---
abstract: '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 (NHANES). Code is available on GitHub.'
author:
- |
    Federico Ferrari\
    Department of Statistical Science, Duke University\
    and\
    David B. Dunson\
    Department of Statistical Science, Duke University
bibliography:
- '99BIB.bib'
title: '**Bayesian Factor Analysis for Inference on Interactions**'
---

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[**Bayesian Factor Analysis for Inference on Interactions**]{}

[*Keywords:*]{} Bayesian Modeling; Chemical Mixtures; Correlated Exposures; Quadratic regression; Statistical Interactions

Introduction {#sec:intro}
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There is 