Get access

Permutation Tests for Random Effects in Linear Mixed Models

Authors

  • Oliver E. Lee,

    Corresponding author
    1. Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109-2029, U.S.A.
      email: oel@umich.edu
    Search for more papers by this author
  • Thomas M. Braun

    Corresponding author
    1. Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109-2029, U.S.A.
      email: tombraun@umich.edu
    Search for more papers by this author

email:oel@umich.edu

email:tombraun@umich.edu

Abstract

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.

Get access to the full text of this article

Ancillary