title: Detecting the violation of variance homogeneity in mixed models.
abstract: Mixed-effects models are increasingly used in many areas of applied science. Despite their popularity, there is virtually no systematic approach for examining the homogeneity of the random-effects covariance structure commonly assumed for such models. We propose two tests for evaluating the homogeneity of the covariance structure assumption across subjects: one is based on the covariance matrices computed from the fitted model and the other is based on the empirical variation computed from the estimated random effects. We used simulation studies to compare performances of the two tests for detecting violations of the homogeneity assumption in the mixed-effects models and showed that they were able to identify abnormal clusters of subjects with dissimilar random-effects covariance structures; in particular, their removal from the fitted model might change the signs and the magnitudes of important predictors in the analysis. In a case study, we applied our proposed tests to a longitudinal cohort study of rheumatoid arthritis patients and compared their abilities to ascertain whether the assumption of covariance homogeneity for subject-specific random effects holds.
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, Singapore.
authors.forename: Xicheng
authors.initials: X
authors.lastname: Fang
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, Singapore.|Centre for Quantitative Medicine, Duke-NUS Graduate Medical School, National University of Singapore, Singapore.|Singapore Eye Research Institute, National University of Singapore, Singapore.
authors.forename: Jialiang
authors.initials: J
authors.lastname: Li
authors.affiliation: Department of Biostatistics, School of Public Health, University of California at Los Angeles, USA.
authors.forename: Weng Kee
authors.initials: WK
authors.lastname: Wong
authors.affiliation: Centre for Biostatistics and Arthritis Research UK Epidemiology Unit, The University of Manchester, UK bo.fu@manchester.ac.uk.
authors.forename: Bo
authors.initials: B
authors.lastname: Fu
mesh_terms: D001172:Arthritis, Rheumatoid; D006801:Humans; D008137:Longitudinal Studies; D011788:Quality of Life; D012044:Regression Analysis; D006113:United Kingdom
keywords: empirical estimator; longitudinal data; mixed-effects models; outlier test; variance homogeneity