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Dimension Reduction Regression in R

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  • Weisberg, Sanford

Abstract

Regression is the study of the dependence of a response variable y on a collection predictors p collected in x. In dimension reduction regression, we seek to find a few linear combinations β1x,...,βdx, such that all the information about the regression is contained in these linear combinations. If d is very small, perhaps one or two, then the regression problem can be summarized using simple graphics; for example, for d=1, the plot of y versus β1x contains all the regression information. When d=2, a 3D plot contains all the information. Several methods for estimating d and relevant functions of β1,..., βdhave been suggested in the literature. In this paper, we describe an R package for three important dimension reduction methods: sliced inverse regression or sir, sliced average variance estimates, or save, and principal Hessian directions, or phd. The package is very general and flexible, and can be easily extended to include other methods of dimension reduction. It includes tests and estimates of the dimension , estimates of the relevant information including β1,..., βd, and some useful graphical summaries as well.

Suggested Citation

  • Weisberg, Sanford, 2002. "Dimension Reduction Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i01).
    • Handle: RePEc:jss:jstsof:v:007:i01
    DOI: http://hdl.handle.net/10.18637/jss.v007.i01
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    Cited by:

    1. Adragni, Kofi Placid & Raim, Andrew M., 2014. "ldr: An R Software Package for Likelihood-Based Sufficient Dimension Reduction," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i03).
    2. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    3. Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    4. Häggström, Jenny & Persson, Emma & Waernbaum, Ingeborg & de Luna, Xavier, 2015. "CovSel: An R Package for Covariate Selection When Estimating Average Causal Effects," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i01).
    5. Alessandro Barbarino & Efstathia Bura, 2017. "A Unified Framework for Dimension Reduction in Forecasting," Finance and Economics Discussion Series 2017-004, Board of Governors of the Federal Reserve System (U.S.).
    6. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Noorbaloochi, Siamak & Nelson, David, 2008. "Conditionally specified models and dimension reduction in the exponential families," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1574-1589, September.
    8. Noorbaloochi Siamak & Nelson David & Asgharian Masoud, 2010. "Balancing and Elimination of Nuisance Variables," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-22, February.
    9. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2022. "Asymptotic and bootstrap tests for subspace dimension," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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