REML estimation for binary data in GLMMs
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.
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Volume (Year): 98 (2007)
Issue (Month): 5 (May)
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- Thomas R. Ten Have & A. Russell Localio, 1999. "Empirical Bayes Estimation of Random Effects Parameters in Mixed Effects Logistic Regression Models," Biometrics, The International Biometric Society, vol. 55(4), pages 1022-1029, December.
- Yun, Sungcheol & Lee, Youngjo, 2004. "Comparison of hierarchical and marginal likelihood estimators for binary outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 639-650, April.
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