Model run using Apollo for R, version 0.2.6 on Darwin by stephane.hess www.ApolloChoiceModelling.com Model name : EM_LC_no_covariates Model description : LC model with class allocation model on Swiss route choice data, EM algorithm Model run at : 2021-11-05 11:29:37 Estimation method : EM algorithm (bfgs) -> Maximum likelihood (bfgs) Model diagnosis : successful convergence Number of individuals : 388 Number of rows in database : 3492 Number of modelled outcomes : 3492 Number of cores used : 1 Model without mixing LL(start) : -1755.951 LL(0, whole model) : -2420.47 LL(C, whole model) : -2420.387 LL(final, whole model) : -1561.787 Rho-square (0) : 0.3548 Adj.Rho-square (0) : 0.3502 Rho-square (C) : 0.3547 Adj.Rho-square (C) : 0.3502 AIC : 3145.57 BIC : 3213.31 LL(0,Class_1) : -2420.47 LL(final,Class_1) : -1770.971 LL(0,Class_2) : -2420.47 LL(final,Class_2) : -2511.897 Estimated parameters : 11 Time taken (hh:mm:ss) : 00:00:25.99 pre-estimation : 00:00:0.61 estimation : 00:00:23.78 post-estimation : 00:00:1.6 Iterations : 46 (EM) & 7 (bfgs) Min abs eigenvalue of Hessian : 15.03279 Unconstrained optimisation. Estimates: Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0) asc_1_a -0.06758 0.064322 -1.0507 0.075041 -0.9006 asc_1_b 0.04111 0.110398 0.3724 0.133176 0.3087 asc_2_a 0.00000 NA NA NA NA asc_2_b 0.00000 NA NA NA NA beta_tt_a -0.03716 0.005255 -7.0726 0.008940 -4.1574 beta_tt_b -0.21772 0.025455 -8.5531 0.045253 -4.8112 beta_tc_a -0.05044 0.013041 -3.8677 0.013162 -3.8321 beta_tc_b -0.79771 0.084761 -9.4113 0.113992 -6.9980 beta_hw_a -0.03446 0.002993 -11.5153 0.004492 -7.6716 beta_hw_b -0.05553 0.005508 -10.0817 0.008078 -6.8743 beta_ch_a -0.62567 0.072958 -8.5757 0.102224 -6.1205 beta_ch_b -2.75555 0.227204 -12.1281 0.280485 -9.8242 delta_a -0.04493 0.174649 -0.2573 0.198481 -0.2264 delta_b 0.00000 NA NA NA NA Summary of class allocation for LC model component : Mean prob. Class_1 0.4888 Class_2 0.5112 Overview of choices for MNL model component Class_1: alt1 alt2 Times available 3492.00 3492.00 Times chosen 1734.00 1758.00 Percentage chosen overall 49.66 50.34 Percentage chosen when available 49.66 50.34 Overview of choices for MNL model component Class_2: alt1 alt2 Times available 3492.00 3492.00 Times chosen 1734.00 1758.00 Percentage chosen overall 49.66 50.34 Percentage chosen when available 49.66 50.34 Classical covariance matrix: asc_1_a asc_1_b beta_tt_a beta_tt_b beta_tc_a beta_tc_b beta_hw_a beta_hw_b asc_1_a 0.004137 -0.001972 -2.003e-06 -1.425e-05 -2.311e-05 -6.826e-06 -1.398e-06 -3.688e-06 asc_1_b -0.001972 0.012188 5.315e-05 -4.7422e-04 6.703e-05 -0.001264 3.667e-06 -1.944e-05 beta_tt_a -2.003e-06 5.315e-05 2.761e-05 -2.619e-05 5.048e-05 -1.647e-05 4.399e-06 -4.468e-06 beta_tt_b -1.425e-05 -4.7422e-04 -2.619e-05 6.4796e-04 -1.804e-07 0.001937 -7.481e-07 5.674e-05 beta_tc_a -2.311e-05 6.703e-05 5.048e-05 -1.804e-07 1.7007e-04 5.371e-05 5.025e-06 -1.099e-06 beta_tc_b -6.826e-06 -0.001264 -1.647e-05 0.001937 5.371e-05 0.007184 2.350e-05 1.5651e-04 beta_hw_a -1.398e-06 3.667e-06 4.399e-06 -7.481e-07 5.025e-06 2.350e-05 8.957e-06 -5.426e-06 beta_hw_b -3.688e-06 -1.944e-05 -4.468e-06 5.674e-05 -1.099e-06 1.5651e-04 -5.426e-06 3.034e-05 beta_ch_a -1.2874e-04 -3.4329e-04 9.257e-05 5.4709e-04 1.3754e-04 0.002323 8.827e-05 -2.912e-05 beta_ch_b -0.001448 7.7278e-04 -1.407e-05 0.004092 3.2968e-04 0.012405 -6.436e-06 5.2970e-04 delta_a 9.0644e-04 -1.1396e-04 -1.6082e-04 -0.001685 -4.0841e-04 -0.006418 -1.2744e-04 -2.963e-05 beta_ch_a beta_ch_b delta_a asc_1_a -1.2874e-04 -0.001448 9.0644e-04 asc_1_b -3.4329e-04 7.7278e-04 -1.1396e-04 beta_tt_a 9.257e-05 -1.407e-05 -1.6082e-04 beta_tt_b 5.4709e-04 0.004092 -0.001685 beta_tc_a 1.3754e-04 3.2968e-04 -4.0841e-04 beta_tc_b 0.002323 0.012405 -0.006418 beta_hw_a 8.827e-05 -6.436e-06 -1.2744e-04 beta_hw_b -2.912e-05 5.2970e-04 -2.963e-05 beta_ch_a 0.005323 0.004243 -0.006921 beta_ch_b 0.004243 0.051622 -0.017905 delta_a -0.006921 -0.017905 0.030502 Robust covariance matrix: asc_1_a asc_1_b beta_tt_a beta_tt_b beta_tc_a beta_tc_b beta_hw_a beta_hw_b asc_1_a 0.005631 -0.003580 -8.890e-05 2.0195e-04 -7.075e-05 4.9792e-04 -3.978e-05 2.228e-05 asc_1_b -0.003580 0.017736 3.5219e-04 -0.002362 2.8409e-04 -0.005895 4.022e-05 -9.076e-05 beta_tt_a -8.890e-05 3.5219e-04 7.991e-05 -2.3565e-04 7.173e-05 -3.7314e-04 1.693e-05 -3.029e-05 beta_tt_b 2.0195e-04 -0.002362 -2.3565e-04 0.002048 -1.3040e-04 0.004595 -2.902e-05 1.4382e-04 beta_tc_a -7.075e-05 2.8409e-04 7.173e-05 -1.3040e-04 1.7324e-04 -2.1282e-04 1.245e-05 -1.669e-05 beta_tc_b 4.9792e-04 -0.005895 -3.7314e-04 0.004595 -2.1282e-04 0.012994 3.091e-05 1.8089e-04 beta_hw_a -3.978e-05 4.022e-05 1.693e-05 -2.902e-05 1.245e-05 3.091e-05 2.018e-05 -1.989e-05 beta_hw_b 2.228e-05 -9.076e-05 -3.029e-05 1.4382e-04 -1.669e-05 1.8089e-04 -1.989e-05 6.526e-05 beta_ch_a -8.1403e-04 -0.001148 1.3347e-04 0.001267 1.0440e-04 0.005161 2.2875e-04 -1.8990e-04 beta_ch_b -0.002673 8.4258e-04 -9.0249e-04 0.008851 -1.9711e-04 0.017422 -1.9144e-04 0.001041 delta_a 0.002131 4.7929e-04 -1.0235e-04 -0.003167 -2.9622e-04 -0.010370 -3.0705e-04 1.8797e-04 beta_ch_a beta_ch_b delta_a asc_1_a -8.1403e-04 -0.002673 0.002131 asc_1_b -0.001148 8.4258e-04 4.7929e-04 beta_tt_a 1.3347e-04 -9.0249e-04 -1.0235e-04 beta_tt_b 0.001267 0.008851 -0.003167 beta_tc_a 1.0440e-04 -1.9711e-04 -2.9622e-04 beta_tc_b 0.005161 0.017422 -0.010370 beta_hw_a 2.2875e-04 -1.9144e-04 -3.0705e-04 beta_hw_b -1.8990e-04 0.001041 1.8797e-04 beta_ch_a 0.010450 0.006098 -0.013512 beta_ch_b 0.006098 0.078672 -0.022865 delta_a -0.013512 -0.022865 0.039395 Classical correlation matrix: asc_1_a asc_1_b beta_tt_a beta_tt_b beta_tc_a beta_tc_b beta_hw_a beta_hw_b asc_1_a 1.000000 -0.277765 -0.005925 -0.008703 -0.02755 -0.001252 -0.007265 -0.01041 asc_1_b -0.277765 1.000000 0.091615 -0.168747 0.04656 -0.135064 0.011098 -0.03197 beta_tt_a -0.005925 0.091615 1.000000 -0.195806 0.73659 -0.036974 0.279736 -0.15437 beta_tt_b -0.008703 -0.168747 -0.195806 1.000000 -5.4331e-04 0.897875 -0.009820 0.40464 beta_tc_a -0.027550 0.046556 0.736590 -5.4331e-04 1.00000 0.048586 0.128743 -0.01530 beta_tc_b -0.001252 -0.135064 -0.036974 0.897875 0.04859 1.000000 0.092638 0.33521 beta_hw_a -0.007265 0.011098 0.279736 -0.009820 0.12874 0.092638 1.000000 -0.32913 beta_hw_b -0.010409 -0.031969 -0.154371 0.404637 -0.01530 0.335213 -0.329135 1.00000 beta_ch_a -0.027434 -0.042620 0.241469 0.294586 0.14456 0.375606 0.404263 -0.07246 beta_ch_b -0.099056 0.030809 -0.011782 0.707569 0.11127 0.644161 -0.009466 0.42325 delta_a 0.080690 -0.005911 -0.175236 -0.378980 -0.17932 -0.433514 -0.243805 -0.03080 beta_ch_a beta_ch_b delta_a asc_1_a -0.02743 -0.099056 0.080690 asc_1_b -0.04262 0.030809 -0.005911 beta_tt_a 0.24147 -0.011782 -0.175236 beta_tt_b 0.29459 0.707569 -0.378980 beta_tc_a 0.14456 0.111268 -0.179317 beta_tc_b 0.37561 0.644161 -0.433514 beta_hw_a 0.40426 -0.009466 -0.243805 beta_hw_b -0.07246 0.423245 -0.030802 beta_ch_a 1.00000 0.255992 -0.543169 beta_ch_b 0.25599 1.000000 -0.451224 delta_a -0.54317 -0.451224 1.000000 Robust correlation matrix: asc_1_a asc_1_b beta_tt_a beta_tt_b beta_tc_a beta_tc_b beta_hw_a beta_hw_b asc_1_a 1.00000 -0.35823 -0.13253 0.05947 -0.07163 0.05821 -0.11801 0.03676 asc_1_b -0.35823 1.00000 0.29583 -0.39185 0.16207 -0.38834 0.06723 -0.08436 beta_tt_a -0.13253 0.29583 1.00000 -0.58251 0.60960 -0.36617 0.42159 -0.41942 beta_tt_b 0.05947 -0.39185 -0.58251 1.00000 -0.21892 0.89082 -0.14276 0.39340 beta_tc_a -0.07163 0.16207 0.60960 -0.21892 1.00000 -0.14184 0.21049 -0.15697 beta_tc_b 0.05821 -0.38834 -0.36617 0.89082 -0.14184 1.00000 0.06036 0.19643 beta_hw_a -0.11801 0.06723 0.42159 -0.14276 0.21049 0.06036 1.00000 -0.54801 beta_hw_b 0.03676 -0.08436 -0.41942 0.39340 -0.15697 0.19643 -0.54801 1.00000 beta_ch_a -0.10612 -0.08434 0.14605 0.27398 0.07759 0.44289 0.49811 -0.22996 beta_ch_b -0.12698 0.02256 -0.35993 0.69736 -0.05339 0.54489 -0.15193 0.45938 delta_a 0.14310 0.01813 -0.05769 -0.35258 -0.11339 -0.45836 -0.34436 0.11723 beta_ch_a beta_ch_b delta_a asc_1_a -0.10612 -0.12698 0.14310 asc_1_b -0.08434 0.02256 0.01813 beta_tt_a 0.14605 -0.35993 -0.05769 beta_tt_b 0.27398 0.69736 -0.35258 beta_tc_a 0.07759 -0.05339 -0.11339 beta_tc_b 0.44289 0.54489 -0.45836 beta_hw_a 0.49811 -0.15193 -0.34436 beta_hw_b -0.22996 0.45938 0.11723 beta_ch_a 1.00000 0.21268 -0.66598 beta_ch_b 0.21268 1.00000 -0.41071 delta_a -0.66598 -0.41071 1.00000 20 worst outliers in terms of lowest average per choice prediction: ID Avg prob per choice 15030 0.2279390 22580 0.3124634 20010 0.3355828 23205 0.3386220 14802 0.3396987 16489 0.3503249 16617 0.3506364 22961 0.3619349 18219 0.3706734 13863 0.3760391 15174 0.3795395 22278 0.3826177 13214 0.3863466 16178 0.3871016 76862 0.3880462 20100 0.3886062 20323 0.4042289 17187 0.4058862 20063 0.4068625 22820 0.4119426 Changes in parameter estimates from starting values: Initial Estimate Difference asc_1_a -0.06758 -0.06758 -1.568e-06 asc_1_b 0.04111 0.04111 2.886e-07 asc_2_a 0.00000 0.00000 0.000 asc_2_b 0.00000 0.00000 0.000 beta_tt_a -0.03717 -0.03716 1.240e-06 beta_tt_b -0.21768 -0.21772 -4.051e-05 beta_tc_a -0.05044 -0.05044 3.524e-06 beta_tc_b -0.79780 -0.79771 8.447e-05 beta_hw_a -0.03447 -0.03446 3.352e-06 beta_hw_b -0.05553 -0.05553 -3.244e-06 beta_ch_a -0.62562 -0.62567 -4.320e-05 beta_ch_b -2.75516 -2.75555 -3.8908e-04 delta_a -0.04493 -0.04493 -2.586e-08 delta_b 0.00000 0.00000 0.000 Settings and functions used in model definition: apollo_control -------------- Value modelName "EM_LC_no_covariates" modelDescr "LC model with class allocation model on Swiss route choice data, EM algorithm" indivID "ID" noValidation "TRUE" noDiagnostics "TRUE" outputDirectory "output/" debug "FALSE" nCores "1" workInLogs "FALSE" seed "13" mixing "FALSE" HB "FALSE" calculateLLC "TRUE" panelData "TRUE" analyticGrad "TRUE" analyticGrad_manualSet "FALSE" Hessian routines attempted -------------- numerical second derivative of LL (using numDeriv) Scaling in estimation -------------- Value asc_1_a 0.06757989 asc_1_b 0.04110949 beta_tt_a 0.03716527 beta_tt_b 0.21768587 beta_tc_a 0.05043967 beta_tc_b 0.79779536 beta_hw_a 0.03446291 beta_hw_b 0.05553232 beta_ch_a 0.62562520 beta_ch_b 2.75515805 delta_a 0.04493434 Scaling used in computing Hessian -------------- Value asc_1_a 0.06758046 asc_1_b 0.04110954 beta_tt_a 0.03716475 beta_tt_b 0.21771973 beta_tc_a 0.05043899 beta_tc_b 0.79771214 beta_hw_a 0.03446332 beta_hw_b 0.05553318 beta_ch_a 0.62566744 beta_ch_b 2.75554676 delta_a 0.04493435 apollo_lcPars ------------- function(apollo_beta, apollo_inputs){ lcpars = list() lcpars[["asc_1" ]] = list( asc_1_a, asc_1_b) lcpars[["asc_2" ]] = list( asc_2_a, asc_2_b) lcpars[["beta_tt"]] = list(beta_tt_a, beta_tt_b) lcpars[["beta_tc"]] = list(beta_tc_a, beta_tc_b) lcpars[["beta_hw"]] = list(beta_hw_a, beta_hw_b) lcpars[["beta_ch"]] = list(beta_ch_a, beta_ch_b) lcpars[["pi_values"]] = list(class_a = 1/(1 + exp(delta_b - delta_a)), class_b = 1/(1 + exp(delta_a - delta_b))) return(lcpars) } 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() ### Define settings for MNL model component that are generic across classes mnl_settings = list( alternatives = c(alt1=1, alt2=2), avail = list(alt1=1, alt2=1), choiceVar = choice ) ### Loop over classes for(s in 1:length(pi_values)){ ### Compute class-specific utilities V=list() V[["alt1"]] = asc_1[[s]] + beta_tc[[s]]*tc1 + beta_tt[[s]]*tt1 + beta_hw[[s]]*hw1 + beta_ch[[s]]*ch1 V[["alt2"]] = asc_2[[s]] + beta_tc[[s]]*tc2 + beta_tt[[s]]*tt2 + beta_hw[[s]]*hw2 + beta_ch[[s]]*ch2 mnl_settings$utilities = V mnl_settings$componentName = paste0("Class_",s) ### Compute within-class choice probabilities using MNL model P[[paste0("Class_",s)]] = apollo_mnl(mnl_settings, functionality) ### Take product across observation for same individual P[[paste0("Class_",s)]] = apollo_panelProd(P[[paste0("Class_",s)]], apollo_inputs ,functionality) } ### Compute latent class model probabilities lc_settings = list(inClassProb = P, classProb=pi_values) P[["model"]] = apollo_lc(lc_settings, apollo_inputs, functionality) ### Prepare and return outputs of function P = apollo_prepareProb(P, apollo_inputs, functionality) return(P) }