Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 98, Issue 5, Pages 896-915Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2006.11.009
Keywords
generalized linear mixed models; hierarchical generalized linear models; restricted maximum likelihood; restricted likelihood; hierarchical likelihood; Laplace method
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Funding
- National Research Foundation of Korea [핵06A2702, R11-2000-073-02001-0] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in mixed linear models. However, its extension to hierarchical generalized linear models (HGLMs) is often hampered by analytically intractable integrals. Numerical integration such as Gauss-Hermite quadrature (GHQ) is generally not recommended when the dimensionality of the integral is high. With binary data various extensions of the REML method have been suggested, but they have had unsatisfactory biases in estimation. In this paper we propose a statistically and computationally efficient REML procedure for the analysis of binary data, which is applicable over a wide class of models and design structures. We propose a bias-correction method for models such as binary matched pairs and discuss how the REML estimating equations for mixed linear models can be modified to implement more general models. (c) 2007 Elsevier Inc. All rights reserved.
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