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REML estimation for binary data in GLMMs


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  • Noh, Maengseok
  • Lee, Youngjo
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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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 5 (May)
    Pages: 896-915

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:896-915

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    Keywords: Generalized linear mixed models Hierarchical generalized linear models Restricted maximum likelihood Restricted likelihood Hierarchical likelihood Laplace method;


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    1. 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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    Cited by:
    1. Lee, Woojoo & Shi, Jian Qing & Lee, Youngjo, 2010. "Approximate conditional inference in mixed-effects models with binary data," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 173-184, January.
    2. Noh, Maengseok & Lee, Youngjo, 2008. "Hierarchical-likelihood approach for nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3517-3527, March.
    3. Youngjo Lee & Myoungjin Jang & Woojoo Lee, 2011. "Prediction interval for disease mapping using hierarchical likelihood," Computational Statistics, Springer, vol. 26(1), pages 159-179, March.
    4. Meza, Cristian & Jaffr├ęzic, Florence & Foulley, Jean-Louis, 2009. "Estimation in the probit normal model for binary outcomes using the SAEM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1350-1360, February.
    5. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    6. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    7. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    8. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer, vol. 79(1), pages 84-104, January.
    9. Sumanta Adhya & Tathagata Banerjee & Gaurangadeb Chattopadhyay, 2012. "Inference on finite population categorical response: nonparametric regression-based predictive approach," AStA Advances in Statistical Analysis, Springer, vol. 96(1), pages 69-98, January.


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