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 effects that may fail to account for more complex relationships governing the data. First, we propose a fully Bayesian model selection approach of grouping the data according to the levels of a categorical predictor to reveal latent group-based fixed effects, heteroscedasticity, and/or hidden interactions. We test for both the presence and structure of such clustering. Second, we discuss a Bayesian model averaging approach to conduct inference in this context via mixture g-priors and fractional Bayes factors. We illustrate our method through simulation studies and empirical data examples representing ANCOVA and two-way unreplicated layouts, although the method we describe is broadly applicable to the class of linear models that include categorical predictors.