| Box's M test for equality of two or more covariance matrices {mvhtests} | R Documentation |
Box's M test for equality of two or more covariance matrices
Description
Box's M test for equality of two or more covariance matrices.
Usage
Mtest.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
According to Mardia, Kent and Bibby (1979, pg. 140), it may be argued that if n_i is small, then the log-likelihood ratio test (function likel.cov) gives too much weight to the contribution of {\bf S}. This consideration led Box (1949) to propose another test statistic in place of that seen in likel.cov . Box's M is given by
M=\gamma\sum_{i=1}^k\left(n_i-1\right)\log{\left|{\bf S}_{i}^{-1}{\bf S}_p \right|},
where \gamma=1-\frac{2p^2+3p-1}{6\left(p+1\right)\left(k-1\right)}\left(\sum_{i=1}^k\frac{1}{n_i-1}-\frac{1}{n-k}\right) and {\bf S}_{i} and {\bf S}_{p} are the i-th unbiased covariance estimator and the pooled covariance matrix, respectively with {\bf S}_p=\frac{\sum_{i=1}^k\left(n_i-1\right){\bf S}_i}{n-k}. Box's M also has an asymptotic \chi^2 distribution with \frac{1}{2}\left(p+1\right)\left(k-1\right) degrees of freedom. Box's approximation seems to be good if each n_i exceeds 20 and if k and p do not exceed 5 (Bibby and Kent (1979) pg. 140).
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]
Mtest.cov(x, ina)