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 neurodevelopment 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 multigroup 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.
Funding Statement
This research was partially supported by grant R01-ES027498 and R01-ES028804 from the National Institute of Environmental Health Sciences (NIEHS) of the National Institutes of Health (NIH).
Acknowledgments
We would like to thank Roberta De Vito for sharing her source code of the Bayesian MSFA model. We would also like to thank Noirrit Kiran Chandra for his feedback on the code which heavily improved its usage both in low- and high-dimensional settings.
Citation
Arkaprava Roy. Isaac Lavine. Amy H. Herring. David B. Dunson. "Perturbed factor analysis: Accounting for group differences in exposure profiles." Ann. Appl. Stat. 15 (3) 1386 - 1404, September 2021. https://doi.org/10.1214/20-AOAS1435
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