Bayesian model selection for generalized linear mixed models
Bayesian model selection for generalized linear mixed models
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DOI：
10.1111/biom.13896
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发表时间：
2023-06-27
期刊：
影响因子：
1.9
通讯作者：
Franck，Christopher T.
中科院分区：
文献类型：
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作者：
Xu，Shuangshuang;Ferreira，Marco A. R.;Franck，Christopher T.
提出了一种广义线性混合模型的贝叶斯模型选择方法。我们考虑随机效应的协方差结构，这些随机效应广泛用于纵向研究、全基因组关联研究和空间统计等领域。由于随机效应无法从GLST分析中积分，因此我们使用伪似然方法近似积分似然函数。我们的贝叶斯方法假设固定效应的先验是平坦的，并包括随机效应方差的近似参考先验和半柯西先验选择。由于固定效应的平坦先验是不合适的，我们开发了一个分数贝叶斯因子方法来获得几个竞争模型的后验概率。与空间随机效应和过度分散随机效应的Poisson GLSINS的仿真研究表明，我们的方法相比，广泛使用的竞争贝叶斯方法，包括偏差信息准则和渡边赤池信息准则表现良好。我们说明了我们的方法的有用性和灵活性，三个案例研究，包括泊松纵向模型，泊松空间模型和逻辑混合模型。我们提出的方法是在R包GLMMselect中实现的，可以在CRAN上使用。
We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome‐wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo‐likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half‐Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.