# Detection of latent heteroscedasticity and group-based regression effects in linear models via Bayesian model selection

## TL;DR

This paper introduces Bayesian model selection methods to detect hidden group structures and heteroscedasticity in linear models, improving the understanding of complex relationships among categorical predictors.

## Contribution

It extends the concept of latent grouping factors to general linear models and provides Bayesian approaches to identify hidden structures and interactions.

## Key findings

- Reveals latent group-based heteroscedasticity in data
- Detects hidden groupings among categorical predictor levels
- Improves model accuracy by accounting for complex structures

## 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 Bayesian model selection-based approaches 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.