A novel method for testing normality in a mixed model of a nested classification

Abstract

Normality is one of the most common assumptions made in the development of statistical models such as the fixed effect model and the random effect model. White and MacDonald [1980. Some large-sample tests for normality in the linear regression model. JASA 75, 16–18] and Bonett and Woodward [1990. Testing residual normality in the ANOVA model. J. Appl. Statist. 17, 383–387] showed that many tests of normality perform well when applied to the residuals of a fixed effect model. The elements of the error vector are not independent in random effects models and standard tests of normality are not expected to perform properly when applied to the residuals of a random effects model. In this paper, we propose a transformation method to convert the correlated error vector into an uncorrelated vector. Moreover, under the normality assumption, the uncorrelated vector becomes an independent vector. Thus, all the existing methods can then be implemented. Monte-Carlo simulations are used to evaluate the feasibility of the transformation. Results show that this transformation method can preserve the Type I error and provide greater powers under most alternatives.