A Generalized Linear Model with Nested Strata of Extra-Poisson Variation
研究了一个带嵌套分层随机乘法误差的缩放泊松广义线性模型，推导了正规方程，并将准似然表示为加权总和与边际校正后的负二项准似然乘积，适用于昆虫诱捕数据等计数资料分析。
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.