Generalized Linear Models With Random Effects; A Gibbs Sampling Approach
针对含随机效应的广义线性模型计算困难的问题，本文提出用吉布斯抽样方法在贝叶斯框架下进行估计，并通过模拟和传染病数据分析展示了方法的灵活性。
Abstract Generalized linear models have unified the approach to regression for a wide variety of discrete, continuous, and censored response variables that can be assumed to be independent across experimental units. In applications such as longitudinal studies, genetic studies of families, and survey sampling, observations may be obtained in clusters. Responses from the same cluster cannot be assumed to be independent. With linear models, correlation has been effectively modeled by assuming there are cluster-specific random effects that derive from an underlying mixing distribution. Extensions of generalized linear models to include random effects has, thus far, been hampered by the need for numerical integration to evaluate likelihoods. In this article, we cast the generalized linear random effects model in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations. The resulting algorithm is flexible to easily accommodate changes in the number of random effects and in their assumed distribution when warranted. The methodology is illustrated through a simulation study and an analysis of infectious disease data.