Reducing subspace models for large‐scale covariance regression

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 info...

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Bibliographic Details
Published in:Biometrics 2022-12, Vol.78 (4), p.1604-1613
Main Author: Franks, Alexander M.
Format: Article
Language:English
Subjects:
Aging
Algorithms
Covariance
covariance regression
envelope model
Estimates
Grassmann manifold
Heterogeneity
high‐dimensional data
large p
Metabolomics
Monte Carlo Method
Regression analysis
small n
spiked covariance model
stiefel manifold
Subspaces
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Summary: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.
ISSN:0006-341X
1541-0420
DOI:10.1111/biom.13531