.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/statistics/models.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_statistics_models.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_statistics_models.py:


Model coding
============

Illustrates how to inspect coding of regression models.

.. GENERATED FROM PYTHON SOURCE LINES 7-17

.. code-block:: Python

    # Author: Christian Brodbeck <christianbrodbeck@nyu.edu>
    from eelbrain import *
    from matplotlib import pyplot


    ds = Dataset()
    ds['A'] = Factor(['a1', 'a0'], repeat=4)
    ds['B'] = Factor(['b1', 'b0'], repeat=2, tile=2)
    ds.head()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <figure><table border="1" frame="hsides" rules="none" cellpadding="2"><tr>
    <td style="text-align:left">#</td>
    <td style="text-align:left">A</td>
    <td style="text-align:left">B</td>
    </tr>
    <tr>
    <td style="text-align:left">0</td>
    <td style="text-align:left">a1</td>
    <td style="text-align:left">b1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">a1</td>
    <td style="text-align:left">b1</td>
    </tr>
    <tr>
    <td style="text-align:left">2</td>
    <td style="text-align:left">a1</td>
    <td style="text-align:left">b0</td>
    </tr>
    <tr>
    <td style="text-align:left">3</td>
    <td style="text-align:left">a1</td>
    <td style="text-align:left">b0</td>
    </tr>
    <tr>
    <td style="text-align:left">4</td>
    <td style="text-align:left">a0</td>
    <td style="text-align:left">b1</td>
    </tr>
    <tr>
    <td style="text-align:left">5</td>
    <td style="text-align:left">a0</td>
    <td style="text-align:left">b1</td>
    </tr>
    <tr>
    <td style="text-align:left">6</td>
    <td style="text-align:left">a0</td>
    <td style="text-align:left">b0</td>
    </tr>
    <tr>
    <td style="text-align:left">7</td>
    <td style="text-align:left">a0</td>
    <td style="text-align:left">b0</td>
    </tr></table></figure>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 18-19

Create a fixed effects model:

.. GENERATED FROM PYTHON SOURCE LINES 19-22

.. code-block:: Python

    m = ds.eval('A * B')
    m





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    A + B + A % B



.. GENERATED FROM PYTHON SOURCE LINES 23-24

Show the model using dummy coding:

.. GENERATED FROM PYTHON SOURCE LINES 24-26

.. code-block:: Python

    m.as_table()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <figure><table border="1" frame="hsides" rules="none" cellpadding="2"><tr>
    <td style="text-align:left">intercept</td>
    <td style="text-align:left">A</td>
    <td style="text-align:left">B</td>
    <td style="text-align:left">A x B</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr></table></figure>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 27-28

Create random effects model:

.. GENERATED FROM PYTHON SOURCE LINES 28-31

.. code-block:: Python

    ds['subject'] = Factor(['s1', 's2'], tile=4, name='subject', random=True)
    m = ds.eval('A * B * subject')
    m




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    A + B + A % B + subject + A % subject + B % subject + A % B % subject



.. GENERATED FROM PYTHON SOURCE LINES 32-33

Show the model using dummy coding:

.. GENERATED FROM PYTHON SOURCE LINES 33-35

.. code-block:: Python

    m.as_table()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <figure><table border="1" frame="hsides" rules="none" cellpadding="2"><tr>
    <td style="text-align:left">intercept</td>
    <td style="text-align:left">A</td>
    <td style="text-align:left">B</td>
    <td style="text-align:left">A x B</td>
    <td style="text-align:left">subject</td>
    <td style="text-align:left">A x subject</td>
    <td style="text-align:left">B x subject</td>
    <td style="text-align:left">A x B x subject</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0</td>
    </tr></table></figure>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 36-37

Or with effect coding:

.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python


    m.as_table('effect')






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <figure><table border="1" frame="hsides" rules="none" cellpadding="2"><tr>
    <td style="text-align:left">intercept</td>
    <td style="text-align:left">A</td>
    <td style="text-align:left">B</td>
    <td style="text-align:left">A x B</td>
    <td style="text-align:left">subject</td>
    <td style="text-align:left">A x subject</td>
    <td style="text-align:left">B x subject</td>
    <td style="text-align:left">A x B x subject</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">1</td>
    <td style="text-align:left">-1</td>
    </tr></table></figure>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 41-42

Plot model matrix:

.. GENERATED FROM PYTHON SOURCE LINES 42-48

.. code-block:: Python

    figure, axes = pyplot.subplots(1, 2, figsize=(6, 3))
    for ax, coding in zip(axes, ['dummy', 'effect']):
        array, names = m.array(coding)
        ax.imshow(array, cmap='coolwarm', vmin=-1, vmax=1)
        ax.set_title(coding)
        ax.set_xticks([i-0.5 for i in range(len(names))], names, rotation=-60, ha='left')



.. image-sg:: /auto_examples/statistics/images/sphx_glr_models_001.png
   :alt: dummy, effect
   :srcset: /auto_examples/statistics/images/sphx_glr_models_001.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_examples_statistics_models.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: models.ipynb <models.ipynb>`

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

      :download:`Download Python source code: models.py <models.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: models.zip <models.zip>`


.. only:: html

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

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