.. _sphx_glr_auto_examples_hybrid_choice_models:

Hybrid choice models
********************

Examples of discrete choice models with latent variables.




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    <div class="sphx-glr-thumbcontainer" tooltip="This module defines the systematic utility functions of the mode-choice model. It illustrates how a choice model is specified independently of the latent-variable model and how latent variables can subsequently be injected into the utility functions.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_choice_latent_variables_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/choice_latent_variables`

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      <div class="sphx-glr-thumbnail-title">Choice model specification used in the latent-variable tutorial.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This script scans the current directory for Python files whose names start with plot_ and automatically generates corresponding SLURM .run submission scripts for each of them.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_generate_jed_run_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/generate_jed_run`

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      <div class="sphx-glr-thumbnail-title">Generate SLURM run scripts for Biogeme experiments.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Pure semantic indicator declarations Michel Bierlaire Sat Mar 14 2026, 16:26:11">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_likert_spec_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/likert_spec`

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      <div class="sphx-glr-thumbnail-title">Likert indicators and Likert types (SPEC ONLY)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This module contains a single constant shared across several examples. It is intentionally isolated so that the number of draws can be modified in one place and propagated consistently throughout the examples.">

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  :doc:`/auto_examples/hybrid_choice_models/number_of_draws`

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      <div class="sphx-glr-thumbnail-title">Number of Monte-Carlo draws used by the hybrid choice model examples.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Pure specification: what depends on what.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_one_latent_variable_spec_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/one_latent_variable_spec`

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      <div class="sphx-glr-thumbnail-title">Latent variables (SPEC ONLY)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Optima data preparation for Biogeme.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_optima_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/optima`

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      <div class="sphx-glr-thumbnail-title">Data preparation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example estimates a multinomial logit model for transportation mode choice using maximum likelihood and Biogeme.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h01_mode_logit_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h01_mode_logit`

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      <div class="sphx-glr-thumbnail-title">Baseline mode choice model: maximum likelihood estimation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example estimates a Gaussian MIMIC model with one latent variable and no choice component. The observed Likert indicators are treated as continuous responses and modeled with Gaussian measurement equations.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h02_lv_mimic_gauss_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h02_lv_mimic_gauss`

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      <div class="sphx-glr-thumbnail-title">Gaussian MIMIC model: maximum likelihood estimation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the second step of a sequential estimation procedure.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h03_mode_lv_gauss_seq_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h03_mode_lv_gauss_seq`

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      <div class="sphx-glr-thumbnail-title">Sequential estimation of a choice model with a latent variable</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example estimates a hybrid mode choice model with one latent variable and Gaussian measurement equations. The observed Likert indicators are treated as continuous responses and modeled with Gaussian measurement equations.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h04_mode_lv_gauss_simult_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h04_mode_lv_gauss_simult`

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      <div class="sphx-glr-thumbnail-title">Gaussian hybrid mode choice model: simultaneous maximum likelihood estimation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example estimates a hybrid mode choice model with one latent variable and ordered-logit measurement equations. The observed Likert indicators are modeled as ordinal responses, and the associated threshold parameters are estimated jointly with the latent-variable and choice-model parameters.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h05_mode_lv_ordlogit_simult_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h05_mode_lv_ordlogit_simult`

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      <div class="sphx-glr-thumbnail-title">Ordered-logit hybrid mode choice model: simultaneous maximum likelihood estimation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h06_mode_lv_ordprobit_simult_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h06_mode_lv_ordprobit_simult`

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      <div class="sphx-glr-thumbnail-title">Ordered-probit hybrid mode choice model: simultaneous maximum likelihood estimation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip=" This example estimates a hybrid choice model where a latent variable, interpreted as a car-centric attitude, influences the utilities of a mode-choice model. The latent variable is described by a structural equation and is measured through several attitudinal indicators using ordered-probit measurement equations.">

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  .. image:: /auto_examples/hybrid_choice_models/images/thumb/sphx_glr_plot_h07_mode_lv_ordprobit_simult_generated_thumb.png
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  :doc:`/auto_examples/hybrid_choice_models/plot_h07_mode_lv_ordprobit_simult_generated`

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      <div class="sphx-glr-thumbnail-title">Simultaneous hybrid choice model with ordered-probit indicators.</div>
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.. toctree::
   :hidden:

   /auto_examples/hybrid_choice_models/choice_latent_variables
   /auto_examples/hybrid_choice_models/generate_jed_run
   /auto_examples/hybrid_choice_models/likert_spec
   /auto_examples/hybrid_choice_models/number_of_draws
   /auto_examples/hybrid_choice_models/one_latent_variable_spec
   /auto_examples/hybrid_choice_models/optima
   /auto_examples/hybrid_choice_models/plot_h01_mode_logit
   /auto_examples/hybrid_choice_models/plot_h02_lv_mimic_gauss
   /auto_examples/hybrid_choice_models/plot_h03_mode_lv_gauss_seq
   /auto_examples/hybrid_choice_models/plot_h04_mode_lv_gauss_simult
   /auto_examples/hybrid_choice_models/plot_h05_mode_lv_ordlogit_simult
   /auto_examples/hybrid_choice_models/plot_h06_mode_lv_ordprobit_simult
   /auto_examples/hybrid_choice_models/plot_h07_mode_lv_ordprobit_simult_generated