statsmodels.stats.multivariate_tools.cancorr

statsmodels.stats.multivariate_tools.cancorr(x1, x2, demean=True, standardize=False)

Canonical correlation coefficient between 2 arrays

Parameters:

x1, x2array_like, 2-D

Two 2-dimensional data arrays, observations in rows, variables in columns.

demeanbool, optional

If demean is true, then the mean is subtracted from each variable.

standardizebool, optional

If standardize is true, then each variable is demeaned and divided by its standard deviation. Rescaling does not change the canonical correlation coefficients.

Returns:

ccorrndarray, 1-D

Canonical correlation coefficients, sorted from largest to smallest. Note, that these are the square root of the eigenvalues.

See also

cc_ranktest

Rank tests based on the smallest canonical correlations.

cc_stats

MANOVA statistics based on the canonical correlations.

CCA

Not yet implemented.

Notes

This is a helper function for other statistical functions. It only calculates the canonical correlation coefficients and does not do a full canonical correlation analysis.

The canonical correlation coefficient is calculated with the generalized matrix inverse and does not raise an exception if one of the data arrays have less than full column rank.

The eigenvalues underlying the canonical correlations are mathematically guaranteed to be real and non-negative, but the generalized eigenvalue problem is solved numerically and can return eigenvalues with a small spurious complex part or a small negative real part. Such numerical noise is clipped to zero before taking the square root, so ccorr is always real-valued.