.. _sphx_glr_auto_examples_latent:

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>


.. toctree::
   :hidden:

   /auto_examples/latent/optima
   /auto_examples/latent/plot_b00factor_analysis
   /auto_examples/latent/plot_b01one_latent_regression
   /auto_examples/latent/plot_b02one_latent_ordered
   /auto_examples/latent/plot_b03choice_only
   /auto_examples/latent/plot_b04latent_choice_seq
   /auto_examples/latent/plot_b04latent_choice_seq_mc
   /auto_examples/latent/plot_b05latent_choice_full
   /auto_examples/latent/plot_b05latent_choice_full_mc
   /auto_examples/latent/plot_b06serial_correlation
   /auto_examples/latent/plot_b07problem
   /auto_examples/latent/plot_b07problem_simul
   /auto_examples/latent/read_or_estimate