A higher-order approximation to likelihood inference in the Poisson mixed model

Sutradhar and Qu (Canad. J. Statist. 26 (1998) 169) have introduced a small variance component (for random effects) based likelihood approximation (LA) approach to estimate the parameters of the Poisson mixed models, and have shown that their LA approach performs better compared to other leading approaches. This paper further improves the LA of Sutradhar and Qu (1998) to accommodate larger values of the variance component, and provides the improved LA (ILA) based estimators for the regression parameters as well as the variance component of the random effects of the model. The results of a simulation study show that the ILA approach leads to significant improvement over the LA approach in estimating the parameters of the model, the variance component of the random effects in particular.