.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/latent/plot_b05latent_choice_full_mc.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_latent_plot_b05latent_choice_full_mc.py: Choice model with a latent variable: maximum likelihood estimation (Monte-Carlo) ================================================================================ Choice model with the latent variable. Mixture of logit with Monte-Carlo integration. Measurement equation for the indicators. Maximum likelihood (full information) estimation. :author: Michel Bierlaire, EPFL :date: Thu Apr 13 18:11:54 2023 .. GENERATED FROM PYTHON SOURCE LINES 14-64 .. code-block:: default import sys import biogeme.biogeme_logging as blog import biogeme.biogeme as bio import biogeme.exceptions as excep from biogeme import models import biogeme.results as res from biogeme.expressions import ( Beta, log, bioDraws, MonteCarlo, Elem, bioNormalCdf, exp, ) from read_or_estimate import read_or_estimate from optima import ( database, age_65_more, moreThanOneCar, moreThanOneBike, individualHouse, male, haveChildren, haveGA, highEducation, WaitingTimePT, Envir01, Envir02, Envir03, Mobil11, Mobil14, Mobil16, Mobil17, Choice, TimePT_scaled, TimeCar_scaled, MarginalCostPT_scaled, CostCarCHF_scaled, distance_km_scaled, PurpHWH, PurpOther, ScaledIncome, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b05latent_choice_full_mc.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b05latent_choice_full_mc.py .. GENERATED FROM PYTHON SOURCE LINES 65-66 Read the estimates from the structural equation estimation. .. GENERATED FROM PYTHON SOURCE LINES 66-77 .. code-block:: default MODELNAME = 'b02one_latent_ordered' try: struct_results = res.bioResults(pickleFile=f'saved_results/{MODELNAME}.pickle') except excep.BiogemeError: print( f'Run first the script {MODELNAME}.py in order to generate the ' f'file {MODELNAME}.pickle, and move it to the directory saved_results' ) sys.exit() struct_betas = struct_results.getBetaValues() .. GENERATED FROM PYTHON SOURCE LINES 78-79 Coefficients .. GENERATED FROM PYTHON SOURCE LINES 79-102 .. code-block:: default coef_intercept = Beta('coef_intercept', struct_betas['coef_intercept'], None, None, 0) coef_age_65_more = Beta( 'coef_age_65_more', struct_betas['coef_age_65_more'], None, None, 0 ) coef_haveGA = Beta('coef_haveGA', struct_betas['coef_haveGA'], None, None, 0) coef_moreThanOneCar = Beta( 'coef_moreThanOneCar', struct_betas['coef_moreThanOneCar'], None, None, 0 ) coef_moreThanOneBike = Beta( 'coef_moreThanOneBike', struct_betas['coef_moreThanOneBike'], None, None, 0 ) coef_individualHouse = Beta( 'coef_individualHouse', struct_betas['coef_individualHouse'], None, None, 0 ) coef_male = Beta('coef_male', struct_betas['coef_male'], None, None, 0) coef_haveChildren = Beta( 'coef_haveChildren', struct_betas['coef_haveChildren'], None, None, 0 ) coef_highEducation = Beta( 'coef_highEducation', struct_betas['coef_highEducation'], None, None, 0 ) .. GENERATED FROM PYTHON SOURCE LINES 103-104 Latent variable: structural equation. .. GENERATED FROM PYTHON SOURCE LINES 106-108 Define a random parameter, normally distributed, designed to be used for Monte-Carlo integration .. GENERATED FROM PYTHON SOURCE LINES 108-111 .. code-block:: default sigma_s = Beta('sigma_s', 1, None, None, 0) error_component = sigma_s * bioDraws('EC', 'NORMAL_MLHS') .. GENERATED FROM PYTHON SOURCE LINES 112-113 Piecewise linear specification for income. .. GENERATED FROM PYTHON SOURCE LINES 113-172 .. code-block:: default thresholds = [None, 4, 6, 8, 10, None] betas_thresholds = [ Beta( 'beta_ScaledIncome_minus_inf_4', struct_betas['beta_ScaledIncome_minus_inf_4'], None, None, 0, ), Beta( 'beta_ScaledIncome_4_6', struct_betas['beta_ScaledIncome_4_6'], None, None, 0, ), Beta( 'beta_ScaledIncome_6_8', struct_betas['beta_ScaledIncome_6_8'], None, None, 0, ), Beta( 'beta_ScaledIncome_8_10', struct_betas['beta_ScaledIncome_8_10'], None, None, 0, ), Beta( 'beta_ScaledIncome_10_inf', struct_betas['beta_ScaledIncome_10_inf'], None, None, 0, ), ] formula_income = models.piecewiseFormula( variable=ScaledIncome, thresholds=thresholds, betas=betas_thresholds, ) CARLOVERS = ( coef_intercept + coef_age_65_more * age_65_more + formula_income + coef_moreThanOneCar * moreThanOneCar + coef_moreThanOneBike * moreThanOneBike + coef_individualHouse * individualHouse + coef_male * male + coef_haveChildren * haveChildren + coef_haveGA * haveGA + coef_highEducation * highEducation + error_component ) .. GENERATED FROM PYTHON SOURCE LINES 173-174 Measurement equations. .. GENERATED FROM PYTHON SOURCE LINES 176-177 Intercepts. .. GENERATED FROM PYTHON SOURCE LINES 177-185 .. code-block:: default INTER_Envir01 = Beta('INTER_Envir01', 0, None, None, 1) INTER_Envir02 = Beta('INTER_Envir02', 0, None, None, 0) INTER_Envir03 = Beta('INTER_Envir03', 0, None, None, 0) INTER_Mobil11 = Beta('INTER_Mobil11', 0, None, None, 0) INTER_Mobil14 = Beta('INTER_Mobil14', 0, None, None, 0) INTER_Mobil16 = Beta('INTER_Mobil16', 0, None, None, 0) INTER_Mobil17 = Beta('INTER_Mobil17', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 186-187 Coefficients. .. GENERATED FROM PYTHON SOURCE LINES 187-195 .. code-block:: default B_Envir01_F1 = Beta('B_Envir01_F1', -1, None, None, 1) B_Envir02_F1 = Beta('B_Envir02_F1', -1, None, None, 0) B_Envir03_F1 = Beta('B_Envir03_F1', 1, None, None, 0) B_Mobil11_F1 = Beta('B_Mobil11_F1', 1, None, None, 0) B_Mobil14_F1 = Beta('B_Mobil14_F1', 1, None, None, 0) B_Mobil16_F1 = Beta('B_Mobil16_F1', 1, None, None, 0) B_Mobil17_F1 = Beta('B_Mobil17_F1', 1, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 196-197 Linear models. .. GENERATED FROM PYTHON SOURCE LINES 197-205 .. code-block:: default MODEL_Envir01 = INTER_Envir01 + B_Envir01_F1 * CARLOVERS MODEL_Envir02 = INTER_Envir02 + B_Envir02_F1 * CARLOVERS MODEL_Envir03 = INTER_Envir03 + B_Envir03_F1 * CARLOVERS MODEL_Mobil11 = INTER_Mobil11 + B_Mobil11_F1 * CARLOVERS MODEL_Mobil14 = INTER_Mobil14 + B_Mobil14_F1 * CARLOVERS MODEL_Mobil16 = INTER_Mobil16 + B_Mobil16_F1 * CARLOVERS MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS .. GENERATED FROM PYTHON SOURCE LINES 206-207 Scale parameters .. GENERATED FROM PYTHON SOURCE LINES 207-215 .. code-block:: default SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, 1.0e-5, None, 1) SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, 1.0e-5, None, 0) SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, 1.0e-5, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 216-217 Symmetric thresholds. .. GENERATED FROM PYTHON SOURCE LINES 217-224 .. code-block:: default delta_1 = Beta('delta_1', 0.1, 1.0e-5, None, 0) delta_2 = Beta('delta_2', 0.2, 1.0e-5, None, 0) tau_1 = -delta_1 - delta_2 tau_2 = -delta_1 tau_3 = delta_1 tau_4 = delta_1 + delta_2 .. GENERATED FROM PYTHON SOURCE LINES 225-226 Ordered probit models. .. GENERATED FROM PYTHON SOURCE LINES 226-345 .. code-block:: default Envir01_tau_1 = (tau_1 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_2 = (tau_2 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_3 = (tau_3 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_4 = (tau_4 - MODEL_Envir01) / SIGMA_STAR_Envir01 IndEnvir01 = { 1: bioNormalCdf(Envir01_tau_1), 2: bioNormalCdf(Envir01_tau_2) - bioNormalCdf(Envir01_tau_1), 3: bioNormalCdf(Envir01_tau_3) - bioNormalCdf(Envir01_tau_2), 4: bioNormalCdf(Envir01_tau_4) - bioNormalCdf(Envir01_tau_3), 5: 1 - bioNormalCdf(Envir01_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir01 = Elem(IndEnvir01, Envir01) Envir02_tau_1 = (tau_1 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_2 = (tau_2 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_3 = (tau_3 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_4 = (tau_4 - MODEL_Envir02) / SIGMA_STAR_Envir02 IndEnvir02 = { 1: bioNormalCdf(Envir02_tau_1), 2: bioNormalCdf(Envir02_tau_2) - bioNormalCdf(Envir02_tau_1), 3: bioNormalCdf(Envir02_tau_3) - bioNormalCdf(Envir02_tau_2), 4: bioNormalCdf(Envir02_tau_4) - bioNormalCdf(Envir02_tau_3), 5: 1 - bioNormalCdf(Envir02_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir02 = Elem(IndEnvir02, Envir02) Envir03_tau_1 = (tau_1 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_2 = (tau_2 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_3 = (tau_3 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_4 = (tau_4 - MODEL_Envir03) / SIGMA_STAR_Envir03 IndEnvir03 = { 1: bioNormalCdf(Envir03_tau_1), 2: bioNormalCdf(Envir03_tau_2) - bioNormalCdf(Envir03_tau_1), 3: bioNormalCdf(Envir03_tau_3) - bioNormalCdf(Envir03_tau_2), 4: bioNormalCdf(Envir03_tau_4) - bioNormalCdf(Envir03_tau_3), 5: 1 - bioNormalCdf(Envir03_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir03 = Elem(IndEnvir03, Envir03) Mobil11_tau_1 = (tau_1 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_2 = (tau_2 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_3 = (tau_3 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_4 = (tau_4 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 IndMobil11 = { 1: bioNormalCdf(Mobil11_tau_1), 2: bioNormalCdf(Mobil11_tau_2) - bioNormalCdf(Mobil11_tau_1), 3: bioNormalCdf(Mobil11_tau_3) - bioNormalCdf(Mobil11_tau_2), 4: bioNormalCdf(Mobil11_tau_4) - bioNormalCdf(Mobil11_tau_3), 5: 1 - bioNormalCdf(Mobil11_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil11 = Elem(IndMobil11, Mobil11) Mobil14_tau_1 = (tau_1 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_2 = (tau_2 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_3 = (tau_3 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_4 = (tau_4 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 IndMobil14 = { 1: bioNormalCdf(Mobil14_tau_1), 2: bioNormalCdf(Mobil14_tau_2) - bioNormalCdf(Mobil14_tau_1), 3: bioNormalCdf(Mobil14_tau_3) - bioNormalCdf(Mobil14_tau_2), 4: bioNormalCdf(Mobil14_tau_4) - bioNormalCdf(Mobil14_tau_3), 5: 1 - bioNormalCdf(Mobil14_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil14 = Elem(IndMobil14, Mobil14) Mobil16_tau_1 = (tau_1 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_2 = (tau_2 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_3 = (tau_3 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_4 = (tau_4 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 IndMobil16 = { 1: bioNormalCdf(Mobil16_tau_1), 2: bioNormalCdf(Mobil16_tau_2) - bioNormalCdf(Mobil16_tau_1), 3: bioNormalCdf(Mobil16_tau_3) - bioNormalCdf(Mobil16_tau_2), 4: bioNormalCdf(Mobil16_tau_4) - bioNormalCdf(Mobil16_tau_3), 5: 1 - bioNormalCdf(Mobil16_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil16 = Elem(IndMobil16, Mobil16) Mobil17_tau_1 = (tau_1 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_2 = (tau_2 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_3 = (tau_3 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_4 = (tau_4 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 IndMobil17 = { 1: bioNormalCdf(Mobil17_tau_1), 2: bioNormalCdf(Mobil17_tau_2) - bioNormalCdf(Mobil17_tau_1), 3: bioNormalCdf(Mobil17_tau_3) - bioNormalCdf(Mobil17_tau_2), 4: bioNormalCdf(Mobil17_tau_4) - bioNormalCdf(Mobil17_tau_3), 5: 1 - bioNormalCdf(Mobil17_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil17 = Elem(IndMobil17, Mobil17) .. GENERATED FROM PYTHON SOURCE LINES 346-349 Choice model Read the estimates from the sequential estimation, and use them as starting values .. GENERATED FROM PYTHON SOURCE LINES 349-360 .. code-block:: default MODELNAME = 'b04latent_choice_seq' try: choice_results = res.bioResults(pickleFile=f'saved_results/{MODELNAME}.pickle') except excep.BiogemeError: print( f'Run first the script {MODELNAME}.py in order to generate the ' f'file {MODELNAME}.pickle, and move it to the directory saved_results' ) sys.exit() choice_betas = choice_results.getBetaValues() .. GENERATED FROM PYTHON SOURCE LINES 361-362 Parameters to estimate. We use the previously estimated values as starting points. .. GENERATED FROM PYTHON SOURCE LINES 362-386 .. code-block:: default ASC_CAR = Beta('ASC_CAR', choice_betas['ASC_CAR'], None, None, 0) ASC_PT = Beta('ASC_PT', 0, None, None, 1) ASC_SM = Beta('ASC_SM', choice_betas['ASC_SM'], None, None, 0) BETA_COST_HWH = Beta('BETA_COST_HWH', choice_betas['BETA_COST_HWH'], None, None, 0) BETA_COST_OTHER = Beta( 'BETA_COST_OTHER', choice_betas['BETA_COST_OTHER'], None, None, 0 ) BETA_DIST = Beta('BETA_DIST', choice_betas['BETA_DIST'], None, None, 0) BETA_TIME_CAR_REF = Beta( 'BETA_TIME_CAR_REF', choice_betas['BETA_TIME_CAR_REF'], None, 0, 0 ) BETA_TIME_CAR_CL = Beta( 'BETA_TIME_CAR_CL', choice_betas['BETA_TIME_CAR_CL'], None, None, 0 ) BETA_TIME_PT_REF = Beta( 'BETA_TIME_PT_REF', choice_betas['BETA_TIME_PT_REF'], None, 0, 0 ) BETA_TIME_PT_CL = Beta( 'BETA_TIME_PT_CL', choice_betas['BETA_TIME_PT_CL'], None, None, 0 ) BETA_WAITING_TIME = Beta( 'BETA_WAITING_TIME', choice_betas['BETA_WAITING_TIME'], None, None, 0 ) .. GENERATED FROM PYTHON SOURCE LINES 387-388 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 388-410 .. code-block:: default BETA_TIME_PT = BETA_TIME_PT_REF * exp(BETA_TIME_PT_CL * CARLOVERS) V0 = ( ASC_PT + BETA_TIME_PT * TimePT_scaled + BETA_WAITING_TIME * WaitingTimePT + BETA_COST_HWH * MarginalCostPT_scaled * PurpHWH + BETA_COST_OTHER * MarginalCostPT_scaled * PurpOther ) BETA_TIME_CAR = BETA_TIME_CAR_REF * exp(BETA_TIME_CAR_CL * CARLOVERS) V1 = ( ASC_CAR + BETA_TIME_CAR * TimeCar_scaled + BETA_COST_HWH * CostCarCHF_scaled * PurpHWH + BETA_COST_OTHER * CostCarCHF_scaled * PurpOther ) V2 = ASC_SM + BETA_DIST * distance_km_scaled .. GENERATED FROM PYTHON SOURCE LINES 411-412 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 412-414 .. code-block:: default V = {0: V0, 1: V1, 2: V2} .. GENERATED FROM PYTHON SOURCE LINES 415-417 Conditional on omega, we have a logit model (called the kernel) for the choice. .. GENERATED FROM PYTHON SOURCE LINES 417-419 .. code-block:: default condprob = models.logit(V, None, Choice) .. GENERATED FROM PYTHON SOURCE LINES 420-422 Conditional on omega, we have the product of ordered probit for the indicators. .. GENERATED FROM PYTHON SOURCE LINES 422-434 .. code-block:: default condlike = ( P_Envir01 * P_Envir02 * P_Envir03 * P_Mobil11 * P_Mobil14 * P_Mobil16 * P_Mobil17 * condprob ) .. GENERATED FROM PYTHON SOURCE LINES 435-436 We integrate over omega using numerical integration .. GENERATED FROM PYTHON SOURCE LINES 436-438 .. code-block:: default loglike = log(MonteCarlo(condlike)) .. GENERATED FROM PYTHON SOURCE LINES 439-443 Create the Biogeme object. As the objective is to illustrate the syntax, we calculate the Monte-Carlo approximation with a small number of draws. To achieve that, we provide a parameter file different from the default one. .. GENERATED FROM PYTHON SOURCE LINES 443-446 .. code-block:: default the_biogeme = bio.BIOGEME(database, loglike, parameter_file='few_draws.toml') the_biogeme.modelName = 'b05latent_choice_full_mc' .. rst-class:: sphx-glr-script-out .. code-block:: none File few_draws.toml has been parsed. .. GENERATED FROM PYTHON SOURCE LINES 447-449 If estimation results are saved on file, we read them to speed up the process. If not, we estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 449-452 .. code-block:: default results = read_or_estimate(the_biogeme=the_biogeme, directory='saved_results') .. GENERATED FROM PYTHON SOURCE LINES 453-457 .. code-block:: default print(f'Estimated betas: {len(results.data.betaValues)}') print(f'Final log likelihood: {results.data.logLike:.3f}') print(f'Output file: {results.data.htmlFileName}') .. rst-class:: sphx-glr-script-out .. code-block:: none Estimated betas: 45 Final log likelihood: -18465.213 Output file: b05latent_choice_full_mc.html .. GENERATED FROM PYTHON SOURCE LINES 458-459 .. code-block:: default results.getEstimatedParameters() .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
ASC_CAR 0.742958 0.196986 3.771629 1.621852e-04
ASC_SM 1.791519 0.964260 1.857920 6.318037e-02
BETA_COST_HWH -1.757110 0.441162 -3.982911 6.807615e-05
BETA_COST_OTHER -0.697573 0.200239 -3.483704 4.945258e-04
BETA_DIST -4.427792 3.363092 -1.316584 1.879781e-01
BETA_TIME_CAR_CL -1.976813 0.244635 -8.080649 6.661338e-16
BETA_TIME_CAR_REF -17.353915 16.843289 -1.030316 3.028616e-01
BETA_TIME_PT_CL -1.406911 0.135353 -10.394416 0.000000e+00
BETA_TIME_PT_REF -6.344359 6.733415 -0.942220 3.460800e-01
BETA_WAITING_TIME -0.006124 0.013396 -0.457145 6.475672e-01
B_Envir02_F1 -0.483629 0.040474 -11.949015 0.000000e+00
B_Envir03_F1 0.516290 0.045491 11.349295 0.000000e+00
B_Mobil11_F1 0.632539 0.072094 8.773770 0.000000e+00
B_Mobil14_F1 0.609179 0.053596 11.366147 0.000000e+00
B_Mobil16_F1 0.562196 0.056835 9.891731 0.000000e+00
B_Mobil17_F1 0.545693 0.057233 9.534561 0.000000e+00
INTER_Envir02 0.469457 0.034042 13.790734 0.000000e+00
INTER_Envir03 -0.386202 0.037744 -10.232207 0.000000e+00
INTER_Mobil11 0.342214 0.077703 4.404150 1.061995e-05
INTER_Mobil14 -0.204999 0.049099 -4.175236 2.976779e-05
INTER_Mobil16 0.098224 0.058688 1.673660 9.419753e-02
INTER_Mobil17 0.092766 0.057999 1.599451 1.097205e-01
SIGMA_STAR_Envir02 0.877760 0.038659 22.705168 0.000000e+00
SIGMA_STAR_Envir03 0.818233 0.038313 21.356753 0.000000e+00
SIGMA_STAR_Mobil11 0.848194 0.046683 18.169142 0.000000e+00
SIGMA_STAR_Mobil14 0.731865 0.034468 21.233484 0.000000e+00
SIGMA_STAR_Mobil16 0.835229 0.041352 20.197938 0.000000e+00
SIGMA_STAR_Mobil17 0.839749 0.042004 19.992111 0.000000e+00
beta_ScaledIncome_10_inf 0.031654 0.122964 0.257422 7.968532e-01
beta_ScaledIncome_4_6 -0.181322 0.190493 -0.951860 3.411681e-01
beta_ScaledIncome_6_8 0.201701 0.287431 0.701735 4.828446e-01
beta_ScaledIncome_8_10 -0.420398 0.404861 -1.038375 2.990953e-01
beta_ScaledIncome_minus_inf_4 0.138475 0.105980 1.306616 1.913433e-01
coef_age_65_more 0.057604 0.072533 0.794183 4.270888e-01
coef_haveChildren 0.022477 0.217052 0.103553 9.175237e-01
coef_haveGA -0.361382 0.106187 -3.403252 6.658884e-04
coef_highEducation -0.182656 0.113751 -1.605754 1.083279e-01
coef_individualHouse -0.039590 0.183022 -0.216313 8.287440e-01
coef_intercept 0.320155 0.301392 1.062253 2.881208e-01
coef_male -0.045521 0.115153 -0.395309 6.926147e-01
coef_moreThanOneBike -0.356653 0.124134 -2.873121 4.064390e-03
coef_moreThanOneCar 0.615459 0.134325 4.581848 4.608846e-06
delta_1 0.320872 0.016226 19.775595 0.000000e+00
delta_2 0.932155 0.042774 21.792621 0.000000e+00
sigma_s 0.796461 0.110991 7.175889 7.183143e-13


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