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Youngjo Lee, Linear and Generalized Linear Models and Their Applications by J. Jiang, Biometrics, Volume 63, Issue 4, December 2007, Pages 1297–1298, https://doi.org/10.1111/j.1541-0420.2007.00905_2.x
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This book, which has grown out of the author's research on this area, deserves close attention. It provides a good reference source for an advanced graduate course and would prove useful for research workers who wish to learn about theoretical developments in this area.
The book consists of two parts, one on linear mixed models and the other on generalized linear mixed models (GLMMs). Chapter 1 opens with real data examples and a review of the linear mixed model, in particular the point estimation of variance components and related topics, including maximum likelihood and restricted (or residual) maximum likelihood methods, and examines the use of their estimating equations under non-Gaussian models. The author reviews their interpretation and modification under various headings: quasi-likelihood, partially observed information, iterative weighted least squares, and the jackknife method. Then comes a review of classical estimation with examples. In Chapter 2, we have confidence intervals, the prediction of random effects, model checking and model selection, and their extensions to non-Gaussian models. Some methods for non-Gaussian models are applicable only on a model-by-model basis, and it is hard to see how theory and method developments for such complex models can be developed without resorting to likelihood methodology. The author ends this chapter with a review of Bayesian methods with derivations of normal likelihood and restricted likelihood under the Bayesian framework. In Chapter 3, he introduces the GLMMs and discusses the difficulties of obtaining marginal likelihood. Approximate inferences, such as the penalized quasi-likelihood method, are covered. He then introduces prediction of random effects, including when the normality assumption does not hold. In Chapter 4 various strands of likelihood-based inferences are reviewed, including quadratures, MCEM, and maximization by parts. He then reviews alternatives such as Bayesian inference, generalized estimating equations, the method of simulated moments, and their extensions to GLMMs. There are extensive studies of the cases when the distributional assumptions are not satisfied or not specified.
