Franks AM. Reducing subspace models for large-scale covariance regression.
Biometrics 2022;
78:1604-1613. [PMID:
34458980 DOI:
10.1111/biom.13531]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Revised: 06/29/2021] [Accepted: 07/08/2021] [Indexed: 12/30/2022]
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.
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