We aim to promote the use of the modified profile likelihood for estimating the variance parameters of a GLMM in analogy to the REML criterion for linear mixed models. Our approach is based on both Quasi-Monte Carlo integration and numerical quadrature, obtaining in either case simulation-free inferential results. The method is illustrated for regression models with binary response and independent clusters, covering also the case of two-part models. Real-data examples and simulations studies support the use of the proposed solution as a natural extension of REML for GLMMs.
R., Bellio e Alessandra Rosalba, Brazzale. "Restricted likelihood inference for generalized linear mixed models" Working paper, Istituto di Ingegneria Biomedica (IsIB), Consiglio Nazionale delle Ricerche (CNR), Padova, 2008.
Restricted likelihood inference for generalized linear mixed models
BRAZZALE, Alessandra Rosalba
2008
Abstract
We aim to promote the use of the modified profile likelihood for estimating the variance parameters of a GLMM in analogy to the REML criterion for linear mixed models. Our approach is based on both Quasi-Monte Carlo integration and numerical quadrature, obtaining in either case simulation-free inferential results. The method is illustrated for regression models with binary response and independent clusters, covering also the case of two-part models. Real-data examples and simulations studies support the use of the proposed solution as a natural extension of REML for GLMMs.
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