Sufficient Dimension Reduction in the Presence of Categorical Predictors

• Activity Number: 57
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kofi Adragni*+ and Elias Al-Najjar
• Companies: and University of Maryland Baltimore County
• Keywords: Principal fitted components ; Sufficient dimension reduction ; Regression

Abstract

Most methodologies for sufficient dimension reduction (SDR) in regression are limited to continuous predictors. However, a very large number of actual data sets do contain variables of both continuous and categorical types. Application of these methods to regressions that include qualitative predictors such as gender or species may be inappropriate. We consider regressions that include a set of qualitative predictors W in addition to a vector X of many-valued predictors and a response Y. Using principal fitted components (PFC) models, a likelihood-based SDR method, we seek the sufficient dimension reduction of X that is constrained through the sub-populations established by W. We provide the estimator of the sufficient reduction subspace and demonstrate how it works through simulations and applications. As the need is arising for effective analysis strategies for high-dimensional data, the results we present significantly widen the applicative scope of PFC for sufficient dimension reduction.