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Bayesian regression analysis of skewed tensor responses

Author

Listed:
  • Inkoo Lee
  • Debajyoti Sinha
  • Qing Mai
  • Xin Zhang
  • Dipankar Bandyopadhyay

Abstract

Tensor regression analysis is finding vast emerging applications in a variety of clinical settings, including neuroimaging, genomics, and dental medicine. The motivation for this paper is a study of periodontal disease (PD) with an order‐3 tensor response: multiple biomarkers measured at prespecified tooth–sites within each tooth, for each participant. A careful investigation would reveal considerable skewness in the responses, in addition to response missingness. To mitigate the shortcomings of existing analysis tools, we propose a new Bayesian tensor response regression method that facilitates interpretation of covariate effects on both marginal and joint distributions of highly skewed tensor responses, and accommodates missing‐at‐random responses under a closure property of our tensor model. Furthermore, we present a prudent evaluation of the overall covariate effects while identifying their possible variations on only a sparse subset of the tensor components. Our method promises Markov chain Monte Carlo (MCMC) tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real data set derived from a clinical study of PD. The R package BSTN available in GitHub implements our model.

Suggested Citation

  • Inkoo Lee & Debajyoti Sinha & Qing Mai & Xin Zhang & Dipankar Bandyopadhyay, 2023. "Bayesian regression analysis of skewed tensor responses," Biometrics, The International Biometric Society, vol. 79(3), pages 1814-1825, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:1814-1825
    DOI: 10.1111/biom.13743
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    References listed on IDEAS

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    1. Yuqing Pan & Qing Mai & Xin Zhang, 2019. "Covariate-Adjusted Tensor Classification in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1305-1319, July.
    2. Brian J. Reich & Dipankar Bandyopadhyay & Howard D. Bondell, 2013. "A Nonparametric Spatial Model for Periodontal Data With Nonrandom Missingness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 820-831, September.
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    4. Lexin Li & Xin Zhang, 2017. "Parsimonious Tensor Response Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1131-1146, July.
    5. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
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    8. Ma, Yanyuan & Genton, Marc G. & Tsiatis, Anastasios A., 2005. "Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 980-989, September.
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