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Whither PQL?

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Book cover Proceedings of the Second Seattle Symposium in Biostatistics

Part of the book series: Lecture Notes in Statistics ((LNS,volume 179))

Abstract

Generalized linear mixed models (GLMM) are generalized linear models with normally distributed random effects in the linear predictor. Penalized quasi-likelihood (PQL), an approximate method of inference in GLMMs, involves repeated fitting of linear mixed models with “working” dependent variables and iterative weights that depend on parameter estimates from the previous cycle of iteration. The generality of PQL, and its implementation in commercially available software, has encouraged the application of GLMMs in many scientific fields. Caution is needed, however, since PQL may sometimes yield badly biased estimates of variance components, especially with binary outcomes.

Recent developments in numerical integration, including adaptive Gaussian quadrature, higher order Laplace expansions, stochastic integration and Markov chain Monte Oarlo (MOMO) algorithms, provide attractive alternatives to PQL for approximate likelihood inference in GLMMs. Analyses of some well known datasets, and simulations based on these analyses, suggest that PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. Adaptive Gaussian quadrature is a viable alternative for nested designs where the numerical integration is limited to a small number of dimensions. Higher order Laplace approximations hold the promise of accurate inference more generally. MOMO is likely the method of choice for the most complex problems that involve high dimensional integrals

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Authors and Affiliations

  1. Department of Biostatistics, University of Washington, USA

    Norman Breslow

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  1. Norman Breslow
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Editors and Affiliations

  1. School of Public Health, Department of Biostatistics, CB #7420, University of North Carolina, Chapel Hill, NC, 27599-7420, USA

    D. Y. Lin

  2. School of Public Health and Community Medicine, Department of Biostatistics, University of Washington, Box 357232, Seattle, WA, 98195, USA

    P. J. Heagerty

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Breslow, N. (2004). Whither PQL?. In: Lin, D.Y., Heagerty, P.J. (eds) Proceedings of the Second Seattle Symposium in Biostatistics. Lecture Notes in Statistics, vol 179. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9076-1_1

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  • DOI: https://doi.org/10.1007/978-1-4419-9076-1_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-20862-6

  • Online ISBN: 978-1-4419-9076-1

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