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Bayesian Factor Analysis for Inference on Interactions

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  • Federico Ferrari
  • David B. Dunson

Abstract

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. Code is available on GitHub. Supplementary materials for this article are available online.

Suggested Citation

  • Federico Ferrari & David B. Dunson, 2021. "Bayesian Factor Analysis for Inference on Interactions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1521-1532, July.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:535:p:1521-1532
    DOI: 10.1080/01621459.2020.1745813
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    Cited by:

    1. Jaejoon Lee & Seongil Jo & Jaeyong Lee, 2022. "Robust sparse Bayesian infinite factor models," Computational Statistics, Springer, vol. 37(5), pages 2693-2715, November.
    2. L Schiavon & A Canale & D B Dunson, 2022. "Generalized infinite factorization models [A latent factor linear mixed model for high-dimensional longitudinal data analysis]," Biometrika, Biometrika Trust, vol. 109(3), pages 817-835.

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