Generalized linear mixed models a pseudo-likelihood approach

A useful extension of the generalized linear model involves the addition of random effects andlor correlated errors. A pseudo-likelihood estimation procedure is developed to fit this class of mixed models based on an approximate marginal model for the mean response. The procedure is implemented via iterated fitting of a weighted Gaussian linear mixed model to a modified dependent variable. The approach allows for flexible specification of covariance structures for both the random effects and the correlated errors. An estimate of an additional dispersion parameter for underlying exponential family distributions is optionally automatic. The method allows for subject-specific and population-averaged inference, and the Salamander data example from McCullagh and Nelder (1989) is used to illustrate both.