Permutation Tests for Random Effects in Mixed Models.

[摘要] Inference regarding the inclusion or exclusion of random effects in mixed models is challenging because the variance components are located on the boundary of their parameter space under the null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical chi-squared distribution.Although it has been proved that the correct asymptotic distribution is a mixture of chi-squared distributions, the appropriate mixture distribution is cumbersome and non-intuitive when the null and alternative hypotheses differ by more than one random effect.This dissertation addresses these challenges through the use of permutation methods. For the first chapter, we focus on linear mixed models and present two permutation tests, one that is based on the Best Linear Unbiased Predictors (BLUPs), and one that is based on the restricted likelihood ratio test statistic. 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.Through simulations we show that our permutation tests are valid for small sample sizes and is more powerful than the asymptotic likelihood ratio test.The proposed tests are also shown to be more robust to violations of distributional assumptions compared with the asymptotic likelihood ratio tests. For the second chapter we extend the linear mixed model permutation methods to inference on random effects in generalized linear mixed models (GLMMs). We use the idea of working variates to approximate the GLMM with a linear mixed model. Through simulations we show that our permutation tests are valid and display power that is comparable to the most powerful score test.For the final chapter we demonstrate the versatility of our permutation tests with an application to linear penalized spline models. By re-expressing the penalized spline model as a mixed model our permutation tests can test the spline model alternative against a linear regression model. The validity and power are examined through simulation, and find that the BLUP based permutation test is the most powerful when compared with the permutation test of Raz and the asymptotic likelihood ratio test.

[发布机构] University of Michigan

[效力级别] Permutations

[关键词] Hypothesis Testing;Permutations;Mixed Models;Variance Components;Statistics and Numeric Data;Science;Biostatistics