:orphan:

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




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


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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-thumbnails">


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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 43...">

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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 4...">

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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...">

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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_spe...">

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

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

  :ref:`sphx_glr_auto_examples_assisted_swissmetro_data.py`

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


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    </div>

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

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





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


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    <div class="sphx-glr-thumbcontainer" tooltip="Prepare data for the Optima case study.">

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

  :ref:`sphx_glr_auto_examples_indicators_optima_data.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b01expressions.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b02estimation.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b03simulation.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b04market_shares.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b05revenues.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b06point_elasticities.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b07cross_elasticities.py`

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


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

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b08arc_elasticities.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip="We calculate and plot willingness to pay. Details about this example are available in Section 4...">

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

  :ref:`sphx_glr_auto_examples_indicators_plot_b09wtp.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Specification of a nested logit model, that will be estimated, and  used for simulation.  Three...">

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

  :ref:`sphx_glr_auto_examples_indicators_scenarios.py`

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


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    </div>

Choice models with one latent variable
**************************************

You find here several examples of so called "hybrid choice
models", discussed in `Bierlaire (2018) Estimating choice
models with latent variables with PandasBiogeme
<http://transp-or.epfl.ch/documents/technicalReports/Bier18b.pdf>`_





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


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    <div class="sphx-glr-thumbcontainer" tooltip="Optima case study.">

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

  :ref:`sphx_glr_auto_examples_latent_optima.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Preliminary analysis of the indicators using factor analysis">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b00factor_analysis_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b00factor_analysis.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip="It is actually a simle linear regression.">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b01one_latent_regression_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b01one_latent_regression.py`

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      <div class="sphx-glr-thumbnail-title">Measurement equations: continuous indicators</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Ordered probit.">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b02one_latent_ordered_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b02one_latent_ordered.py`

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      <div class="sphx-glr-thumbnail-title">Measurement equations: discrete indicators</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Choice model with latent variable. No measurement equation for the indicators.">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b03choice_only_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b03choice_only.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of logit. Measurement equation for the indicators. Sequential estimation.">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b04latent_choice_seq_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b04latent_choice_seq.py`

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      <div class="sphx-glr-thumbnail-title">Choice model with a latent variable: sequential estimation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of logit, with Monte-Carlo integration Measurement equation for the indicators. Sequent...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b04latent_choice_seq_mc_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b04latent_choice_seq_mc.py`

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      <div class="sphx-glr-thumbnail-title">Choice model with a latent variable: sequential estimation (Monte-Carlo)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of logit. Measurement equation for the indicators. Maximum likelihood (full information...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b05latent_choice_full_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b05latent_choice_full.py`

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      <div class="sphx-glr-thumbnail-title">Choice model with a latent variable: maximum likelihood estimation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Choice model with the latent variable. Mixture of logit with Monte-Carlo integration. Measureme...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b05latent_choice_full_mc_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b05latent_choice_full_mc.py`

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      <div class="sphx-glr-thumbnail-title">Choice model with a latent variable: maximum likelihood estimation (Monte-Carlo)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Choice model with the latent variable. Mixture of logit, with agent effect to deal with serial ...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b06serial_correlation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b06serial_correlation.py`

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


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    <div class="sphx-glr-thumbcontainer" tooltip=" This file is the same as b02one_latent_ordered.py, where the starting  values for the sigma ha...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b07problem_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b07problem.py`

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      <div class="sphx-glr-thumbnail-title">Illustration of a common estimation problem</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" This file is an updated version of 07problem.py, where  the probabilities are simulated in ord...">

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  .. image:: /auto_examples/latent/images/thumb/sphx_glr_plot_b07problem_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latent_plot_b07problem_simul.py`

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      <div class="sphx-glr-thumbnail-title">Investigation of the estimation problem</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Function to estimate the parameters, or read them from a file, if available.">

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

  :ref:`sphx_glr_auto_examples_latent_read_or_estimate.py`

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


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    </div>

Choice models with another latent variable
******************************************

You find here another example of a "hybrid choice models".





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


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    <div class="sphx-glr-thumbcontainer" tooltip="Read the data from file, and define variables.">

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

  :ref:`sphx_glr_auto_examples_latentbis_optima.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Data processing for the optima case study</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Ordered probit.">

.. only:: html

  .. image:: /auto_examples/latentbis/images/thumb/sphx_glr_plot_m01_latent_variable_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latentbis_plot_m01_latent_variable.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Measurement equations: discrete indicators</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of logit. Measurement equation for the indicators. Sequential estimation.">

.. only:: html

  .. image:: /auto_examples/latentbis/images/thumb/sphx_glr_plot_m02_sequential_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latentbis_plot_m02_sequential_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Choice model with latent variable: sequential estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of logit. Measurement equation for the indicators. Maximum likelihood (full information...">

.. only:: html

  .. image:: /auto_examples/latentbis/images/thumb/sphx_glr_plot_m03_simultaneous_estimation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_latentbis_plot_m03_simultaneous_estimation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Choice model with the latent variable: maximum likelihood estimation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Function to estimate the parameters, or read them from a file, if available.">

.. only:: html

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

  :ref:`sphx_glr_auto_examples_latentbis_read_or_estimate.py`

.. raw:: html

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


.. 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">


.. raw:: html

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

.. 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 v...">

.. 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>


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

.. 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>


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

.. 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 inte...">

.. 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 inte...">

.. 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 integ...">

.. 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 in...">

.. 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 2000 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 in...">

.. 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 in...">

.. 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 2000 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 in...">

.. 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 in...">

.. 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 2000 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 in...">

.. 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 in...">

.. 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 2000 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 in...">

.. 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 in...">

.. 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 2000 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 in...">

.. 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>


.. raw:: html

    </div>

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

Examples of the use of various Biogeme objects for programming.




.. raw:: html

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


.. 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 fu...">

.. 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...">

.. 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</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>


.. 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">


.. 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_flycheck_plot_b01logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_flycheck_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 cross-nested logit model using sampling of alternatives.">

.. only:: html

  .. image:: /auto_examples/sampling/images/thumb/sphx_glr_flycheck_plot_b03cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_sampling_flycheck_plot_b03cnl.py`

.. raw:: html

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


.. 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">


.. raw:: html

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

.. only:: html

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

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01logit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Estimation 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_b01logit_all_algos_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01logit_all_algos.py`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Same model as b01logit, using bioLinearUtility, segmentations  and features.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b01logit_bis_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01logit_bis.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Illustration of additional features 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_b01logit_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b01logit_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simulation of a logit model</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_b02weight_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b02weight.py`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip=" Illustrates a heteroscedastic specification. A different scale is  associated with different s...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b03scale_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b03scale.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b04validation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b04validation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b05normal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05normal_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of logit models</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_b05normal_mixture_all_algos_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05normal_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 normal mixture of logit models, using numerical integration.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b05normal_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05normal_mixture_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of logit models</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_b05normal_mixture_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b05normal_mixture_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simulation of a mixture model</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_b06unif_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06unif_mixture.py`

.. raw:: html

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


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b06unif_mixture_MHLS_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06unif_mixture_MHLS.py`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a mixture of logit models, using numerical integration. The mixing distribution is u...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b06unif_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b06unif_mixture_integral.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of logit models</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_b07discrete_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b07discrete_mixture.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b08boxcox_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b08boxcox.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b09nested_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b09nested.py`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a nested logit model, using the original syntax for nests. Since biogeme 3.13, a new...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b09nested_old_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b09nested_old.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b10nested_bottom_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b10nested_bottom.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b10nested_bottom_old_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b10nested_bottom_old.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b11cnl_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11cnl.py`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Example of a cross-nested logit model, using the original syntax for nests. Since biogeme 3.13,...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b11cnl_old_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11cnl_old.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cross-nested logit (old syntax)</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b11cnl_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11cnl_simul.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b11cnl_sparse_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b11cnl_sparse.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b12panel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b12panel.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of logit 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 datafile is organized...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b12panel_flat_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b12panel_flat.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b13panel_simul_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b13panel_simul.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b14nested_endogenous_sampling_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b14nested_endogenous_sampling.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b15panel_discrete_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b15panel_discrete.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b15panel_discrete_bis_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b15panel_discrete_bis.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b16panel_discrete_socio_eco_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b16panel_discrete_socio_eco.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b17lognormal_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b17lognormal_mixture.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b17lognormal_mixture_integral_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b17lognormal_mixture_integral.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b18ordinal_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b18ordinal_logit.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b18ordinal_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b18ordinal_probit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b19individual_level_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b19individual_level_parameters.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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_b20multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b20multiple_models.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21multiple_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 catalogs used by the assisted specification algorithm. Note that this scri...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21multiple_models_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21multiple_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 containg the pareto optimal specification...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b21process_pareto_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b21process_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 the estimation of several versions of the model using assisted specification algorit...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22multiple_models_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22multiple_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...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22multiple_models_spec_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22multiple_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 containg the pareto optimal specification...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b22process_pareto_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b22process_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.">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b23binary_logit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b23binary_logit.py`

.. raw:: html

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


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b23binary_probit_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b23binary_probit.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">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 (ba...">

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b24halton_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b24halton_mixture.py`

.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/swissmetro/images/thumb/sphx_glr_plot_b25triangular_mixture_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b25triangular_mixture.py`

.. raw:: html

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

.. only:: html

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

  :ref:`sphx_glr_auto_examples_swissmetro_plot_b26triangular_panel_mixture.py`

.. raw:: html

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

.. 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>


.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/assisted/index.rst
   /auto_examples/indicators/index.rst
   /auto_examples/latent/index.rst
   /auto_examples/latentbis/index.rst
   /auto_examples/montecarlo/index.rst
   /auto_examples/programmers/index.rst
   /auto_examples/sampling/index.rst
   /auto_examples/swissmetro/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>`_