3.11.15.1.2. statsmodels.stats.multivariate_tools.cc_ranktest

statsmodels.stats.multivariate_tools.cc_ranktest(x1, x2, demean=True, fullrank=False)

rank tests based on smallest canonical correlation coefficients

Anderson canonical correlations test (LM test) and Cragg-Donald test (Wald test) Assumes homoskedasticity and independent observations, overrejects if there is heteroscedasticity or autocorrelation.

The Null Hypothesis is that the rank is k - 1, the alternative hypothesis is that the rank is at least k.

Parameters:

x1, x2 : ndarrays, 2_D

two 2-dimensional data arrays, observations in rows, variables in columns

demean : bool

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

fullrank : bool

If true, then only the test that the matrix has full rank is returned. If false, the test for all possible ranks are returned. However, no the p-values are not corrected for the multiplicity of tests.

Returns:

value : float

value of the test statistic

p-value : float

p-value for the test Null Hypothesis tha the smallest canonical correlation coefficient is zero. based on chi-square distribution

df : int

degrees of freedom for thechi-square distribution in the hypothesis test

ccorr : ndarray, 1d

All canonical correlation coefficients sorted from largest to smallest.

See also

cancorr, cc_stats

Notes

Degrees of freedom for the distribution of the test statistic are based on number of columns of x1 and x2 and not on their matrix rank. (I’m not sure yet what the interpretation of the test is if x1 or x2 are of reduced rank.)