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Bayesian variable selection for multioutcome models through shared shrinkage

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  • Debamita Kundu
  • Riten Mitra
  • Jeremy T. Gaskins

Abstract

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few nonzero components, those covariates that are most important. This article extends the “global‐local” shrinkage idea to a scenario where one wishes to model multiple response variables simultaneously. Here, we have developed a variable selection method for a K‐outcome model (multivariate regression) that identifies the most important covariates across all outcomes. The prior for all regression coefficients is a mean zero normal with coefficient‐specific variance term that consists of a predictor‐specific factor (shared local shrinkage parameter) and a model‐specific factor (global shrinkage term) that differs in each model. The performance of our modeling approach is evaluated through simulation studies and a data example.

Suggested Citation

  • Debamita Kundu & Riten Mitra & Jeremy T. Gaskins, 2021. "Bayesian variable selection for multioutcome models through shared shrinkage," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 295-320, March.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:295-320
    DOI: 10.1111/sjos.12455
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    References listed on IDEAS

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    Cited by:

    1. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).

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