Log-likelihood ratio test for equality of two or more covariance matrices.
likel.cov(x, ina, a = 0.05)A vector with the the test statistic, the p-value, the degrees of freedom and the critical value of the test.
A matrix containing Euclidean data.
A vector denoting the groups of the data.
The significance level, set to 0.05 by default.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
Tthe hypothesis test is that of the equality of at least two covariance matrices: \(H_0:\pmb{\Sigma}_1=\ldots=\pmb{\Sigma}_k\). The algorithm is taken from Mardia, Bibby and Kent (1979, pg. 140). The log-likelihood ratio test is the multivariate generalization of Bartlett's test of homogeneity of variances. The test statistic takes the following form $$ -2log{\lambda}=n\log{\left|{\bf S}\right|}-\sum_{i=1}^kn_i\log{\left|{\bf S_i}\right|}=\sum_{i=1}^kn_i\log{\left|{\bf S}_i^{-1}{\bf S}\right|}, $$ where \({\bf S}_i\) is the \(i\)-th sample biased covariance matrix and \({\bf S}=n^{-1}\sum_{i=1}^kn_i{\bf S}_i\) is the maximum likelihood estimate of the common covariance matrix (under the null hypothesis) with \(n=\sum_{i=1}^kn_i\). The degrees of freedom of the asymptotic chi-square distribution are \(\frac{1}{2}\left(p+1\right)\left(k-1\right)\).
Mardia K.V., Kent J.T. and Bibby J.M. (1979). Multivariate Analysis. London: Academic Press.
equal.cov, Mtest.cov
x <- as.matrix( iris[, 1:4] )
ina <- iris[, 5]
likel.cov(x, ina)
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