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Maximum likelihood algorithms for generalized linear mixed models. (English) Zbl 0889.62061

Summary: Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the “joint-maximization” or penalized quasi-likelihood methods and explain why the latter can perform poorly.

MSC:

62J12 Generalized linear models (logistic models)
65C99 Probabilistic methods, stochastic differential equations
62F10 Point estimation
65C05 Monte Carlo methods
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