:orphan:

Gallery of examples
###################




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Assisted specification with Biogeme
***********************************

Examples discussed in `Bierlaire and Ortelli (2023) Assisted Specification with Biogeme 3.2.12
<https://transp-or.epfl.ch/documents/technicalReports/BierOrte23.pdf>`_




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    <div class="sphx-glr-thumbcontainer" tooltip="We combine the following specifications:">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_everything_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_everything_spec.py`

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      <div class="sphx-glr-thumbnail-title">Combination of many specifications</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Logit model.">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b00logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b00logit.py`

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      <div class="sphx-glr-thumbnail-title">Base model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Investigate several choice models:">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b01model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b01model.py`

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      <div class="sphx-glr-thumbnail-title">Investigation of several choice models</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Investigate of nonlinear specifications for the travel time variables:">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b02nonlinear_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b02nonlinear.py`

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      <div class="sphx-glr-thumbnail-title">Catalog of nonlinear specifications</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Investigate alternative specific parameters:">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b03alt_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b03alt_spec.py`

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      <div class="sphx-glr-thumbnail-title">Catalog for alternative specific coefficients</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Investigate the segmentations of parameters.">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b04segmentation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b04segmentation.py`

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      <div class="sphx-glr-thumbnail-title">Catalog for segmented parameters</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We consider 4 specifications for the constants:">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b05alt_spec_segmentation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b05alt_spec_segmentation.py`

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      <div class="sphx-glr-thumbnail-title">Segmentations and alternative specific specification</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We combine many specifications, defined in everything_spec_section. This leads to a total of 432 specifications. When the total number of specifications exceeds 100, Biogeme raises an ValueOutOfRange exception when the estimate_catalog is called. See Bierlaire and Ortelli (2023).">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b06everything_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b06everything.py`

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      <div class="sphx-glr-thumbnail-title">Combine many specifications: exception is raised</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We combine many specifications, defined in everything_spec_section. This leads to a total of 432 specifications. The algorithm implemented in the AssistedSpecification object is used to investigate some of these specifications. See Bierlaire and Ortelli (2023).">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b07everything_assisted_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b07everything_assisted.py`

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      <div class="sphx-glr-thumbnail-title">Combine many specifications: assisted specification algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We consider the model with 432 specifications defined in everything_spec_section. We select one specification and estimate it. See Bierlaire and Ortelli (2023).">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b08selected_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b08selected_specification.py`

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      <div class="sphx-glr-thumbnail-title">One model among many</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="After running the assisted specification algorithm for the 432 specifications in everything_spec_section, we use post-processing to re-estimate all Pareto optimal models, and display some information about the algorithm. See Bierlaire and Ortelli (2023).">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_b09post_processing_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_b09post_processing.py`

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      <div class="sphx-glr-thumbnail-title">Re-estimation of best models</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Illustration of the concept of catalog. See Bierlaire and Ortelli (2023)">

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  .. image:: /auto_examples/assisted/images/thumb/sphx_glr_plot_simple_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_assisted_plot_simple_example.py`

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      <div class="sphx-glr-thumbnail-title">Example of a catalog</div>
    </div>


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Biogeme examples for Bayesian inference with the Swissmetro data
****************************************************************

You find here several examples of models that illustrate how to specify models to be estimated with Biogeme using
Bayesian inference. To the extent possible, we have used the same examples illustrating the maximum
likelihood estimation. The names of the files should correspond too.





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    <div class="sphx-glr-thumbcontainer" tooltip=" Three alternatives:">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01a_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b01a_logit.py`

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      <div class="sphx-glr-thumbnail-title">1a. Estimation of a logit model (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" This example illustrates how to change the prior distribution of the parameters.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01b_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b01b_logit.py`

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      <div class="sphx-glr-thumbnail-title">1b. Estimation of a logit model (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of simulation with a logit model">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01c_logit_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b01c_logit_simul.py`

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      <div class="sphx-glr-thumbnail-title">1c. Simulation of a logit model (traditional and Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a logit model with a weighted sample">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b02_weight_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b02_weight.py`

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      <div class="sphx-glr-thumbnail-title">2. Logit and sample with weights (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Although normalizing the scale to 1 is a common practice in random utility models, it is sometimes preferable to normalize another parameter. For instance, normalizing the cost coefficient to -1 sets the units of the utility function as currency units (CHF here), and the estimated coefficients are easily interpreted as willingness to pay. In that case, the scale must be estimated.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b03_scale_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b03_scale.py`

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      <div class="sphx-glr-thumbnail-title">3. Moneymetric and heteroscedastic specification</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of the out-of-sample validation of a logit model in a Bayesian estimation context.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b04_validation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b04_validation.py`

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      <div class="sphx-glr-thumbnail-title">4. Out-of-sample validation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of a normal mixture of logit models, using Bayesian inference.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b05_normal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b05_normal_mixture.py`

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      <div class="sphx-glr-thumbnail-title">5. Mixture of logit models: normal distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of a uniform mixture of logit models, using Bayesian inference.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b06_unif_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b06_unif_mixture.py`

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      <div class="sphx-glr-thumbnail-title">6. Mixture of logit models: uniform distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit (or latent class model).">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b07_discrete_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b07_discrete_mixture.py`

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      <div class="sphx-glr-thumbnail-title">7. Latent class model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a logit model, with a Box-Cox transform of variables.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b08_boxcox_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b08_boxcox.py`

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      <div class="sphx-glr-thumbnail-title">8. Box-Cox transforms</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a nested logit model.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b09_nested_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b09_nested.py`

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      <div class="sphx-glr-thumbnail-title">9. Nested logit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a nested logit model where the normalization is done at the  bottom level.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b10_nested_bottom_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b10_nested_bottom.py`

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      <div class="sphx-glr-thumbnail-title">10. Nested logit model normalized from bottom</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a cross-nested logit model with two nests:">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b11_cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b11_cnl.py`

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      <div class="sphx-glr-thumbnail-title">11. Cross-nested logit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a mixture of logit models. The datafile is organized as panel data. Note that, with Bayesian estimation, there is no need to calculate a Monte-Carlo integration.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b12_panel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b12_panel.py`

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      <div class="sphx-glr-thumbnail-title">12. Mixture of logit with panel data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit models, also called latent class model.  The datafile is organized as panel data.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b15_panel_discrete_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b15_panel_discrete.py`

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      <div class="sphx-glr-thumbnail-title">15. Discrete mixture with panel data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit models, also called latent class model. The class membership model includes socio-economic variables. The datafile is organized as panel data.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b16_panel_discrete_socio_eco_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b16_panel_discrete_socio_eco.py`

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      <div class="sphx-glr-thumbnail-title">16. Latent class model with panel data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a mixture of logit models. The mixing distribution is distributed as a log normal.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b17_lognormal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b17_lognormal_mixture.py`

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      <div class="sphx-glr-thumbnail-title">17. Mixture with lognormal distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of an ordinal logit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b18a_ordinal_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b18a_ordinal_logit.py`

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      <div class="sphx-glr-thumbnail-title">18a. Ordinal logit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of an ordinal probit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b18b_ordinal_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b18b_ordinal_probit.py`

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      <div class="sphx-glr-thumbnail-title">18. Ordinal probit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of the individual level parameters for the model defined in plot_b05_normal_mixture.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b19_individual_level_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b19_individual_level_parameters.py`

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      <div class="sphx-glr-thumbnail-title">19. Calculation of individual level parameters</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a binary logit model. Two alternatives: Train and Car.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b23a_binary_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b23a_binary_logit.py`

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      <div class="sphx-glr-thumbnail-title">23a. Binary logit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a binary probit model. Two alternatives: Train and Car. All observations such that the Swissmetro was chosen haven been removed from the sample.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b23b_binary_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b23b_binary_probit.py`

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      <div class="sphx-glr-thumbnail-title">23b. Binary probit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a mixture of logit models.  The mixing distribution is specified by the user. Here, a triangular  distribution.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b25_triangular_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b25_triangular_mixture.py`

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      <div class="sphx-glr-thumbnail-title">25. Triangular mixture of logit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a mixture of logit models.  The mixing distribution is user-defined (triangular, here).  The datafile is organized as panel data.">

.. only:: html

  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b26triangular_panel_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_plot_b26triangular_panel_mixture.py`

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      <div class="sphx-glr-thumbnail-title">26. Triangular mixture with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation for Swissmetro, and definition of the variables. The data is designed to estimate binary logit models. All observations such that Swissmetro was chosen are removed.">

.. only:: html

  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_swissmetro_binary_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_swissmetro_binary.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro (binary choice)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation and definition of the variables.">

.. only:: html

  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_swissmetro_data_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_swissmetro_data.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation for Swissmetro, and definition of the variables in panel configuration">

.. only:: html

  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_swissmetro_panel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_bayesian_swissmetro_swissmetro_panel.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Panel data preparation for Swissmetro</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Biogeme examples for hybrid choice models
*****************************************

This directory provides example implementations of MIMIC and hybrid
choice models estimated with Biogeme, using both maximum likelihood
and Bayesian methods. The examples range from latent-variable-only
models to fully integrated hybrid choice models and are intended as
reproducible references and learning material.





.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Choice model specification with optional latent-variable interactions.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_choice_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_choice_model.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Choice model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Central configuration for running estimation scripts.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_config_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_config.py`

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      <div class="sphx-glr-thumbnail-title">Configuration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation pipeline for discrete and hybrid choice models.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_estimate_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_estimate.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Model estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate SLURM .run job scripts for batch execution on the JED cluster.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_generate_jed_run_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_generate_jed_run.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Prepare for server</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Definitions of latent variables used in the hybrid choice model.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_latent_variables_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_latent_variables.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Latent variables</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Definition of Likert indicators and Likert scale types used in the hybrid choice model.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_likert_indicators_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_likert_indicators.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Likert indicators</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Construction of the MIMIC (latent-variable) component of the hybrid choice model.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_mimic_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_mimic.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MIMIC model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Optima data preparation for Biogeme.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_optima_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_optima.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script runs a standard discrete choice model without any latent variables, estimated by maximum likelihood using Biogeme.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b01_choice_only_ml_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b01_choice_only_ml.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1. Choice model only - maximum likelihood estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script estimates a pure MIMIC model (measurement and structural components only) using maximum likelihood, without an associated discrete choice model.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b02_mimic_ml_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b02_mimic_ml.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2. MIMIC model - maximum likelihood estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script estimates a hybrid choice model that combines:">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b03_hybrid_ml_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b03_hybrid_ml.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">3. Hybrid choice model - maximum likelihood estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script estimates a standard discrete choice model without any latent variables using Bayesian estimation in Biogeme.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b04_choice_only_bayes_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b04_choice_only_bayes.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">4. Choice model only - Bayesian estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script estimates a pure MIMIC model (latent-variable structural and measurement equations only) using Bayesian estimation in Biogeme, without an associated discrete choice model.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b05_mimic_bayes_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b05_mimic_bayes.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">5. MIMIC model - Bayesian estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script estimates the full hybrid choice model, combining:">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_plot_b06_hybrid_bayes_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_plot_b06_hybrid_bayes.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">6. Hybrid choice model - Bayesian estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Utility functions to either read previously estimated parameters from disk or run a new estimation if no results are available.">

.. only:: html

  .. image:: /auto_examples/hybrid_choice/images/thumb/sphx_glr_read_or_estimate_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_hybrid_choice_read_or_estimate.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Read or estimate model parameters</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Calculating indicators with Biogeme
***********************************

Examples discussed in `Bierlaire (2018) Calculating indicators with PandasBiogeme
<http://transp-or.epfl.ch/documents/technicalReports/Bier18a.pdf>`_





.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of manipulating mathematical expressions and calculation of derivatives.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b01expressions_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b01expressions.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Examples of mathematical expressions</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" We estimate a nested logit model, and we perform simulation using the  estimated model.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b02estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b02estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Estimation and simulation of a nested logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use an estimated model to perform various simulations.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b03simulation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b03simulation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simulation of a choice model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use an estimated model to calculate market shares.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b04market_shares_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b04market_shares.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calculation of market shares</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use an estimated model to calculate revenues.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b05revenues_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b05revenues.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calculation of revenues</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use a previously estimated nested logit model and calculate  disaggregate and aggregate direct point elasticities.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b06point_elasticities_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b06point_elasticities.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Direct point elasticities</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use a previously estimated nested logit model and calculate disaggregate and aggregate cross point elasticities.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b07cross_elasticities_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b07cross_elasticities.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cross point elasticities</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We use a previously estimated nested logit model and calculate arc elasticities.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b08arc_elasticities_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b08arc_elasticities.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arc elasticities</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We calculate and plot willingness to pay. Details about this example are available in Section 4 of Bierlaire (2018) Calculating indicators with PandasBiogeme">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_plot_b09wtp_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_plot_b09wtp.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calculation of willingness to pay</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Specification of a nested logit model, that will be estimated, and  used for simulation.  Three alternatives: public transportation, car  and slow modes.  RP data.  Based on the Optima data.  It contains a  function that generates scenarios where the current cost of public  transportation is multiplied by a factor.">

.. only:: html

  .. image:: /auto_examples/indicators/images/thumb/sphx_glr_scenarios_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_indicators_scenarios.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Specification of a nested logit model</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Examples for the MDCEV model
****************************


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:35:52">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_gamma_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_gamma_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File gamma_specification.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:36:06">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_generalized_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_generalized_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File generalized_specification.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:36:49 Specification of the &quot;non monotonic utility&quot; MDCEV model.">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_non_monotonic_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_non_monotonic_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File non_monotonic_specification.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:36:50 Estimation of a MDCEV model with the &quot;gamma_profile&quot; specification.">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_gamma_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_gamma_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File gamma_estimation.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:38:12 Forecasting with a MDCEV model and the &quot;gamma_profile&quot; specification.">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_gamma_forecasting_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_gamma_forecasting.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File gamma_forecasting.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 16:51:40">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_generalized_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_generalized_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File generalized_estimation.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:05:32">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_generalized_forecasting_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_generalized_forecasting.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File generalized_forecasting.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:14:53">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_non_monotonic_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_non_monotonic_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File non_monotonic_estimation.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:27:35">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_non_monotonic_forecasting_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_non_monotonic_forecasting.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File non_monotonic_forecasting.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:28:50">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_translated_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_translated_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File translated_estimation.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:34:35">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_plot_translated_forecasting_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_plot_translated_forecasting.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File translated_forecasting.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:07:29">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_process_data_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_process_data.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File process_data.py</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:06:56">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Specification of the baseline utilities of a MDCEV model.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Fri Jul 25 2025, 17:59:01">

.. only:: html

  .. image:: /auto_examples/mdcev_no_outside_good/images/thumb/sphx_glr_translated_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_mdcev_no_outside_good_translated_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">File translated_specification.py</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Monte-Carlo integration with Biogeme
************************************

Example discussed in `Bierlaire (2019) Monte-Carlo integration with
Biogeme
<https://transp-or.epfl.ch/documents/technicalReports/Bier19.pdf>`_





.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Creation of the Biogeme object for a mixtures of logit models where the integral is approximated using MonteCarlo integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_b07estimation_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_b07estimation_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Specification of the mixtures of logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a simple integral using Monte-Carlo integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b01simple_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b01simple_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simple integral</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a simple integral using numerical integration and Monte-Carlo integration with various types of draws, including Halton draws base 13. It illustrates how to use draws that are not directly available in Biogeme.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b02simple_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b02simple_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Various integration methods</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a simple integral using Monte-Carlo integration. It illustrates how to use antithetic draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b03antithetic_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b03antithetic.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Antithetic draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a simple integral using Monte-Carlo integration. It illustrates how to use antithetic draws, explicitly generated.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b03antithetic_explicit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b03antithetic_explicit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Antithetic draws explicitly generated</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a mixtures of logit models where the integral is calculated using numerical integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b04normal_mixture_numerical_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b04normal_mixture_numerical.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Numerical integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of a mixtures of logit models where the integral is calculated using numerical integration and Monte-Carlo integration with various types of draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b05normal_mixture_monte_carlo_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b05normal_mixture_monte_carlo.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Monte-Carlo integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is calculated using numerical integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b06estimation_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b06estimation_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Estimation of mixtures of logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 10_000 draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_500_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_500.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 500 draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with antithetic draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_anti_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_anti.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 10_000 antithetic draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with antithetic draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_anti_500_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_anti_500.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 500 antithetic draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with Halton draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_halton_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_halton.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 10_000 Halton draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with Halton draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_halton_500_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_halton_500.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 500 Halton draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with MLHS draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_mlhs_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_mlhs.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 10_000 MLHS draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with MLHS draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_mlhs_500_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_mlhs_500.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 500 MLHS draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with antithetic MLHS draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_mlhs_anti_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_mlhs_anti.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 10_000 antithetic MLHS draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with antithetic MLHS draws.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_plot_b07estimation_monte_carlo_mlhs_anti_500_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_plot_b07estimation_monte_carlo_mlhs_anti_500.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixtures of logit with Monte-Carlo 2000 antithetic MLHS draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reading data and defining variables.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_swissmetro_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_swissmetro.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Use only the first observation for simulation.">

.. only:: html

  .. image:: /auto_examples/montecarlo/images/thumb/sphx_glr_swissmetro_one_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_montecarlo_swissmetro_one.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro: one observation</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Programming with Biogeme
************************

Examples of the use of various Biogeme objects for programming.




.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_biogeme_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_biogeme.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.biogeme</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_biogeme_logging_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_biogeme_logging.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.biogeme_logging</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of usage of the cnl module.  This is for programmers who need examples of use of the functions of the class. The examples are designed to illustrate the syntax.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_cnl.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.cnl</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_database_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_database.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.database</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of usage of the distributions module.  This is for programmers who need examples of use of the functions of the class. The examples are designed to illustrate the syntax.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_distributions_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_distributions.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.distributions</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_draws_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_draws.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_expressions_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_expressions.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.expressions</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_filenames_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_filenames.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.filenames</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_loglikelihood_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_loglikelihood.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.loglikelihood</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_models.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_nests_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_nests.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.nests</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_optimization_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_optimization.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.optimization</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_results_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_results.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.results_processing</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_segmentation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_segmentation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.segmentation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_tools_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_tools.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.tools</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Examples of use of several functions.">

.. only:: html

  .. image:: /auto_examples/programmers/images/thumb/sphx_glr_plot_version_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_programmers_plot_version.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">biogeme.version</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Sampling of alternatives
************************

Examples discussed in `Bierlaire and Paschalidis (2023) Estimating MEV
models with samples of alternatives
<https://transp-or.epfl.ch/documents/technicalReports/BierPasc23.pdf>`_




.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Script reading the list of alternatives and identifying subsets">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_alternatives_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_alternatives.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">List of alternatives</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Function to compare estimated parameters with true parameters.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_compare_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_compare.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Compare parameters</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a logit model using sampling of alternatives.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_plot_b01logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_plot_b01logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a nested logit model using sampling of alternatives.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_plot_b02nested_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_plot_b02nested.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Nested logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a cross-nested logit model using sampling of alternatives.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_plot_b03cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_plot_b03cnl.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cross-nested logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Script containing the model specification.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Model specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Script containing the model specification.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_specification_sampling_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_specification_sampling.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Model specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Value of the parameters used to generate synthetic choices.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_true_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_true_parameters.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">True parameters</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Biogeme examples for the Swissmetro data
****************************************

You find here several examples of models that can be estimated and simulated with Biogeme.





.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <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.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_generate_jed_run_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_generate_jed_run.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generate SLURM run scripts for Biogeme experiments.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Three alternatives:">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01a_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01a_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1a. Estimation of a logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Same model as b01logit, using LinearUtility, segmentations">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01b_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01b_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1b. Illustration of additional features of Biogeme</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Same model as b01logit, estimated using the quick_estimate, that skips the calculation of the second orders statistics.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01c_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01c_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1c. Illustration of the quick_estimate of Biogeme</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of simulation with a logit model">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01d_logit_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01d_logit_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1d. Simulation of a logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Estimation of a logit model with several algorithms.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01e_logit_all_algos_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01e_logit_all_algos.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">1e. Logit model with several algorithms</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a logit model with Weighted Exogenous Sample Maximum  Likelihood (WESML).">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b02_weight_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b02_weight.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2. Estimation with weights: WESML</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Although normalizing the scale to 1 is a common practice in random utility models, it is sometimes preferable to normalize another parameter. For instance, normalizing the cost coefficient to -1 sets the units of the utility function as currency units (CHF here), and the estimated coefficients are easily interpreted as willingness to pay. In that case, the scale must be estimated.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b03_scale_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b03_scale.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">3. Moneymetric and heteroscedastic specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of the out-of-sample validation of a logit model.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b04_validation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b04_validation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">4. Out-of-sample validation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a normal mixture of logit models, using Monte-Carlo integration.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b05a_normal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05a_normal_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">5a. Mixture of logit models with Monte-Carlo integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a normal mixture of logit models, using numerical integration.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b05b_normal_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05b_normal_mixture_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">5b. Mixture of logit models with numerical integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of the mixture model, with estimation of the integration error.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b05c_normal_mixture_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05c_normal_mixture_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">5c. Simulation of a mixture model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of the use of different algorithms to estimate the model.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b05d_normal_mixture_all_algos_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05d_normal_mixture_all_algos.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a uniform mixture of logit models, using Monte-Carlo integration.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b06a_unif_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06a_unif_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">6a. Mixture of logit models with uniform distribution</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a uniform mixture of logit models, using Monte-Carlo  integration.  The mixing distribution is uniform.  The draws are from  the Modified Hypercube Latin Square.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b06b_unif_mixture_MHLS_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06b_unif_mixture_MHLS.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">6b. Mixture of logit models with uniform MLHS draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="6c. Mixture of logit models with uniform distribution and numerical integration ===============================================================================">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b06c_unif_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06c_unif_mixture_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">"</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a discrete mixture of logit (or latent class model).">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b07_discrete_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b07_discrete_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">7. Latent class model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a logit model, with a Box-Cox transform of variables.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b08_boxcox_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b08_boxcox.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">8. Box-Cox transforms</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a nested logit model.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b09_nested_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b09_nested.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">9. Nested logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a nested logit model where the normalization is done at the  bottom level.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b10_nested_bottom_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b10_nested_bottom.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">10. Nested logit model normalized from bottom</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a cross-nested logit model with two nests:">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b11a_cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11a_cnl.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">11a. Cross-nested logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Illustration of the application of an estimated CNL model.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b11b_cnl_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11b_cnl_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">11b. Simulation of a cross-nested logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a cross-nested logit model with two nests:">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b11c_cnl_sparse_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11c_cnl_sparse.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">11c. Cross-nested logit with a sparse structure</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a mixture of logit models, using Monte-Carlo integration.  The datafile is organized as panel data.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b12_panel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b12_panel.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">12. Mixture of logit with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculates each contribution to the log likelihood function using simulation. We also calculate the individual parameters.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b13_panel_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b13_panel_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">13. Simulation of panel model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The sample is said to be endogenous if the probability for an individual to be in the sample depends on the choice that has been made. In that case, the ESML estimator is not appropriate anymore, and corrections need to be made. See Bierlaire, Bolduc, McFadden (2008).">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b14_nested_endogenous_sampling_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b14_nested_endogenous_sampling.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">14. Nested logit with corrections for endogeneous sampling</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a discrete mixture of logit models, also called latent  class model.  The datafile is organized as panel data.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b15a_panel_discrete_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b15a_panel_discrete.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">15a. Discrete mixture with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a discrete mixture of logit models, also called latent  class model.  The datafile is organized as panel data.  Compared to  plot_b15a_panel_discrete, we integrate before the discrete  mixture to show that it is equivalent.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b15b_panel_discrete_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b15b_panel_discrete.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">15b. Discrete mixture with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a discrete mixture of logit models, also called latent class model. The class membership model includes socio-economic variables. The datafile is organized as panel data.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b16_panel_discrete_socio_eco_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b16_panel_discrete_socio_eco.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">16. Discrete mixture with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a mixture of logit models, using Monte-Carlo integration. The mixing distribution is distributed as a log normal.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b17a_lognormal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b17a_lognormal_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">17a. Mixture with lognormal distribution</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a mixture of logit models.  The mixing distribution is distributed as a log normal.  Compared to plot_b17a_lognormal_mixture, the integration is performed using numerical integration instead of Monte-Carlo approximation.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b17b_lognormal_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b17b_lognormal_mixture_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">17b. Mixture with lognormal distribution and numerical integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of an ordinal logit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b18a_ordinal_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b18a_ordinal_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">18a. Ordinal logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of an ordinal probit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b18b_ordinal_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b18b_ordinal_probit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">18b. Ordinal probit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of the individual level parameters for the model defined in plot_b05normal_mixture.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b19_individual_level_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b19_individual_level_parameters.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">19. Calculation of individual level parameters</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of the estimation of several specifications of the model.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b20_multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b20_multiple_models.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">20. Estimation of several models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of the estimation of several versions of the model using  assisted specification algorithm. The catalog of specifications is  defined in plot_b21b_multiple_models_spec. All specifications  are estimated. Have a look at plot_b22a_multiple_models for an  example where the number of specifications is too high to be  enumerated.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21a_multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21a_multiple_models.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">21a. Assisted specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Specification of the catalogs used by the assisted specification algorithm. Note that this script does not perform any estimation. It is imported by other scripts: plot_b21a_multiple_models, plot_b21c_process_pareto.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21b_multiple_models_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21b_multiple_models_spec.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">21b. Specification of a catalog of models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The assisted specification algorithm generates a file containing the pareto optimal specification. This script is designed to re-estimate the Pareto optimal models. The catalog of specifications is defined in plot_b21b_multiple_models_spec .">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21c_process_pareto_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21c_process_pareto.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">21c. Re-estimate the Pareto optimal models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in plot_b22multiple_models_spec . Compared to plot_b21multiple_models, the number fo specifications exceeds the maximum limit, so a heuristic is applied.  See Bierlaire and Ortelli, 2023 for a detailed description of the use of the assisted specification algorithm.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22a_multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22a_multiple_models.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Assisted specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Specification of the Catalog of expressions for the assisted specification algorithm. Note that this script does not perform any estimation. It is imported by other scripts: plot_b22multiple_models, plot_b22process_pareto.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22b_multiple_models_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22b_multiple_models_spec.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Specification of a catalog of models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The assisted specification algorithm generates a file containing the pareto optimal specification. This script is designed to re-estimate the Pareto optimal models. The catalog of specifications is defined in plot_b22multiple_models_spec .">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22c_process_pareto_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22c_process_pareto.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Re-estimate the Pareto optimal models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a binary logit model. Two alternatives: Train and Car. All observations such that the Swissmetro was chosen haven been removed from the sample.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b23a_binary_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b23a_binary_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">23a. Binary logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a binary probit model. Two alternatives: Train and Car. All observations such that the Swissmetro was chosen haven been removed from the sample.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b23b_binary_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b23b_binary_probit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">23b. Binary probit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a mixture of logit models, using quasi Monte-Carlo integration with Halton draws (base 5). The mixing distribution is normal.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b24_halton_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b24_halton_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">24. Mixture of logit with Halton draws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a mixture of logit models, using Monte-Carlo integration.  The mixing distribution is specified by the user. Here, a triangular  distribution.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b25_triangular_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b25_triangular_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">25. Triangular mixture of logit</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a mixture of logit models, using Monte-Carlo integration.  The mixing distribution is user-defined (triangular, here).  The datafile is organized as panel data.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b26_triangular_panel_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b26_triangular_panel_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">26. Triangular mixture with panel data</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation for Swissmetro, and definition of the variables. The data is designed to estimate binary logit models. All observations such that Swissmetro was chosen are removed.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_swissmetro_binary_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_swissmetro_binary.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro (binary choice)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation and definition of the variables.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_swissmetro_data_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_swissmetro_data.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation for Swissmetro, and definition of the variables in panel configuration">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_swissmetro_panel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_swissmetro_panel.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Panel data preparation for Swissmetro</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Timing function evaluation
**************************

We perform here the timing on some functions. The results clearly depend on the computer where it is run.





.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Tue Jul 2 14:48:52 2024">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_plot01_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_plot01_logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Timing of a logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Tue Jul 2 14:49:25 2024">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_plot02_cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_plot02_cnl.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Timing of a cross-nested logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Tue Jul 2 14:48:52 2024">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_plot03_mixtures_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_plot03_mixtures.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Timing of a logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Tue Jul 2 14:48:52 2024">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_plot_comparison_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_plot_comparison.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Comparison of execution times</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Data preparation and definition of the variables.">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_swissmetro_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_swissmetro.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data preparation for Swissmetro</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Thu Jul 31 2025, 13:40:20">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_timing_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_timing.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tool for timing an expression</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire Sun Jul 27 2025, 16:55:31">

.. only:: html

  .. image:: /auto_examples/timing/images/thumb/sphx_glr_timing_expression_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_timing_timing_expression.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Timing of any expression</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Some simple examples for beginners
**********************************






.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example extracted from Ben-Akiva and Lerman (1985)">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_plot_b01_first_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_plot_b01_first_model.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Estimation of a binary logit model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We illustrate how to obtain information about configuration parameters, and how to modify them.">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_plot_b02_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_plot_b02_parameters.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Configuring Biogeme with parameters</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The Python language allows to organize your model specification in different files.">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_plot_b03_importing_specification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_plot_b03_importing_specification.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Importing model specification</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The estimation results are saved by Biogeme so that they can be re-used without the need for re-estimating the model Michel Bierlaire, EPFL Sun Jun 15 2025, 07:36:09">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_plot_b04_estimation_results_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_plot_b04_estimation_results.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Estimation results</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Michel Bierlaire, EPFL Sun Jun 15 2025, 08:30:48">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_plot_b05_simulation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_plot_b05_simulation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Using the estimated model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example extracted from Ben-Akiva and Lerman (1985)">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_tutorial_data_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_tutorial_data.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data definition for the simple tutorial</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example extracted from Ben-Akiva and Lerman (1985)">

.. only:: html

  .. image:: /auto_examples/tutorials/images/thumb/sphx_glr_tutorial_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_tutorials_tutorial_model.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Model specification for the simple tutorial</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/assisted/index.rst
   /auto_examples/bayesian_swissmetro/index.rst
   /auto_examples/hybrid_choice/index.rst
   /auto_examples/indicators/index.rst
   /auto_examples/mdcev_no_outside_good/index.rst
   /auto_examples/montecarlo/index.rst
   /auto_examples/programmers/index.rst
   /auto_examples/sampling/index.rst
   /auto_examples/swissmetro/index.rst
   /auto_examples/timing/index.rst
   /auto_examples/tutorials/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_