A Bayesian partial membership model for multiple exposures with uncertain group memberships

Alexis Zavez, Emeir M. McSorley, Alison J. Yeates, Sally Thurston

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We present a Bayesian partial membership model that estimates the associations between an outcome, a small number of latent variables, and multiple observed exposures where the number of latent variables is specified a priori. We assign one observed exposure as the sentinel marker for each latent variable. The model allows non-sentinel exposures to have complete membership in one latent group, or partial membership across two or more latent groups. MCMC sampling is used to determine latent group partial memberships for the non-sentinel exposures, and estimate all model parameters. We compare the performance of our model to competing approaches in a simulation study and apply our model to inflammatory marker data measured in a large mother-child cohort of the Seychelles Child Development Study (SCDS). In simulations, our model estimated model parameters with little bias, adequate coverage, and tighter credible intervals compared to competing approaches. Under our partial membership model with two latent groups, SCDS inflammatory marker classifications generally aligned with the scientific literature. Incorporating additional SCDS inflammatory markers and more latent groups produced similar groupings of markers that also aligned with the literature. Associations between covariates and birth weight were similar across latent variable models and were consistent with earlier work in this SCDS cohort. Supplementary materials accompanying this paper appear online.

Original languageEnglish
Pages (from-to)377-400
Number of pages24
JournalJournal of Agricultural, Biological and Environmental Statistics
Issue number3
Early online date14 Feb 2023
Publication statusPublished online - 14 Feb 2023

Bibliographical note

Funding Information:
This work was supported by the National Institute of Environmental Health Sciences of the National Institutes of Health under Grant T32ES007271, Grant P30ES001247, and Grant R03ES027514. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Publisher Copyright:
© 2023, International Biometric Society.


  • Immune response
  • Inflammation
  • Latent variables
  • Seychelles Child Development Study
  • Multiple exposures
  • Markov chain Monte Carlo


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