Bayesian Factor Analysis for Inference on Interactions


Journal Article

© 2020, © 2020 American Statistical Association. This article is motivated by the problem of inference on interactions among chemical exposures impacting human health outcomes. Chemicals often co-occur in the environment or in synthetic mixtures and as a result exposure levels can be highly correlated. We propose a latent factor joint model, which includes shared factors in both the predictor and response components while assuming conditional independence. By including a quadratic regression in the latent variables in the response component, we induce flexible dimension reduction in characterizing main effects and interactions. We propose a Bayesian approach to inference under this factor analysis for interactions (FIN) framework. Through appropriate modifications of the factor modeling structure, FIN can accommodate higher order interactions. We evaluate the performance using a simulation study and data from the National Health and Nutrition Examination Survey. Code is available on GitHub. Supplementary materials for this article are available online.

Full Text

Duke Authors

Cited Authors

  • Ferrari, F; Dunson, DB

Published Date

  • January 1, 2020

Published In

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2020.1745813

Citation Source

  • Scopus