Robustness of asymptotic and bootstrap tests for multivariate homogeneity of covariance matrices

Abstract

The present work emphasizes the importance of testing hypothesis on homogeneity of covariance matrices from multivariate k populations. The violation of the assumption of the homogeneity of covariance matrices affects the performance of the tests and the coverage probability of the confidence regions. This work intends to apply two tests of homogeneity of covariance and to evaluate type I error rates and power using Monte Carlo simulation in normal populations and robustness in non normal populations. Multivariate Bartlett's test (MBT) and its bootstrap version (MBTB) were used. Different configurations are tested combining sample sizes, number of variates, correlation and number of populations. Results show that the bootstrap test was considered superior to the asymptotic test and robust, since it controls the type error I rate.

Likelihood ratio test between two groups of castor oil plant traits

“…However, with 14 or more variables, the type I error rates increased, and the test became liberal (it exceeded the upper limit of 99% of the CI=6.255%). A hypothesis test is classified as liberal when the type I error rates are higher than the minimum significance level that is established (α) (SILVA et al, 2008). With samples larger than n=50 ( Figure 1B), increases in the total number of variables did not affect the type I error rate, and it stayed close to 5%.…”

“…When evaluating the behavior of two tests for the equality of variance matrices of k populations (multivariate Bartlett test and its bootstrap version) with the use of a Monte Carlo simulation, in normal and non-normal populations, in combinations of the sample sizes (n), number of variables (p), correlations (r) and number of populations (k), SILVA et al (2008) reported that the multivariate Bartlett test controls the type I error in almost all combinations for k=2; however, it becomes liberal when k is increased to 5. In both situations (k=2 and 5), the type I error rates increased greatly with the increase in the number of variables in sample sizes varying from 5 to 50.…”