itdr: An R package of Integral Transformation Methods to Estimate the SDR Subspaces in Regression

TL;DR

The itdr R package provides new integral transformation methods, including Fourier and convolution techniques, for estimating SDR subspaces in regression models, especially with univariate and multivariate responses, advancing SDR research.

Contribution

This paper introduces the first implementation of integral transformation methods for SDR subspace estimation in R, including novel Fourier-based strategies for univariate and multivariate responses.

Findings

Successfully applied to five datasets demonstrating effectiveness.

Enables recovery of CMS and CS with various Fourier strategies.

Provides a comprehensive, user-friendly tool for SDR analysis.

Abstract

Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and user-friendly tool that introduces several functions based on integral transformation methods for estimating SDR subspaces. In particular, the itdr package incorporates two key methods, namely the Fourier method (FM) and the convolution method (CM). These methods allow for estimating the SDR subspaces, namely the central mean subspace (CMS) and the central subspace (CS), in cases where the response is univariate. Furthermore, the itdr package facilitates the recovery of the CMS through the iterative Hessian transformation (IHT) method for univariate responses. Additionally, it enables the recovery of the CS by employing various Fourier transformation strategies, such as the inverse dimension reduction method, the minimum discrepancy approach using Fourier transformation, and the Fourier transform sparse inverse regression approach, specifically designed for cases with multivariate responses. To demonstrate its capabilities, the itdr package is applied to five different datasets. Furthermore, this package is the pioneering implementation of integral transformation methods for estimating SDR subspaces, thus promising significant advancements in SDR research.