Title: Bayesian Model Selection with Latent Group-Based Effects and Variances with the R Package slgf
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. I extend the notion of a “latent grouping factor” to linear models in general. This methodology 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, I offer Bayesian model selection-based approaches to reveal latent group-based heteroscedasticity, regression effects, and/or interactions. Because the presence of latent group structures is frequently unknown a priori to the researcher, I use fractional Bayes factor methods and mixture of g-priors to overcome lack of prior information. I illustrate the performance of my approach through simulation studies and empirical case studies, and I present the new R package slgf which enables the user to easily implement this approach.