.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/hybrid_choice_models/plot_h06_mode_lv_ordprobit_simult.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_hybrid_choice_models_plot_h06_mode_lv_ordprobit_simult.py: Ordered-probit hybrid mode choice model: simultaneous maximum likelihood estimation =================================================================================== This example estimates a hybrid mode choice model with one latent variable and ordered-probit measurement equations. The observed Likert indicators are treated as ordinal responses. Their thresholds, the latent-variable model, and the choice-model parameters are estimated jointly. The model is the ordered-probit counterpart of ``plot_h05_mode_lv_ordlogit_simult``. The hybrid structure, the latent variable, the choice utilities, and the simultaneous maximum-likelihood estimation strategy are the same. Only the ordinal measurement distribution changes: the indicator probabilities are based on normal cumulative distributions instead of logistic cumulative distributions. The latent-variable structure is imported from a separate semantic specification file. This script adds the ordered-probit measurement configuration, the normalization constraints required for identification, the mode-choice utilities, and the simultaneous maximum-likelihood estimation setup. The script performs the following steps: - load the latent-variable and indicator specifications, - define an ordered-probit measurement configuration for all indicators, - define the normalization constraints used for identification, - resolve the semantic specification into an estimable model, - build the Biogeme expressions from the resolved model, - build the choice utilities, including the latent-variable term, - combine the ordered-probit measurement and choice conditional likelihoods, - integrate the combined conditional likelihood over the latent variable, - estimate the hybrid model, or reload previously saved estimation results, - display the estimated parameters as grouped pandas and LaTeX tables. Michel Bierlaire Sat Jun 13 2026, 15:13:40 .. GENERATED FROM PYTHON SOURCE LINES 38-78 .. code-block:: Python from __future__ import annotations from choice_latent_variables import generate_availability, generate_utility_functions from likert_spec import likert_indicators, likert_types from number_of_draws import NUMBER_OF_DRAWS from one_latent_variable_spec import latent_variables from optima import Choice, read_data import biogeme.biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.expressions import MonteCarlo, log from biogeme.latent_variables import ( BuildContext, EstimationMode, Fixing, IndicatorMeasurementSpec, MeasurementConfiguration, MeasurementIntercept, MeasurementLoading, MeasurementModel, MeasurementSigma, NormalizationPlan, PositiveParameterSpec, PositivityMode, build_biogeme_model, resolve_model, ) from biogeme.models import logit from biogeme.results_processing import ( get_latex_estimated_parameters, get_latex_general_statistics, get_pandas_estimated_parameters, ) logger = blog.get_screen_logger(level=blog.INFO) DEFAULT_MEASUREMENT_SIGMA_START = 10.0 .. GENERATED FROM PYTHON SOURCE LINES 79-85 Ordered-probit measurement configuration for all Likert indicators. ------------------------------------------------------------------- The semantic specification, the latent variable, and the mode-choice component are the same as in the ordered-logit example. Only the ordinal measurement distribution changes: ordered logit uses the logistic CDF, whereas ordered probit uses the normal CDF. .. GENERATED FROM PYTHON SOURCE LINES 85-98 .. code-block:: Python measurement_configuration = MeasurementConfiguration( specifications=[ IndicatorMeasurementSpec( indicator_name=indicator.name, measurement_model=MeasurementModel.ORDERED_PROBIT, measurement_sigma=PositiveParameterSpec( start=DEFAULT_MEASUREMENT_SIGMA_START ), ) for indicator in likert_indicators ] ) .. GENERATED FROM PYTHON SOURCE LINES 99-101 Load the Optima data. --------------------- .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. code-block:: Python database = read_data() .. GENERATED FROM PYTHON SOURCE LINES 104-111 Define the build context for maximum likelihood estimation. ----------------------------------------------------------- The build context specifies how the semantic latent-variable specification is translated into estimable Biogeme expressions. We start from the default maximum-likelihood context and explicitly select the log-exp parameterization for positive parameters. The ordinal options control the construction and numerical treatment of ordered-probit thresholds. .. GENERATED FROM PYTHON SOURCE LINES 111-121 .. code-block:: Python default_context = BuildContext.default(EstimationMode.MAXIMUM_LIKELIHOOD) context = BuildContext( estimation_mode=default_context.estimation_mode, draw_type=default_context.draw_type, positivity_mode=PositivityMode.LOG_EXP, naming=default_context.naming, ordinal_eps=default_context.ordinal_eps, ordinal_enforce_order=default_context.ordinal_enforce_order, ) .. GENERATED FROM PYTHON SOURCE LINES 122-146 Identification constraints for the latent variable -------------------------------------------------- Two layers of normalization are needed in this ordered-probit specification. They are the same as in :mod:`plot_h05_mode_lv_ordlogit_simult`. 1. Ordinal measurement-scale normalization The latent response underlying the ordinal indicators has an arbitrary scale. We therefore fix one measurement sigma to 1.0 in order to anchor the overall scale of the ordered-probit measurement model. 2. Latent-variable normalization by reference indicator The latent variable itself is not directly observed, so its location and orientation must also be fixed. We use indicator ``Envir01`` as the reference indicator: - its intercept is fixed to 0.0, which anchors the location of the latent variable; - its loading on ``car_centric_attitude`` is fixed to -1.0, which anchors the scale and fixes the orientation of the latent variable. The negative sign means that higher values of ``car_centric_attitude`` imply lower expected values for ``Envir01``. With these constraints in place, the remaining intercepts, loadings, and thresholds are interpreted relative to the chosen reference and measurement scale. .. GENERATED FROM PYTHON SOURCE LINES 146-171 .. code-block:: Python normalization_plan = NormalizationPlan() normalization_plan.add( Fixing( MeasurementSigma('Envir01'), 1.0, note='ordered-probit measurement model: scale normalization', ) ) normalization_plan.add( Fixing( MeasurementIntercept('Envir01'), 0.0, note='car_centric_attitude reference indicator: location', ) ) normalization_plan.add( Fixing( MeasurementLoading('car_centric_attitude', 'Envir01'), -1.0, note='car_centric_attitude reference indicator: scale and orientation', ) ) .. GENERATED FROM PYTHON SOURCE LINES 172-177 Resolve the semantic specification. ----------------------------------- The resolver combines the latent-variable specification, the indicator definitions, the ordered-probit measurement configuration, and the normalization plan into an internal resolved model. .. GENERATED FROM PYTHON SOURCE LINES 177-186 .. code-block:: Python resolved_model = resolve_model( latent_variables=latent_variables, likert_indicators=likert_indicators, likert_types=likert_types, measurement_configuration=measurement_configuration, context=context, normalization_plan=normalization_plan, ) .. GENERATED FROM PYTHON SOURCE LINES 187-193 Build the Biogeme expressions. ------------------------------ The builder translates the resolved model into expressions that can be used by Biogeme for simultaneous maximum-likelihood estimation. It also provides report-ready parameter groups based on the parameters that are actually estimated. .. GENERATED FROM PYTHON SOURCE LINES 193-195 .. code-block:: Python built_model = build_biogeme_model(resolved_model) .. GENERATED FROM PYTHON SOURCE LINES 196-198 Choice utilities including the latent-variable term. ---------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 198-200 .. code-block:: Python utilities = generate_utility_functions(built_model.latent_expressions) .. GENERATED FROM PYTHON SOURCE LINES 201-203 Conditional likelihood of the mode choice model ----------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 203-206 .. code-block:: Python availability = generate_availability() conditional_choice_likelihood = logit(utilities, availability, Choice) .. GENERATED FROM PYTHON SOURCE LINES 207-213 Combined conditional likelihood. -------------------------------- The ordered-probit measurement component and the mode-choice component are multiplied conditionally on the latent variable. The product is later integrated over the latent-variable distribution, so all components are estimated jointly in one likelihood. .. GENERATED FROM PYTHON SOURCE LINES 213-217 .. code-block:: Python combined_conditional_likelihood = ( built_model.conditional_likelihood * conditional_choice_likelihood ) .. GENERATED FROM PYTHON SOURCE LINES 218-223 Log-likelihood. --------------- The combined conditional likelihood is integrated over the latent variable by Monte Carlo. Taking the logarithm of the resulting integrated likelihood yields the log-likelihood used for simultaneous maximum-likelihood estimation. .. GENERATED FROM PYTHON SOURCE LINES 223-226 .. code-block:: Python integrated_likelihood = MonteCarlo(combined_conditional_likelihood) log_likelihood = log(integrated_likelihood) .. GENERATED FROM PYTHON SOURCE LINES 227-230 Estimate the model with Biogeme. -------------------------------- Existing results are reloaded from the YAML file when available. .. GENERATED FROM PYTHON SOURCE LINES 230-243 .. code-block:: Python biogeme = BIOGEME( database, log_likelihood, number_of_draws=NUMBER_OF_DRAWS, calculating_second_derivatives='never', max_iterations=5_000, group_of_parameters=built_model.parameter_groups, ) biogeme.model_name = 'plot_h06_mode_lv_ordprobit_simult' yaml_file_name = f'saved_results/{biogeme.model_name}.yaml' results = biogeme.estimate_or_load(yaml_file_name=yaml_file_name) .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. Estimation results are read from saved_results/plot_h06_mode_lv_ordprobit_simult.yaml. No estimation is performed. .. GENERATED FROM PYTHON SOURCE LINES 244-245 Display a compact summary and the estimated parameters. .. GENERATED FROM PYTHON SOURCE LINES 245-264 .. code-block:: Python print(results.short_summary()) pandas_results = get_pandas_estimated_parameters( estimation_results=results, group_of_parameters=built_model.parameter_groups, ) for group_name, pandas_table in pandas_results.items(): print(group_name if group_name else 'Estimated parameters') print(pandas_table) general_statistics = get_latex_general_statistics(estimation_results=results) print(general_statistics) estimated_parameters = get_latex_estimated_parameters( estimation_results=results, group_of_parameters=built_model.parameter_groups, ) for group_name, latex_table in estimated_parameters.items(): print(group_name if group_name else 'Estimated parameters') print(latex_table) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model plot_h06_mode_lv_ordprobit_simult Nbr of parameters: 41 Sample size: 889 Excluded data: 0 Final log likelihood: -10513.91 Akaike Information Criterion: 21109.81 Bayesian Information Criterion: 21306.21 Structural equation Name ... BHHH p-value 0 struct_car_centric_attitude_intercept ... 0.075114 1 struct_car_centric_attitude_top_manager ... 0.403969 2 struct_car_centric_attitude_car_oriented_parents ... 0.000905 3 struct_car_centric_attitude_high_education ... 0.000083 4 struct_car_centric_attitude_low_education ... 0.124619 5 struct_car_centric_attitude_used_to_go_to_scho... ... 0.833168 6 struct_car_centric_attitude_sigma_log ... 0.000768 [7 rows x 5 columns] Measurement equation: Envir02 Name ... BHHH p-value 9 measurement_intercept_Envir02 ... 5.537825e-05 10 measurement_coefficient_car_centric_attitude_E... ... 6.661338e-16 11 measurement_Envir02_sigma_log ... 5.168503e-01 [3 rows x 5 columns] Measurement equation: Envir06 Name ... BHHH p-value 12 measurement_intercept_Envir06 ... 3.654128e-08 13 measurement_coefficient_car_centric_attitude_E... ... 2.220446e-16 14 measurement_Envir06_sigma_log ... 2.903386e-03 [3 rows x 5 columns] Measurement equation: Mobil03 Name ... BHHH p-value 15 measurement_intercept_Mobil03 ... 0.000049 16 measurement_coefficient_car_centric_attitude_M... ... 0.000095 17 measurement_Mobil03_sigma_log ... 0.115023 [3 rows x 5 columns] Measurement equation: Mobil05 Name ... BHHH p-value 18 measurement_intercept_Mobil05 ... 5.035287e-04 19 measurement_coefficient_car_centric_attitude_M... ... 2.897928e-07 20 measurement_Mobil05_sigma_log ... 1.421514e-02 [3 rows x 5 columns] Measurement equation: Mobil08 Name ... BHHH p-value 21 measurement_intercept_Mobil08 ... 4.099686e-02 22 measurement_coefficient_car_centric_attitude_M... ... 1.875502e-07 23 measurement_Mobil08_sigma_log ... 2.136033e-02 [3 rows x 5 columns] Measurement equation: Mobil09 Name ... BHHH p-value 24 measurement_intercept_Mobil09 ... 1.430767e-06 25 measurement_coefficient_car_centric_attitude_M... ... 2.782219e-13 26 measurement_Mobil09_sigma_log ... 3.559064e-01 [3 rows x 5 columns] Measurement equation: Mobil10 Name ... BHHH p-value 27 measurement_intercept_Mobil10 ... 0.082884 28 measurement_coefficient_car_centric_attitude_M... ... 0.046027 29 measurement_Mobil10_sigma_log ... 0.004523 [3 rows x 5 columns] Measurement equation: LifSty07 Name ... BHHH p-value 30 measurement_intercept_LifSty07 ... 0.618804 31 measurement_coefficient_car_centric_attitude_L... ... 0.001783 32 measurement_LifSty07_sigma_log ... 0.041254 [3 rows x 5 columns] Thresholds Name Value BHHH std err. BHHH t-stat. BHHH p-value 7 likert_delta_0_log -2.488002 0.273636 -9.092392 0.000000 8 likert_delta_1_log -0.289956 0.152476 -1.901651 0.057217 Other parameters Name Value ... BHHH t-stat. BHHH p-value 33 choice_scale_parameter 0.063369 ... 6.691395 2.210521e-11 34 choice_asc_pt -12.198163 ... -2.539270 1.110839e-02 35 choice_beta_time_pt -16.186182 ... -4.050445 5.112029e-05 36 choice_asc_car 0.483516 ... 0.120118 9.043895e-01 37 choice_beta_time_car -33.694551 ... -5.030607 4.889290e-07 38 choice_beta_car_centric_attitude_car 8.809996 ... 4.504705 6.646528e-06 39 choice_beta_dist_work -3.241247 ... -5.939673 2.855909e-09 40 choice_beta_dist_other_purposes -5.206535 ... -5.543031 2.972801e-08 [8 rows x 5 columns] %% General statistics \section{General statistics} \begin{tabular}{ll} Number of estimated parameters & 41 \\ Sample size & 889 \\ Excluded observations & 0 \\ Init log likelihood & -21721.48 \\ Final log likelihood & -10513.91 \\ Likelihood ratio test for the init. model & 22415.15 \\ Rho-square for the init. model & 0.516 \\ Rho-square-bar for the init. model & 0.514 \\ Akaike Information Criterion & 21109.81 \\ Bayesian Information Criterion & 21306.21 \\ Final gradient norm & 1.2349E-01 \\ Number of draws & 50000 \\ Draws generation time & 0:00:13.090624 \\ Types of draws & struct\_car\_centric\_attitude\_draws: NORMAL\_MLHS\_ANTI \\ Bootstrapping time & None \\ Algorithm & \verb$BFGS with trust region for simple bound constraints$ \\ Cause of termination & \verb$Relative gradient = 4.7e-06 <= 6.1e-06$ \\ Number of function evaluations & \verb$1536$ \\ Number of gradient evaluations & \verb$899$ \\ Number of hessian evaluations & \verb$0$ \\ Number of iterations & \verb$637$ \\ Optimization time & \verb$3:39:20.228159$ \\ Proportion of Hessian calculation & \verb$0/449 = 0.0%$ \\ Relative gradient & \verb$4.668e-06$ \\ \end{tabular} Structural equation \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 0 & struct\_car\_centric\_attitude\_intercept & -0&275 & 0&155 & -1&78 & 0&0751 \\ 1 & struct\_car\_centric\_attitude\_top\_manager & 0&152 & 0&183 & 0&835 & 0&404 \\ 2 & struct\_car\_centric\_attitude\_car\_oriented\_parents & 0&436 & 0&131 & 3&32 & 0&000905 \\ 3 & struct\_car\_centric\_attitude\_high\_education & -0&646 & 0&164 & -3&93 & 8&34e-05 \\ 4 & struct\_car\_centric\_attitude\_low\_education & 0&246 & 0&160 & 1&54 & 0&125 \\ 5 & struct\_car\_centric\_attitude\_used\_to\_go\_to\_school\_by\_car & 0&150 & 0&710 & 0&211 & 0&833 \\ 6 & struct\_car\_centric\_attitude\_sigma\_log & 0&286 & 0&0849 & 3&36 & 0&000768 \\ \end{tabular} Measurement equation: Envir02 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 9 & measurement\_intercept\_Envir02 & 0&828 & 0&205 & 4&03 & 5&54e-05 \\ 10 & measurement\_coefficient\_car\_centric\_attitude\_Envir02 & -0&472 & 0&0585 & -8&06 & 6&66e-16 \\ 11 & measurement\_Envir02\_sigma\_log & -0&120 & 0&185 & -0&648 & 0&517 \\ \end{tabular} Measurement equation: Envir06 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 12 & measurement\_intercept\_Envir06 & 1&37 & 0&249 & 5&51 & 3&65e-08 \\ 13 & measurement\_coefficient\_car\_centric\_attitude\_Envir06 & -0&318 & 0&0385 & -8&25 & 2&22e-16 \\ 14 & measurement\_Envir06\_sigma\_log & -0&492 & 0&165 & -2&98 & 0&00290 \\ \end{tabular} Measurement equation: Mobil03 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 15 & measurement\_intercept\_Mobil03 & 1&01 & 0&247 & 4&06 & 4&88e-05 \\ 16 & measurement\_coefficient\_car\_centric\_attitude\_Mobil03 & -0&198 & 0&0506 & -3&90 & 9&54e-05 \\ 17 & measurement\_Mobil03\_sigma\_log & 0&309 & 0&196 & 1&58 & 0&115 \\ \end{tabular} Measurement equation: Mobil05 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 18 & measurement\_intercept\_Mobil05 & 1&41 & 0&404 & 3&48 & 0&000504 \\ 19 & measurement\_coefficient\_car\_centric\_attitude\_Mobil05 & -0&509 & 0&0992 & -5&13 & 2&90e-07 \\ 20 & measurement\_Mobil05\_sigma\_log & 0&555 & 0&227 & 2&45 & 0&0142 \\ \end{tabular} Measurement equation: Mobil08 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 21 & measurement\_intercept\_Mobil08 & 0&244 & 0&119 & 2&04 & 0&0410 \\ 22 & measurement\_coefficient\_car\_centric\_attitude\_Mobil08 & 0&423 & 0&0812 & 5&21 & 1&88e-07 \\ 23 & measurement\_Mobil08\_sigma\_log & 0&495 & 0&215 & 2&30 & 0&0214 \\ \end{tabular} Measurement equation: Mobil09 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 24 & measurement\_intercept\_Mobil09 & 1&24 & 0&257 & 4&82 & 1&43e-06 \\ 25 & measurement\_coefficient\_car\_centric\_attitude\_Mobil09 & -0&326 & 0&0446 & -7&30 & 2&78e-13 \\ 26 & measurement\_Mobil09\_sigma\_log & -0&166 & 0&180 & -0&923 & 0&356 \\ \end{tabular} Measurement equation: Mobil10 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 27 & measurement\_intercept\_Mobil10 & 4&32 & 2&49 & 1&73 & 0&0829 \\ 28 & measurement\_coefficient\_car\_centric\_attitude\_Mobil10 & 1&89 & 0&948 & 2&00 & 0&0460 \\ 29 & measurement\_Mobil10\_sigma\_log & 1&56 & 0&548 & 2&84 & 0&00452 \\ \end{tabular} Measurement equation: LifSty07 \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 30 & measurement\_intercept\_LifSty07 & -0&0481 & 0&0968 & -0&498 & 0&619 \\ 31 & measurement\_coefficient\_car\_centric\_attitude\_LifSty07 & 0&157 & 0&0503 & 3&12 & 0&00178 \\ 32 & measurement\_LifSty07\_sigma\_log & 0&453 & 0&222 & 2&04 & 0&0413 \\ \end{tabular} Thresholds \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 7 & likert\_delta\_0\_log & -2&49 & 0&274 & -9&09 & 0&00 \\ 8 & likert\_delta\_1\_log & -0&290 & 0&152 & -1&90 & 0&0572 \\ \end{tabular} Other parameters \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l} & & \multicolumn{2}{l}{} & \multicolumn{2}{l}{BHHH} & \multicolumn{4}{l}{} \\ Parameter & & \multicolumn{2}{l}{Coeff.} & \multicolumn{2}{l}{Asympt.} & \multicolumn{4}{l}{} \\ number & Description & \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error} & \multicolumn{2}{l}{$t$-stat} & \multicolumn{2}{l}{$p$-value} \\ \hline 33 & choice\_scale\_parameter & 0&0634 & 0&00947 & 6&69 & 2&21e-11 \\ 34 & choice\_asc\_pt & -12&2 & 4&80 & -2&54 & 0&0111 \\ 35 & choice\_beta\_time\_pt & -16&2 & 4&00 & -4&05 & 5&11e-05 \\ 36 & choice\_asc\_car & 0&484 & 4&03 & 0&120 & 0&904 \\ 37 & choice\_beta\_time\_car & -33&7 & 6&70 & -5&03 & 4&89e-07 \\ 38 & choice\_beta\_car\_centric\_attitude\_car & 8&81 & 1&96 & 4&50 & 6&65e-06 \\ 39 & choice\_beta\_dist\_work & -3&24 & 0&546 & -5&94 & 2&86e-09 \\ 40 & choice\_beta\_dist\_other\_purposes & -5&21 & 0&939 & -5&54 & 2&97e-08 \\ \end{tabular} .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.394 seconds) .. _sphx_glr_download_auto_examples_hybrid_choice_models_plot_h06_mode_lv_ordprobit_simult.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download 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