Canal
Detection of Latent Heteroscedasticity and Group-Based Effects in Linear Models via Bayesian Model Selection (303762)
Christopher T. Franck, Virginia Tech
*Thomas Anthony Metzger, Virginia Tech
Keywords: Bayesian, model selection, heteroscedasticity
Categorical predictors are widely used in linear models in a variety of applications. Standard modeling approaches make potentially simplistic assumptions regarding the structure of categorical model effects that may obfuscate more complex relationships governing the data. We propose a fully Bayesian model selection approach of clustering the data according to the levels of a categorical predictor to reveal latent group-based fixed effects, heteroscedasticity, and/or hidden interactions. Through the use of mixture g-priors and fractional Bayes factors, we test for both the presence and structure of such clustering. We illustrate our method in the context of one-way ANOVA, unreplicated two-way layouts, and ANCOVA by analyzing empirical data sets that depict common statistical applications, although the method we describe is broadly applicable to the class of linear models that include categorical predictors.