Permutation Tests for Random Effects in Linear Mixed Models
Article first published online: 27 SEP 2011
© 2011, The International Biometric Society
Volume 68, Issue 2, pages 486–493, June 2012
How to Cite
Lee, O. E. and Braun, T. M. (2012), Permutation Tests for Random Effects in Linear Mixed Models. Biometrics, 68: 486–493. doi: 10.1111/j.1541-0420.2011.01675.x
- Issue published online: 26 JUN 2012
- Article first published online: 27 SEP 2011
- Received December 2010. Revised July 2011. Accepted August 2011.
- Hypothesis testing;
- Longitudinal data;
- Variance components
Summary Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ2 distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ2 distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve 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 and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.