Log-likelihood ratio test for equality of two or more covariance matrices {mvhtests} | R Documentation |
Log-likelihood ratio test for equality of two or more covariance matrices
Description
Log-likelihood ratio test for equality of two or more covariance matrices.
Usage
likel.cov(x, ina, a = 0.05)
Arguments
x |
A matrix containing Euclidean data. |
ina |
A vector denoting the groups of the data. |
a |
The significance level, set to 0.05 by default. |
Details
Tthe hypothesis test is that of the equality of at least two covariance matrices: . 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
where is the
-th sample biased covariance matrix and
is the maximum likelihood estimate of the common covariance matrix (under the null hypothesis) with
. The degrees of freedom of the asymptotic chi-square distribution are
.
Value
A vector with the the test statistic, the p-value, the degrees of freedom and the critical value of the test.
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
References
Mardia K.V., Kent J.T. and Bibby J.M. (1979). Multivariate Analysis. London: Academic Press.
See Also
Examples
x <- as.matrix( iris[, 1:4] )
ina <- iris[, 5]
likel.cov(x, ina)