Bayesian Factor Analysis for Inference on Interactions

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.

Powering Research through Innovative Methods for Mixtures in Epidemiology (PRIME) Program: Novel and Expanded Statistical Methods

“…Estimates interactions between highly correlated chemical exposures and effect on health outcomes. [12] Duke GIF-SIS Generalized infinite factor model Shrinkage prior to the loadings matrix of infinite factor models that incorporate meta covariates to inform the sparsity structure and has desirable shrinkage properties. Addresses how to incorporate a priori known structure among variables when fitting a member of the broad class of factorization models.…”

Moving beyond Ordinary Factor Analysis in Studies of Personality and Personality Disorder: A Computational Modeling Perspective

“…to quantify patterns of covariance among observed variables – with no assumptions regarding the underlying mechanisms of those behaviors [58] (e.g., cognitive, physiological, neural; for a conceptual exception, see Beauchaine and Zisner [26]). Although Bayesian FA exists and can accommodate nested hierarchies, interactions across levels of analysis, and complex nonlinearities [59], it has also been applied agnostically with respect to underlying neural, cognitive, and physiological mechanisms of behavior.…”

“…3). Furthermore, statistical approaches such as hierarchical Bayesian analysis (HBA; described below) offer unified frameworks within which such models can be developed [53, 59].…”

“…Using such a framework, complex nested family effects and broader social dynamics can emerge from simple decision mechanisms/rules that individuals follow within immediate, proximal, and more distal social networks [74]. Such models are already used to infer etiological factors of disease spread following chemical exposures, and to identify possible contributing factors to spatially correlated disease expressions [59, 75].…”

Gene‐gene interaction analysis incorporating network information via a structured Bayesian approach

“…10 There are also a few recent Bayesian methodological developments without reinforcing hierarchy, such as the works of Ren et al 11 and Ferrari and Dunson. 12 With the high dimensions of genetic measurements but limited sample sizes, the existing interaction analysis usually suffers from a lack of information, which leads to unsatisfactory results. To improve identification and prediction performance, in main-effect-only analysis, a promising direction is to incorporate biological network information, and there are roughly two strategies.…”