Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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MBRDR: R-package for response dimension reduction in multivariate regression

  • Heesung Ahn (Department of Statistics, Ewha Womans University) ;
  • Jae Keun Yoo (Department of Statistics, Ewha Womans University)
  • Received : 2024.01.04
  • Accepted : 2024.02.03
  • Published : 2024.03.31
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Abstract

In multivariate regression with a high-dimensional response Y ∈ ℝr and a relatively low-dimensional predictor X ∈ ℝp (where r ≥ 2), the statistical analysis of such data presents significant challenges due to the exponential increase in the number of parameters as the dimension of the response grows. Most existing dimension reduction techniques primarily focus on reducing the dimension of the predictors (X), not the dimension of the response variable (Y). Yoo and Cook (2008) introduced a response dimension reduction method that preserves information about the conditional mean E(Y | X). Building upon this foundational work, Yoo (2018) proposed two semi-parametric methods, principal response reduction (PRR) and principal fitted response reduction (PFRR), then expanded these methods to unstructured principal fitted response reduction (UPFRR) (Yoo, 2019). This paper reviews these four response dimension reduction methodologies mentioned above. In addition, it introduces the implementation of the mbrdr package in R. The mbrdr is a unique tool in the R community, as it is specifically designed for response dimension reduction, setting it apart from existing dimension reduction packages that focus solely on predictors.

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Acknowledgement

For Jae Keun Yoo and Heesung Ahn, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (RS-2023-00240564 and RS-2023-00217022).

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