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Reducing subspace models for large‐scale covariance regression

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  • Alexander M. Franks

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.

Suggested Citation

  • Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:4:p:1604-1613
    DOI: 10.1111/biom.13531
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    References listed on IDEAS

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    1. Z. Su & G. Zhu & X. Chen & Y. Yang, 2016. "Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression," Biometrika, Biometrika Trust, vol. 103(3), pages 579-593.
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