The Annals of Statistics

Generalized score test of homogeneity for mixed effects models

Hongtu Zhu and Heping Zhang

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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.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1545-1569.

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F05: Asymptotic properties of tests
Secondary: 62F40: Bootstrap, jackknife and other resampling methods

Functional central limit theorem latent variable random quadratic form score test variance component


Zhu, Hongtu; Zhang, Heping. Generalized score test of homogeneity for mixed effects models. Ann. Statist. 34 (2006), no. 3, 1545--1569. doi:10.1214/009053606000000380.

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