This article concerns a class of generalized linear mixed models for two-level grouped data, where the random effects are uniquely indexed by groups and are independent. We derive necessary and sufficient conditions for the marginal likelihood to be expressed in explicit form. These models are unified under the conjugate generalized linear mixed models framework, where conjugate refers to the fact that the marginal likelihood can be expressed in closed form, rather than implying inference via the Bayesian paradigm. The proposed framework allows simultaneous conjugacy for Gaussian, Poisson and gamma responses, and thus can accommodate both unit- and group-level covariates. Only group-level covariates can be incorporated for the binomial distribution. In a simulation of Poisson data, our framework outperformed its competitors in terms of computational time, and was competitive in terms of robustness against misspecification of the random effects distributions.

中文翻译：

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使用共轭广义线性混合模型分析分组数据

本文涉及用于两级分组数据的一类广义线性混合模型，其中随机效应由组唯一索引并且是独立的。我们得出了以明确形式表示边际可能性的必要和充分条件。这些模型在共轭广义线性混合模型框架下是统一的，其中共轭是指边际可能性可以用封闭形式表示的事实，而不是暗示通过贝叶斯范式进行推断。提出的框架允许对高斯响应，泊松响应和伽马响应同时进行共轭，因此可以同时适应单元级和组级协变量。对于二项分布，只能合并组级协变量。在Poisson数据的模拟中，