Source code for statsmodels.graphics.agreement

'''
Bland-Altman mean-difference plots

Author: Joses Ho
License: BSD-3
'''

import numpy as np

from . import utils



[docs]
def mean_diff_plot(m1, m2, sd_limit=1.96, ax=None, scatter_kwds=None,
                   mean_line_kwds=None, limit_lines_kwds=None):
    """
    Construct a Tukey/Bland-Altman Mean Difference Plot.

    Tukey's Mean Difference Plot (also known as a Bland-Altman plot) is a
    graphical method to analyze the differences between two methods of
    measurement. The mean of the measures is plotted against their difference.

    For more information see
    https://en.wikipedia.org/wiki/Bland-Altman_plot

    Parameters
    ----------
    m1 : array_like
        A 1-d array.
    m2 : array_like
        A 1-d array.
    sd_limit : float
        The limit of agreements expressed in terms of the standard deviation of
        the differences. If `md` is the mean of the differences, and `sd` is
        the standard deviation of those differences, then the limits of
        agreement that will be plotted are md +/- sd_limit * sd.
        The default of 1.96 will produce 95% confidence intervals for the means
        of the differences. If sd_limit = 0, no limits will be plotted, and
        the ylimit of the plot defaults to 3 standard deviations on either
        side of the mean.
    ax : AxesSubplot
        If `ax` is None, then a figure is created. If an axis instance is
        given, the mean difference plot is drawn on the axis.
    scatter_kwds : dict
        Options to to style the scatter plot. Accepts any keywords for the
        matplotlib Axes.scatter plotting method
    mean_line_kwds : dict
        Options to to style the scatter plot. Accepts any keywords for the
        matplotlib Axes.axhline plotting method
    limit_lines_kwds : dict
        Options to to style the scatter plot. Accepts any keywords for the
        matplotlib Axes.axhline plotting method

    Returns
    -------
    Figure
        If `ax` is None, the created figure.  Otherwise the figure to which
        `ax` is connected.

    References
    ----------
    Bland JM, Altman DG (1986). "Statistical methods for assessing agreement
    between two methods of clinical measurement"

    Examples
    --------

    Load relevant libraries.

    >>> import statsmodels.api as sm
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt

    Making a mean difference plot.

    >>> # Seed the random number generator.
    >>> # This ensures that the results below are reproducible.
    >>> np.random.seed(9999)
    >>> m1 = np.random.random(20)
    >>> m2 = np.random.random(20)
    >>> f, ax = plt.subplots(1, figsize = (8,5))
    >>> sm.graphics.mean_diff_plot(m1, m2, ax = ax)
    >>> plt.show()

    .. plot:: plots/graphics-mean_diff_plot.py
    """
    fig, ax = utils.create_mpl_ax(ax)

    if len(m1) != len(m2):
        raise ValueError('m1 does not have the same length as m2.')
    if sd_limit < 0:
        raise ValueError(f'sd_limit ({sd_limit}) is less than 0.')

    means = np.mean([m1, m2], axis=0)
    diffs = m1 - m2
    mean_diff = np.mean(diffs)
    std_diff = np.std(diffs, axis=0)

    scatter_kwds = scatter_kwds or {}
    if 's' not in scatter_kwds:
        scatter_kwds['s'] = 20
    mean_line_kwds = mean_line_kwds or {}
    limit_lines_kwds = limit_lines_kwds or {}
    for kwds in [mean_line_kwds, limit_lines_kwds]:
        if 'color' not in kwds:
            kwds['color'] = 'gray'
        if 'linewidth' not in kwds:
            kwds['linewidth'] = 1
    if 'linestyle' not in mean_line_kwds:
        kwds['linestyle'] = '--'
    if 'linestyle' not in limit_lines_kwds:
        kwds['linestyle'] = ':'

    ax.scatter(means, diffs, **scatter_kwds) # Plot the means against the diffs.
    ax.axhline(mean_diff, **mean_line_kwds)  # draw mean line.

    # Annotate mean line with mean difference.
    ax.annotate(f'mean diff:\n{np.round(mean_diff, 2)}',
                xy=(0.99, 0.5),
                horizontalalignment='right',
                verticalalignment='center',
                fontsize=14,
                xycoords='axes fraction')

    if sd_limit > 0:
        half_ylim = (1.5 * sd_limit) * std_diff
        ax.set_ylim(mean_diff - half_ylim,
                    mean_diff + half_ylim)
        limit_of_agreement = sd_limit * std_diff
        lower = mean_diff - limit_of_agreement
        upper = mean_diff + limit_of_agreement
        for j, lim in enumerate([lower, upper]):
            ax.axhline(lim, **limit_lines_kwds)
        ax.annotate(f'-{sd_limit} SD: {lower:0.2g}',
                    xy=(0.99, 0.07),
                    horizontalalignment='right',
                    verticalalignment='bottom',
                    fontsize=14,
                    xycoords='axes fraction')
        ax.annotate(f'+{sd_limit} SD: {upper:0.2g}',
                    xy=(0.99, 0.92),
                    horizontalalignment='right',
                    fontsize=14,
                    xycoords='axes fraction')

    elif sd_limit == 0:
        half_ylim = 3 * std_diff
        ax.set_ylim(mean_diff - half_ylim,
                    mean_diff + half_ylim)

    ax.set_ylabel('Difference', fontsize=15)
    ax.set_xlabel('Means', fontsize=15)
    ax.tick_params(labelsize=13)
    fig.tight_layout()
    return fig