 beta_6 0.3414 beta_7 -0.3482 beta_8 0.3630 beta_9 -0.3804 beta_10 1.0000 20 worst outliers in terms of lowest average per choice prediction: row Avg prob per choice 1034 2.076348e-05 1834 9.745219e-05 521 1.176700e-04 1611 2.759273e-04 493 4.550683e-04 379 4.918966e-04 951 8.380524e-04 1454 8.501047e-04 532 8.883320e-04 1033 9.620854e-04 447 1.107823e-03 1616 1.115168e-03 718 1.150420e-03 1849 1.208615e-03 1626 1.395018e-03 953 1.586158e-03 1925 2.005892e-03 1718 2.310141e-03 916 2.562053e-03 1272 2.981755e-03 Changes in parameter estimates from starting values: Initial Estimate Difference beta_1 0.000 1.0162 1.0162 beta_2 0.000 -1.0204 -1.0204 beta_3 0.000 1.0395 1.0395 beta_4 0.000 -1.0239 -1.0239 beta_5 0.000 0.9648 0.9648 beta_6 0.000 -0.9560 -0.9560 beta_7 0.000 1.0384 1.0384 beta_8 0.000 -0.9793 -0.9793 beta_9 0.000 1.0030 1.0030 beta_10 0.000 -1.0131 -1.0131 Settings and functions used in model definition: apollo_control -------------- Value modelName "MNL_iterative_coding" modelDescr "MNL model using iterative coding for alternatives and attributes" indivID "ID" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" noValidation "FALSE" noDiagnostics "FALSE" calculateLLC "TRUE" panelData "FALSE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" overridePanel "FALSE" preventOverridePanel "FALSE" noModification "FALSE" Hessian routines attempted -------------------------- numerical jacobian of LL analytical gradient Scaling in estimation --------------------- Value beta_1 1.0163073 beta_2 1.0204145 beta_3 1.0395933 beta_4 1.0238713 beta_5 0.9646630 beta_6 0.9561798 beta_7 1.0384499 beta_8 0.9793024 beta_9 1.0031886 beta_10 1.0131883 Scaling used in computing Hessian --------------------------------- Value beta_1 1.0162228 beta_2 1.0203784 beta_3 1.0394747 beta_4 1.0238719 beta_5 0.9647520 beta_6 0.9560274 beta_7 1.0383882 beta_8 0.9792587 beta_9 1.0030244 beta_10 1.0131364 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) }