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Sufficient dimension reduction in multivariate regressions with categorical predictors

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  • Hilafu, Haileab
  • Yin, Xiangrong

Abstract

In this paper, we present a novel sufficient dimension reduction method for multivariate regressions with categorical predictors. We adopt ideas from a previous work byChiaromonte et al. (2002) who proposed sufficient dimension reduction in regressions with categorical predictors and the work by Li et al. (2008) who proposed the projective-resampling idea to multivariate response problems. In addition, we incorporate a variable selection procedure. Simulation studies show the efficacy of our method. We present a real data analysis through our proposed method to discover new association between personal characteristics and dietary factors which influence plasma beta-carotene and retinol levels in human serum.

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  • Hilafu, Haileab & Yin, Xiangrong, 2013. "Sufficient dimension reduction in multivariate regressions with categorical predictors," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 139-147.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:139-147
    DOI: 10.1016/j.csda.2013.02.014
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    Cited by:

    1. Yang Liu & Francesca Chiaromonte & Bing Li, 2017. "Structured Ordinary Least Squares: A Sufficient Dimension Reduction approach for regressions with partitioned predictors and heterogeneous units," Biometrics, The International Biometric Society, vol. 73(2), pages 529-539, June.
    2. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Hilafu, Haileab & Wu, Wenbo, 2017. "Partial projective resampling method for dimension reduction: With applications to partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 1-14.
    4. Liu, Xuejing & Huo, Lei & Wen, Xuerong Meggie & Paige, Robert, 2017. "A link-free approach for testing common indices for three or more multi-index models," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 236-245.

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