Abstract–Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way unreplicated layout has shown that hidden groupings among the levels of one categorical predictor frequently interact with the ungrouped factor. We extend the notion of a “latent grouping factor” to linear models in general. The proposed work allows researchers to determine whether an apparent grouping of the levels of a categorical predictor reveals a plausible hidden structure given the observed data. Specifically, we offer a Bayesian model selection-based approach to reveal latent group-based heteroscedasticity, regression effects, and/or interactions. Failure to account for such structures can produce misleading conclusions. Since the presence of latent group structures is frequently unknown a priori to the researcher, we use fractional Bayes factor methods and mixture g-priors to overcome lack of prior information.

中文翻译：

---

通过贝叶斯模型选择检测线性模型中的潜在异方差和基于组的回归效应

摘要——标准线性建模方法对分类效应的结构做出了潜在的简单假设，这些假设可能会混淆更复杂的数据关系。例如，最近关注双向非复制布局的工作表明，一个分类预测变量的级别之间的隐藏分组经常与未分组的因素相互作用。我们将“潜在分组因子”的概念扩展到一般的线性模型。拟议的工作使研究人员能够确定，给定观察到的数据，分类预测变量的层次的明显分组是否揭示了一个看似合理的隐藏结构。具体来说，我们提供了一种基于贝叶斯模型选择的方法来揭示基于潜在组的异方差性、回归效应和/或相互作用。不考虑这些结构可能会产生误导性的结论。由于潜在组结构的存在对于研究人员来说通常是先验未知的，因此我们使用分数贝叶斯因子方法和混合 g-先验来克服先验信息的缺乏。