Where Can I Find Mad (mean Absolute Deviation) In Scipy?

It seems scipy once provided a function mad to calculate the mean absolute deviation for a set of numbers: http://projects.scipy.org/scipy/browser/trunk/scipy/stats/models/utils.py

Solution 1:

[EDIT] Since this keeps on getting downvoted: I know that median absolute deviation is a more commonly-used statistic, but the questioner asked for mean absolute deviation, and here's how to do it:

from numpy import mean, absolute

def mad(data, axis=None):
    return mean(absolute(data - mean(data, axis)), axis)

Solution 2:

For what its worth, I use this for MAD:

defmad(arr):
    """ Median Absolute Deviation: a "Robust" version of standard deviation.
        Indices variabililty of the sample.
        https://en.wikipedia.org/wiki/Median_absolute_deviation 
    """
    arr = np.ma.array(arr).compressed() # should be faster to not use masked arrays.
    med = np.median(arr)
    return np.median(np.abs(arr - med))

Solution 3:

The current version of statsmodels has mad in statsmodels.robust:

>>>import numpy as np>>>from statsmodels import robust>>>a = np.matrix( [...    [ 80, 76, 77, 78, 79, 81, 76, 77, 79, 84, 75, 79, 76, 78 ],...    [ 66, 69, 76, 72, 79, 77, 74, 77, 71, 79, 74, 66, 67, 73 ]... ], dtype=float )>>>robust.mad(a, axis=1)
array([ 2.22390333,  5.18910776])

Note that by default this computes the robust estimate of the standard deviation assuming a normal distribution by scaling the result a scaling factor; from help:

Signature: robust.mad(a,c=0.67448975019608171, 
                      axis=0, 
                      center=<function median at 0x10ba6e5f0>)

The version in R makes a similar normalization. If you don't want this, obviously just set c=1.

(An earlier comment mentioned this being in statsmodels.robust.scale. The implementation is in statsmodels/robust/scale.py (see github) but the robust package does not export scale, rather it exports the public functions in scale.py explicitly.)

Solution 4:

It looks like scipy.stats.models was removed in august 2008 due to insufficient baking. Development has migrated to statsmodels.

Solution 5:

If you enjoy working in Pandas (like I do), it has a useful function for the mean absolute deviation:

import pandas as pd
df = pd.DataFrame()
df['a'] = [1, 1, 2, 2, 4, 6, 9]
df['a'].mad()

Output: 2.3673469387755106