.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_metaregls.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_plot_metaregls.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_metaregls.py:


Meta-regression
===============
Normative modeling when data are measured with errors

.. GENERATED FROM PYTHON SOURCE LINES 8-10

Imports
--------

.. GENERATED FROM PYTHON SOURCE LINES 10-20

.. code-block:: Python

    import numpy as np
    import scipy
    import matplotlib.pyplot as plt

    from sknormod import NormodOLS
    from sknormod.metareg import NormodMetaregLS
    from sknormod.plotting import plot_scatter_with_lines
    from sknormod.datasets import make_gaussian









.. GENERATED FROM PYTHON SOURCE LINES 21-23

The problem
-----------

.. GENERATED FROM PYTHON SOURCE LINES 23-39

.. code-block:: Python

    n_subj = 100
    age, y = make_gaussian(n_subj, interpolate_mu=[95, 98, 92])
    # We also generate a quadratic feature of age to capture potential nonlinear
    # relationships.
    X = np.column_stack((age, age**2))

    error_se = np.ones(len(y)) * 1.5
    y_observed = y + scipy.stats.norm.rvs(scale=error_se, size=len(error_se))

    scatter = plt.scatter(age, y_observed, zorder=2, label="Observed")
    errorbar = plt.errorbar(age, y, yerr=error_se*2, fmt='o', color="red",
                            ecolor='black', zorder=1, label="True")
    plt.title('TODO: make nicer plots')
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_metaregls_001.png
   :alt: TODO: make nicer plots
   :srcset: /auto_examples/images/sphx_glr_plot_metaregls_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 40-42

Fit models
----------

.. GENERATED FROM PYTHON SOURCE LINES 42-57

.. code-block:: Python


    normod_ols = NormodOLS()
    normod_metareg = NormodMetaregLS()
    normod_truth = NormodOLS()

    normod_ols.fit(X, y_observed)
    normod_metareg.fit(X, y_observed, y_se=error_se)
    normod_truth.fit(X, y)

    centiles = np.linspace(0.1, 0.9, 9)
    centiles_ols = normod_ols.predict_distr_p(X, centiles)
    centiles_metareg = normod_metareg.predict_distr_p(X, centiles)
    centiles_truth = normod_truth.predict_distr_p(X, centiles)









.. GENERATED FROM PYTHON SOURCE LINES 58-60

Plot
----

.. GENERATED FROM PYTHON SOURCE LINES 60-79

.. code-block:: Python

    estimated_centiles = list((
        normod.predict_distr_p(X, np.linspace(0.1, 0.9, 9))
        for normod in [normod_ols, normod_metareg, normod_truth]
    ))


    fig, axes = plt.subplots(1, 3, figsize=(12, 4))
    titles = ["OLS", "Metareg", "True"]
    for i_col, ax in enumerate(axes.flat):
        plt.sca(ax)
        plot_scatter_with_lines(age, y_observed,
                                lines=estimated_centiles[i_col], cbar=False)
        plt.scatter(age, y, color='red')
        ax.set_title(titles[i_col])
    plt.tight_layout()
    plt.show()






.. image-sg:: /auto_examples/images/sphx_glr_plot_metaregls_002.png
   :alt: OLS, Metareg, True
   :srcset: /auto_examples/images/sphx_glr_plot_metaregls_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/brick/Code/scikit-normod/sknormod/plotting.py:6: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
      plt.scatter(x, y, c=c, cmap="coolwarm")





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.540 seconds)


.. _sphx_glr_download_auto_examples_plot_metaregls.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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