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Activity Number: 340 - SPEED: Bayesian Methods, Part 1
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #304817 Presentation 1 Presentation 2
Title: Bayesian Model Selection and Averaging in the Presence of Latent Heteroscedasticity in Linear Models
Author(s): Thomas Metzger* and Christopher Franck
Companies: Virginia Tech and Virginia Tech
Keywords: fractional Bayes factor; mixture g-prior; model selection; model averaging; 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 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.

Authors who are presenting talks have a * after their name.

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