Estimation using penalized quasilikelihood and quasi-pseudo-likelihood in Poisson mixed models

We consider two estimation schemes based on penalized quasilikelihood and quasi-pseudo-likelihood in Poisson mixed models. The asymptotic bias in regression coefficients and variance components estimated by penalized quasilikelihood (PQL) is studied for small values of the variance components. We show the PQL estimators of both regression coefficients and variance components in Poisson mixed models have a smaller order of bias compared to those for binomial data. Unbiased estimating equations based on quasi-pseudo-likelihood are proposed and are shown to yield consistent estimators under some regularity conditions. The finite sample performance of these two methods is compared through a simulation study.