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. We provide an R package, slgf, that implements our methodology in practice, and demonstrate its usage in practice. / Doctor of Philosophy / Statistical models are a powerful tool for describing a broad range of phenomena in our world. However, many common statistical models may make assumptions that are overly simplistic and fail to account for key trends and patterns in data. Specifically, we search for hidden structures formed by partitioning a dataset into two groups. These two groups may have distinct variability, statistical effects, or other hidden effects that are missed by conventional approaches. We illustrate the ability of our method to detect these patterns through a variety of disciplines and data layouts, and provide software for researchers to implement this approach in practice.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/93226 |
| Date | 22 August 2019 |
| Creators | Metzger, Thomas Anthony |
| Contributors | Statistics, Franck, Christopher T., House, Leanna L., Gramacy, Robert B., Ferreira, Marco A. R. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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