Perturbed factor analysis: Accounting for group differences in exposure profiles

TL;DR

This paper introduces Perturbed Factor Analysis (PFA), a novel Bayesian method for identifying common exposure factors across groups while accounting for group-specific differences, demonstrated on NHANES phthalate data.

Contribution

The paper proposes a new PFA model that improves multi-group factor analysis by allowing flexible group differences through data perturbation, with efficient Bayesian inference algorithms.

Findings

PFA effectively captures common exposure factors across groups.

Application to NHANES data reveals group differences in phthalate exposure profiles.

Simulation studies show PFA's advantages over existing models.

Abstract

In this article, we investigate group differences in phthalate exposure profiles using NHANES data. Phthalates are a family of industrial chemicals used in plastics and as solvents. There is increasing evidence of adverse health effects of exposure to phthalates on reproduction and neuro-development, and concern about racial disparities in exposure. We would like to identify a single set of low-dimensional factors summarizing exposure to different chemicals, while allowing differences across groups. Improving on current multi-group additive factor models, we propose a class of Perturbed Factor Analysis (PFA) models that assume a common factor structure after perturbing the data via multiplication by a group-specific matrix. Bayesian inference algorithms are defined using a matrix normal hierarchical model for the perturbation matrices. The resulting model is just as flexible as current approaches in allowing arbitrarily large differences across groups but has substantial advantages that we illustrate in simulation studies. Applying PFA to NHANES data, we learn common factors summarizing exposures to phthalates, while showing clear differences across groups.