Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 2, 263--291

On Exact Quasilikelihood Inference in Generalized Linear Mixed Models

Brajendra C. Sutradhar , Memorial University of

Newfoundland, St. John's, Canada

SUMMARY. It is well-known that the penalized quasi-likelihood (PQL) approach may not yield consistent estimators for the parameters of the generalized linear mixed model (GLMM). Jiang (1998) introduced a  method of moments (MM) to estimate the parameters of the GLMM. The moment estimators may however be highly inefficient. To overcome this inefficiency problem, recently Jiang and Zhang (2001) suggest an improvement over the method of moments. It is however demonstrated in this paper that the estimators obtained based on the improved method of moments (IMM) may also be highly inefficient as compared to the estimators obtained based on a proposed quasi-likelihood (QL) approach. The QL estimators are consistent and highly efficient, the exact maximum likelihood estimators being fully efficient (i.e., optimal) which are however known to be difficult to compute.

AMS (1991) subject classification. Primary 62G05; secondary 62A10, 62F10.

Key words and phrases. Efficiency, moment, likelihood and quasilikelihood estimators, regression effects and variance component of the random effects..

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