title: A note on permutation tests for variance components in multilevel generalized linear mixed models.
abstract: In many applications of generalized linear mixed models to multilevel data, it is of interest to test whether a random effects variance component is zero. It is well known that the usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In this note we propose a permutation test, based on randomly permuting the indices associated with a given level of the model, that has the correct Type I error rate under the null. Results from a simulation study suggest that it is more powerful than tests based on mixtures of chi-square distributions. The proposed test is illustrated using data on the familial aggregation of sleep disturbance.
authors.affiliation: Harvard Medical School, Boston, MA, USA. fitzmaur@hsph.harvard.edu
authors.forename: Garrett M
authors.initials: GM
authors.lastname: Fitzmaurice
authors.forename: Stuart R
authors.initials: SR
authors.lastname: Lipsitz
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D001699:Biometry / Q000379:methods*; D016000:Cluster Analysis; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016014:Linear Models; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity