Reducing subspace models for large‐scale covariance regression

Alexander M. Franks

Biometrics, 2022, vol. 78, issue 4, 1604-1613

Abstract: We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean‐level differences. We use a Monte Carlo EM algorithm to identify a low‐dimensional subspace that explains differences in both means and covariances as a function of covariates, and then use MCMC to estimate the posterior uncertainty conditional on the inferred low‐dimensional subspace. We demonstrate the utility of our model on a motivating application on the metabolomics of aging. We also provide R code that can be used to develop and test other generalizations of the response envelope model.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:bla:biomet:v:78:y:2022:i:4:p:1604-1613

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