Generalized score test of homogeneity for mixed effects models

• 成果类型: Article
• 署名作者: Zhu, Hongtu; Zhang, Heping
• 署名单位: Columbia University; New York State Psychiatry Institute; Yale University; Jiangxi Normal University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000380
• 发表日期: 2006
• 页码: 1545-1569
• 关键词: likelihood ratio tests; segregation analysis; quadratic-forms; inference

摘要

Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the existing testing procedures depend on restrictive assumptions. In this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero. Under some mild conditions, not only do we derive asymptotic distributions of the test statistics, but also propose a resampling procedure for approximating their asymptotic distributions conditional on the observed data. To overcome the technical challenge, we establish an invariance principle for random quadratic forms indexed by a parameter. A simulation study is conducted to investigate the empirical performance of the test statistics. A real data set is analyzed to illustrate the application of our theoretical results.