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Abstract:
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This work is motivated by the problem of inference on interactions among chemical exposures impacting multivariate human health outcomes. Typical analyses consider the effect of correlated chemical exposures on univariate quantities. However, data from environmental epidemiology studies usually contain multiple correlated measurements, like BMI, waist circumference and other body measures. We propose to use latent factor models both for the exposures and outcomes and we induce a multivariate regression via the latent variables. We propose a Bayesian approach to inference under this Structural Equation Model framework, which allows for joint modeling of multivariate outcomes while characterizing the covariance structure of both exposure measurements and dependent variables. We include a quadratic regression in the latent variables associated with the multivariate response and the latent variables associated with the predictor, which provides dimension reduction in characterizing main effects and interactions. With this specification we allow for shrinkage on the regression coefficients whenever the outcomes load on the same set of factors.
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