.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/mass-univariate-statistics/sensor-lm.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_mass-univariate-statistics_sensor-lm.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_mass-univariate-statistics_sensor-lm.py:


.. _exa-lm:

Multiple regression
===================

Multiple regression designs apply to at least two scenarios.

 - Analyzing a single subject's data when trials are associated with one or multiple continuous variables.
 - Analyzing group data when subjects are associated with one or multiple individual difference variables.

Here the analysis is illustrated for a simulated dataset from a single subject. Group analysis works analogously, except that each case in the datatset would represent a different subject rather than a different trial. 

For such group analysis, it is necessary to reduce each subject's data to a single case first because multiple regression assumes a fixed effects model. 
Such designs are described under :ref:`exa-two-stage`.

Simulated data
--------------

.. GENERATED FROM PYTHON SOURCE LINES 21-28

.. code-block:: Python

    # sphinx_gallery_thumbnail_number = 2
    from eelbrain import *


    data = datasets.simulate_erp(snr=0.5)
    data.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">cloze</td>
    <td style="text-align:left">predictability</td>
    <td style="text-align:left">n_chars</td>
    </tr>
    <tr>
    <td style="text-align:left">0</td>
    <td style="text-align:left">0.026139</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">4</td>
    </tr>
    <tr>
    <td style="text-align:left">1</td>
    <td style="text-align:left">0.99529</td>
    <td style="text-align:left">high</td>
    <td style="text-align:left">5</td>
    </tr>
    <tr>
    <td style="text-align:left">2</td>
    <td style="text-align:left">0.93062</td>
    <td style="text-align:left">high</td>
    <td style="text-align:left">3</td>
    </tr>
    <tr>
    <td style="text-align:left">3</td>
    <td style="text-align:left">0.82404</td>
    <td style="text-align:left">high</td>
    <td style="text-align:left">7</td>
    </tr>
    <tr>
    <td style="text-align:left">4</td>
    <td style="text-align:left">0.17041</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">4</td>
    </tr>
    <tr>
    <td style="text-align:left">5</td>
    <td style="text-align:left">0.18508</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">4</td>
    </tr>
    <tr>
    <td style="text-align:left">6</td>
    <td style="text-align:left">0.23345</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">4</td>
    </tr>
    <tr>
    <td style="text-align:left">7</td>
    <td style="text-align:left">0.80784</td>
    <td style="text-align:left">high</td>
    <td style="text-align:left">3</td>
    </tr>
    <tr>
    <td style="text-align:left">8</td>
    <td style="text-align:left">0.24979</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">7</td>
    </tr>
    <tr>
    <td style="text-align:left">9</td>
    <td style="text-align:left">0.26753</td>
    <td style="text-align:left">low</td>
    <td style="text-align:left">4</td>
    </tr></table>
    <figcaption>NDVars: eeg</figcaption></figure>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 29-30

The data represents 80 trials from a simulated word reading paradigm, where each word is associated with a word length (`n_chars`) and predictability (`cloze`).

.. GENERATED FROM PYTHON SOURCE LINES 30-33

.. code-block:: Python


    p = plot.Scatter('cloze', 'n_chars', data=data, h=3)




.. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_001.png
   :alt: sensor lm
   :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 34-35

Plot the average of each level on `n_chars` to illustrate the linear increase of the response around 130 ms with `n_char`.

.. GENERATED FROM PYTHON SOURCE LINES 35-38

.. code-block:: Python


    p = plot.TopoButterfly('eeg', 'n_chars', data=data, t=.130, axh=2, w=6)




.. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_002.png
   :alt: sensor lm
   :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 39-45

Multiple regression
-------------------
Fit a multiple regression model.
Estimate $p$-values using a cluster-based permuatation test, using a cluster-forming threshold of uncorrected $p$=.05.
For this example, only 500 permutations are used.
When accuracy counts, it is recommended to use 10,000 permutations (the default).

.. GENERATED FROM PYTHON SOURCE LINES 45-48

.. code-block:: Python


    lm = testnd.LM('eeg', 'n_chars + cloze', data=data, tstart=0.050, tstop=0.500, pmin=0.05, samples=500)








.. GENERATED FROM PYTHON SOURCE LINES 49-50

A quick plot suggests an early effect related to `n_chars` around 130 ms, and a later effect of `cloze` around 400 ms:

.. GENERATED FROM PYTHON SOURCE LINES 50-53

.. code-block:: Python


    p = plot.TopoButterfly(lm, t=0.130, axh=2, w=6)




.. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_003.png
   :alt: sensor lm
   :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 54-55

Detailed plots of the two effects show that the cluster is quite variable due to noise in the data.

.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: Python


    p = plot.TopoArray(lm.masked_parameter_map('n_chars'), t=[0.110, 0.130, 0.150], title='N Chars')
    p = plot.TopoArray(lm.masked_parameter_map('cloze'), t=[0.380, 0.400, 0.420], title='Cloze')




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_004.png
         :alt: N Chars
         :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_005.png
         :alt: Cloze
         :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_005.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 60-61

To access some of the test results we need to know the index of different effects:

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: Python


    lm.effects





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

 .. code-block:: none


    ('intercept', 'n_chars', 'cloze')



.. GENERATED FROM PYTHON SOURCE LINES 65-66

Create a plot that shows the spatial cluster extent across time.

.. GENERATED FROM PYTHON SOURCE LINES 66-84

.. code-block:: Python

    EFFECTS = [
        ('n_chars', (0.110, 0.150)),
        ('cloze', (0.380, 0.420)),
    ]

    t_maps = []
    for effect, time in EFFECTS:
        # t-maps are retrieved by effect name
        t = lm.t(effect).mean(time=time)
        # p-maps are stored in a list, so we need to know the index of te effect
        index = lm.effects.index(effect)
        # We are interested in the maximal spatial cluster extent, i.e., any sensor that is part of the cluster at any time
        p = lm.p[index].min(time=time)
        # Create a masked average t map
        t_av = t.mask(p > 0.05)
        t_maps.append(t_av)

    p = plot.Topomap(t_maps, columns=2)



.. image-sg:: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_006.png
   :alt: n_chars, cloze
   :srcset: /auto_examples/mass-univariate-statistics/images/sphx_glr_sensor-lm_006.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_examples_mass-univariate-statistics_sensor-lm.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: sensor-lm.ipynb <sensor-lm.ipynb>`

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

      :download:`Download Python source code: sensor-lm.py <sensor-lm.py>`

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

      :download:`Download zipped: sensor-lm.zip <sensor-lm.zip>`


.. only:: html

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

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