Permutation Tests for Random Effects in Linear Mixed Models

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Oliver Lee*+
• Companies: University of Michigan
• Keywords: Variance component ; Randomization Test ; Mixed Models ; Random Effects

Abstract

It has been proven that the correct null distribution for testing the inclusion or exclusion of random effects in linear mixed models is a mixture of chi-squared distributions. However, the appropriate mixture distribution is rather cumbersome and non-intuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests whose statistics are based on weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within- and among-subjects and are valid both asymptotically as well as in small samples. We examine the size of our tests via simulation in a variety of settings and compare it to the size based upon the classical mixture-of-chi-squares approach.