A generalized linear model with nested strata of extra-Poisson variation
Richard Morton · Biometrika · 1987
We consider a scaled Poisson generalized linear model with random multiplicative errors associated with each stratum of a nested block structure. The normal equations are obtained. The quasi-likelihood is shown to be the product of a sequence of negative binomial quasi-likelihoods using weighted totals and correcting for margins. This is achieved by extending the definition of the quasi-likelihood which now includes a vector of weights. The usual asymptotic results still hold. Data on trap catches of insects provide a numerical example.