Kullback {asbio}

Kullback test for equal covariance matrices.

Description

Provides Kullback's (1959) test for multivariate homoscedasticity.

Usage

Kullback(Y, X)

Arguments

Y

An n x p matrix of quantitative variables

X

An n x 1 vector of categorical assignments (e.g. factor levels)

Details

Multivariate general linear models assume equal covariance matrices for all factor levels or factor level combinations. Legendre and Legendre (1998) recommend this test for verifying homoscedasticity. P-values concern a null hypothesis of equal population covariance matrices. P-values from the test are conservative with respect to type I error.

Value

Returns a dataframe with the test statistic (which follows a chi-square distribution if H_0 is true), the chi-square degrees of freedom, and the calculated p-value. Invisible objects include the within group dispersion matrix.

Author(s)

Pierre Legendre is the author of the most recent version of this function asbio ver >= 1.0. Stephen Ousley discovered an error in the original code. Ken Aho was the author of the original function

References

Kullback, S. (1959) Information Theory and Statistics. John Wiley and Sons.

Legendre, P, and Legendre, L. (1998) Numerical Ecology, 2nd English edition. Elsevier, Amsterdam, The Netherlands.

Examples

Y1<-rnorm(100,10,2)
Y2<-rnorm(100,15,2)
Y3<-rnorm(100,20,2)
Y<-cbind(Y1,Y2,Y3)
X<-factor(c(rep(1,50),rep(2,50)))
Kullback(Y,X)