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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

    as
    1. Wenjing Wang & Xin Zhang & Lexin Li, 2019. "Common reducing subspace model and network alternation analysis," Biometrics, The International Biometric Society, vol. 75(4), pages 1109-1120, December.
    2. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
    3. 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.
    4. Robert J. Boik, 2002. "Spectral models for covariance matrices," Biometrika, Biometrika Trust, vol. 89(1), pages 159-182, March.
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    8. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.
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