.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/latent/plot_b06serial_correlation.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_b06serial_correlation.py: Serial correlation ================== Choice model with the latent variable. Mixture of logit, with agent effect to deal with serial correlation. Measurement equation for the indicators. Maximum likelihood (full information) estimation. :author: Michel Bierlaire, EPFL :date: Thu Apr 13 18:16:37 2023 .. GENERATED FROM PYTHON SOURCE LINES 15-65 .. 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, bioDraws, MonteCarlo, Elem, bioNormalCdf, exp, log, ) 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, PurpHWH, PurpOther, distance_km_scaled, ScaledIncome, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b06serial_correlation.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b06serial_correlation.py .. GENERATED FROM PYTHON SOURCE LINES 66-67 Read the estimates from the structural equation estimation. .. GENERATED FROM PYTHON SOURCE LINES 67-78 .. code-block:: default MODELNAME = 'b05latent_choice_full' 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() betas = struct_results.getBetaValues() .. GENERATED FROM PYTHON SOURCE LINES 79-80 Coefficients. .. GENERATED FROM PYTHON SOURCE LINES 80-99 .. code-block:: default coef_intercept = Beta('coef_intercept', betas['coef_intercept'], None, None, 0) coef_age_65_more = Beta('coef_age_65_more', betas['coef_age_65_more'], None, None, 0) coef_haveGA = Beta('coef_haveGA', betas['coef_haveGA'], None, None, 0) coef_moreThanOneCar = Beta( 'coef_moreThanOneCar', betas['coef_moreThanOneCar'], None, None, 0 ) coef_moreThanOneBike = Beta( 'coef_moreThanOneBike', betas['coef_moreThanOneBike'], None, None, 0 ) coef_individualHouse = Beta( 'coef_individualHouse', betas['coef_individualHouse'], None, None, 0 ) coef_male = Beta('coef_male', betas['coef_male'], None, None, 0) coef_haveChildren = Beta('coef_haveChildren', betas['coef_haveChildren'], None, None, 0) coef_highEducation = Beta( 'coef_highEducation', betas['coef_highEducation'], None, None, 0 ) .. GENERATED FROM PYTHON SOURCE LINES 100-101 Latent variable: structural equation. .. GENERATED FROM PYTHON SOURCE LINES 103-105 Define a random parameter, normally distributed, designed to be used for Monte-Carlo integration. .. GENERATED FROM PYTHON SOURCE LINES 105-108 .. code-block:: default omega = bioDraws('omega', 'NORMAL') sigma_s = Beta('sigma_s', betas['sigma_s'], None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 109-111 Deal with serial correlation by including an error component that is individual specific .. GENERATED FROM PYTHON SOURCE LINES 111-174 .. code-block:: default error_component = bioDraws('error_component', 'NORMAL') ec_sigma = Beta('ec_sigma', 10, None, None, 0) thresholds = [None, 4, 6, 8, 10, None] betas_thresholds = [ Beta( 'beta_ScaledIncome_minus_inf_4', betas['beta_ScaledIncome_minus_inf_4'], None, None, 0, ), Beta( 'beta_ScaledIncome_4_6', betas['beta_ScaledIncome_4_6'], None, None, 0, ), Beta( 'beta_ScaledIncome_6_8', betas['beta_ScaledIncome_6_8'], None, None, 0, ), Beta( 'beta_ScaledIncome_8_10', betas['beta_ScaledIncome_8_10'], None, None, 0, ), Beta( 'beta_ScaledIncome_10_inf', 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 + sigma_s * omega + ec_sigma * error_component ) .. GENERATED FROM PYTHON SOURCE LINES 175-176 Measurement equations. .. GENERATED FROM PYTHON SOURCE LINES 178-179 Intercepts. .. GENERATED FROM PYTHON SOURCE LINES 179-187 .. code-block:: default INTER_Envir01 = Beta('INTER_Envir01', 0, None, None, 1) INTER_Envir02 = Beta('INTER_Envir02', betas['INTER_Envir02'], None, None, 0) INTER_Envir03 = Beta('INTER_Envir03', betas['INTER_Envir03'], None, None, 0) INTER_Mobil11 = Beta('INTER_Mobil11', betas['INTER_Mobil11'], None, None, 0) INTER_Mobil14 = Beta('INTER_Mobil14', betas['INTER_Mobil14'], None, None, 0) INTER_Mobil16 = Beta('INTER_Mobil16', betas['INTER_Mobil16'], None, None, 0) INTER_Mobil17 = Beta('INTER_Mobil17', betas['INTER_Mobil17'], None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 188-189 Coefficients. .. GENERATED FROM PYTHON SOURCE LINES 189-197 .. code-block:: default B_Envir01_F1 = Beta('B_Envir01_F1', -1, None, None, 1) B_Envir02_F1 = Beta('B_Envir02_F1', betas['B_Envir02_F1'], None, None, 0) B_Envir03_F1 = Beta('B_Envir03_F1', betas['B_Envir03_F1'], None, None, 0) B_Mobil11_F1 = Beta('B_Mobil11_F1', betas['B_Mobil11_F1'], None, None, 0) B_Mobil14_F1 = Beta('B_Mobil14_F1', betas['B_Mobil14_F1'], None, None, 0) B_Mobil16_F1 = Beta('B_Mobil16_F1', betas['B_Mobil16_F1'], None, None, 0) B_Mobil17_F1 = Beta('B_Mobil17_F1', betas['B_Mobil17_F1'], None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 198-199 Linear models. .. GENERATED FROM PYTHON SOURCE LINES 199-207 .. 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 208-209 Scale parameters. .. GENERATED FROM PYTHON SOURCE LINES 209-229 .. code-block:: default SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, None, None, 1) SIGMA_STAR_Envir02 = Beta( 'SIGMA_STAR_Envir02', betas['SIGMA_STAR_Envir02'], None, None, 0 ) SIGMA_STAR_Envir03 = Beta( 'SIGMA_STAR_Envir03', betas['SIGMA_STAR_Envir03'], None, None, 0 ) SIGMA_STAR_Mobil11 = Beta( 'SIGMA_STAR_Mobil11', betas['SIGMA_STAR_Mobil11'], None, None, 0 ) SIGMA_STAR_Mobil14 = Beta( 'SIGMA_STAR_Mobil14', betas['SIGMA_STAR_Mobil14'], None, None, 0 ) SIGMA_STAR_Mobil16 = Beta( 'SIGMA_STAR_Mobil16', betas['SIGMA_STAR_Mobil16'], None, None, 0 ) SIGMA_STAR_Mobil17 = Beta( 'SIGMA_STAR_Mobil17', betas['SIGMA_STAR_Mobil17'], None, None, 0 ) .. GENERATED FROM PYTHON SOURCE LINES 230-231 Symmetric thresholds. .. GENERATED FROM PYTHON SOURCE LINES 231-238 .. code-block:: default delta_1 = Beta('delta_1', betas['delta_1'], 0, 10, 0) delta_2 = Beta('delta_2', betas['delta_2'], 0, 10, 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 239-240 Ordered probit models. .. GENERATED FROM PYTHON SOURCE LINES 240-360 .. 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 361-362 Choice model. .. GENERATED FROM PYTHON SOURCE LINES 362-374 .. code-block:: default ASC_CAR = Beta('ASC_CAR', betas['ASC_CAR'], None, None, 0) ASC_PT = Beta('ASC_PT', 0, None, None, 1) ASC_SM = Beta('ASC_SM', betas['ASC_SM'], None, None, 0) BETA_COST_HWH = Beta('BETA_COST_HWH', betas['BETA_COST_HWH'], None, None, 0) BETA_COST_OTHER = Beta('BETA_COST_OTHER', betas['BETA_COST_OTHER'], None, None, 0) BETA_DIST = Beta('BETA_DIST', betas['BETA_DIST'], None, None, 0) BETA_TIME_CAR_REF = Beta('BETA_TIME_CAR_REF', betas['BETA_TIME_CAR_REF'], None, 0, 0) BETA_TIME_CAR_CL = Beta('BETA_TIME_CAR_CL', betas['BETA_TIME_CAR_CL'], -10, 10, 0) BETA_TIME_PT_REF = Beta('BETA_TIME_PT_REF', betas['BETA_TIME_PT_REF'], None, 0, 0) BETA_TIME_PT_CL = Beta('BETA_TIME_PT_CL', betas['BETA_TIME_PT_CL'], -10, 10, 0) BETA_WAITING_TIME = Beta('BETA_WAITING_TIME', betas['BETA_WAITING_TIME'], None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 375-376 Definition of utility functions. .. GENERATED FROM PYTHON SOURCE LINES 376-399 .. 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 + ec_sigma * error_component ) 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 + ec_sigma * error_component ) V2 = ASC_SM + BETA_DIST * distance_km_scaled .. GENERATED FROM PYTHON SOURCE LINES 400-401 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 401-403 .. code-block:: default V = {0: V0, 1: V1, 2: V2} .. GENERATED FROM PYTHON SOURCE LINES 404-406 Conditional on the random parameters, we have a logit model (called the kernel) for the choice. .. GENERATED FROM PYTHON SOURCE LINES 406-408 .. code-block:: default condprob = models.logit(V, None, Choice) .. GENERATED FROM PYTHON SOURCE LINES 409-411 Conditional on the random parameters, we have the product of ordered probit for the indicators. .. GENERATED FROM PYTHON SOURCE LINES 411-422 .. code-block:: default condlike = ( P_Envir01 * P_Envir02 * P_Envir03 * P_Mobil11 * P_Mobil14 * P_Mobil16 * P_Mobil17 * condprob ) .. GENERATED FROM PYTHON SOURCE LINES 423-424 We integrate over omega using Monte-Carlo integration .. GENERATED FROM PYTHON SOURCE LINES 424-426 .. code-block:: default loglike = log(MonteCarlo(condlike)) .. GENERATED FROM PYTHON SOURCE LINES 427-431 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 431-434 .. code-block:: default the_biogeme = bio.BIOGEME(database, loglike, parameter_file='few_draws.toml') the_biogeme.modelName = 'b06serial_correlation' .. rst-class:: sphx-glr-script-out .. code-block:: none File few_draws.toml has been parsed. .. GENERATED FROM PYTHON SOURCE LINES 435-437 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 437-439 .. code-block:: default results = read_or_estimate(the_biogeme=the_biogeme, directory='saved_results') .. GENERATED FROM PYTHON SOURCE LINES 440-443 .. code-block:: default 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 Final log likelihood: -18417.351 Output file: b06serial_correlation.html .. GENERATED FROM PYTHON SOURCE LINES 444-445 .. code-block:: default results.getEstimatedParameters() .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
ASC_CAR 0.677918 0.118821 5.705362 1.160958e-08
ASC_SM 0.147046 0.371161 0.396178 6.919739e-01
BETA_COST_HWH -1.421139 0.340155 -4.177920 2.941871e-05
BETA_COST_OTHER -0.524558 0.159631 -3.286071 1.015955e-03
BETA_DIST -1.444146 0.410454 -3.518414 4.341348e-04
BETA_TIME_CAR_CL -0.975343 0.191484 -5.093593 3.513413e-07
BETA_TIME_CAR_REF -9.108861 1.954747 -4.659867 3.164139e-06
BETA_TIME_PT_CL -0.391177 0.172399 -2.269025 2.326683e-02
BETA_TIME_PT_REF -3.072080 0.851753 -3.606776 3.100252e-04
BETA_WAITING_TIME -0.020170 0.009610 -2.098932 3.582290e-02
B_Envir02_F1 -0.468439 0.033150 -14.131085 0.000000e+00
B_Envir03_F1 0.495903 0.032464 15.275625 0.000000e+00
B_Mobil11_F1 0.588725 0.044983 13.087809 0.000000e+00
B_Mobil14_F1 0.591351 0.038213 15.475093 0.000000e+00
B_Mobil16_F1 0.537261 0.045819 11.725805 0.000000e+00
B_Mobil17_F1 0.528113 0.044784 11.792447 0.000000e+00
INTER_Envir02 0.454209 0.030126 15.076807 0.000000e+00
INTER_Envir03 -0.363741 0.028421 -12.798197 0.000000e+00
INTER_Mobil11 0.401404 0.037345 10.748638 0.000000e+00
INTER_Mobil14 -0.175758 0.027889 -6.302049 2.937364e-10
INTER_Mobil16 0.139032 0.033870 4.104877 4.045306e-05
INTER_Mobil17 0.130712 0.032974 3.964070 7.368269e-05
SIGMA_STAR_Envir02 0.900076 0.033571 26.810796 0.000000e+00
SIGMA_STAR_Envir03 0.840075 0.033452 25.112477 0.000000e+00
SIGMA_STAR_Mobil11 0.875531 0.039540 22.143078 0.000000e+00
SIGMA_STAR_Mobil14 0.744281 0.032704 22.758265 0.000000e+00
SIGMA_STAR_Mobil16 0.856487 0.038523 22.233330 0.000000e+00
SIGMA_STAR_Mobil17 0.858778 0.037807 22.714729 0.000000e+00
beta_ScaledIncome_10_inf 0.103554 0.035567 2.911504 3.596934e-03
beta_ScaledIncome_4_6 -0.261303 0.109658 -2.382896 1.717705e-02
beta_ScaledIncome_6_8 0.307877 0.130825 2.353349 1.860516e-02
beta_ScaledIncome_8_10 -0.609012 0.151895 -4.009431 6.086523e-05
beta_ScaledIncome_minus_inf_4 0.132927 0.058350 2.278116 2.271965e-02
coef_age_65_more 0.043546 0.075900 0.573723 5.661553e-01
coef_haveChildren -0.004666 0.056683 -0.082319 9.343931e-01
coef_haveGA -0.698801 0.099494 -7.023522 2.163381e-12
coef_highEducation -0.243846 0.064620 -3.773536 1.609499e-04
coef_individualHouse -0.096344 0.055662 -1.730895 8.347056e-02
coef_intercept 0.390638 0.160522 2.433555 1.495135e-02
coef_male 0.066949 0.053628 1.248395 2.118863e-01
coef_moreThanOneBike -0.377094 0.071787 -5.252978 1.496594e-07
coef_moreThanOneCar 0.641977 0.067389 9.526398 0.000000e+00
delta_1 0.320811 0.012238 26.213302 0.000000e+00
delta_2 0.967383 0.034374 28.143052 0.000000e+00
ec_sigma 0.600340 0.130531 4.599193 4.241302e-06
sigma_s -0.561037 0.161111 -3.482312 4.971044e-04


.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.840 seconds) .. _sphx_glr_download_auto_examples_latent_plot_b06serial_correlation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b06serial_correlation.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b06serial_correlation.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_