ldr: An R Software Package for Likelihood-Based Sufficient Dimension Reduction

Abstract

In regression settings, a sufficient dimension reduction (SDR) method seeks the core information in a p-vector predictor that completely captures its relationship with a response. The reduced predictor may reside in a lower dimension d < p, improving ability to visualize data and predict future observations, and mitigating dimensionality issues when carrying out further analysis. We introduce ldr, a new R software package that implements three recently proposed likelihood-based methods for SDR: covariance reduction, likelihood acquired directions, and principal fitted components. All three methods reduce the dimensionality of the data by pro jection into lower dimensional subspaces. The package also implements a variable screening method built upon principal fitted components which makes use of flexible basis functions to capture the dependencies between the predictors and the response. Examples are given to demonstrate likelihood-based SDR analyses using ldr, including estimation of the dimension of reduction subspaces and selection of basis functions. The ldr package provides a framework that we hope to grow into a comprehensive library of likelihood-based SDR methodologies.