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Empirical scientists often are faced with incomplete data and desire imputations for their missing data values. The expectation–maximization algorithm is a generic tool that offers maximum likelihood solutions for such data sets. This article pursues this type of solution for Poisson random variables, utilizing a generalized linear model extension that mirrors the linear analysis of a covariance regression specification. This formulation allows a mixed model to be implemented and contrasted with a Poisson-gamma mixture (i.e., negative binomial) model. Simple comparisons are made between model specification results for a population counts example, with and without a constraint on the total of the missing counts.

实证研究常面临数据缺失问题,需要相应的数据插补方法。最大期望算法(EM)为此类数据集进行最大似然求解提供了通用工具。本文通过提出一个可包含线性协方差回归(ANCOVA)等在内的扩展广义线性模型,将该类解决方案拓展到泊松随机变量。该方法允许建立混合模型,并可与泊松-伽玛混合模型(即负二项式)对比。以人口计数为案例对有无缺失数据条件下模型的设定与结果进行了简要的对比。