A Generalized Linear Model with Nested Strata of Extra-Poisson Variation

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Abstract
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.

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