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June 2006 Generalized score test of homogeneity for mixed effects models
Hongtu Zhu, Heping Zhang
Ann. Statist. 34(3): 1545-1569 (June 2006). DOI: 10.1214/009053606000000380


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.


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Hongtu Zhu. Heping Zhang. "Generalized score test of homogeneity for mixed effects models." Ann. Statist. 34 (3) 1545 - 1569, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62018
MathSciNet: MR2278367
Digital Object Identifier: 10.1214/009053606000000380

Primary: 62F05
Secondary: 62F40

Keywords: functional central limit theorem , latent variable , random quadratic form , score test , variance component

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
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