Generalized Linear Models with Random Effects: Unified Analysis via H-Likelihood, by Youngjo Lee, John A. Nelder, Yudi Pawitan. Monographs on statistics and applied probability 106. Boca Raton, FL: Chapman & Hall/CRC, 2006.
QA279 .L43 2006 New Book Shelf Link to MNCAT record.
John Nelder pioneered these topics in several highly-cited works:
â€śGeneralized linear modelsâ€? (with R. W. M. Wedderburn), Journal of the Royal Statistical Society, Series A: General, 135, 370-384; Link to article
Generalized linear models (with P. McCullagh). Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1983. Link to MNCAT record.
â€śHierarchical generalized linear modelsâ€? (with Y. Lee), Journal of the Royal Statistical Society, Series B 58 (1996), no. 4, 619--678. Link to article
and others. The current monograph greatly extends the class of GLMs: â€śFirst, to the fixed effects may be added one or more sets of random effects on the same linear scale; secondly GLMs may be fitted simultaneously to both mean and dispersion; thirdly the random effects may themselves be correlated, allowing the expression of models for both temporal and spatial correlation; lastly random effects may appear in the model for the dispersion as well as that for the mean. To allow likelihood-based inferences for the new model class, the idea of h-likelihood is introduced as a criterion to be maximized. This allows a single algorithm, expressed as a set of interlinked GLMs, to be used for fitting all members of the class. The algorithm does not require the use of quadrature in the fitting, and neither are prior probabilities required. The result is that the algorithm is orders of magnitude faster than some existing alternatives.â€? Applications to survival data, financial data, and denoising signals are discussed.