Search

Most methodologies for sufficient dimension reduction (SDR) in regression are limited to continuous predictors, although many data sets do contain both continuous and categorical variables. Application of these methods to regressions that include qualitative predictors such as gender or species may be inappropriate. Regressions that include a set of qualitative predictors W in addition to a vector X of many-valued predictors and a response Y are considered. Using principal fitted components (PFC) models, a likelihood-based SDR method, a sufficient dimension reduction of X that is constrained through the sub-populations established by W is sought. An estimator of the sufficient reduction subspace is provided and its use is demonstrated through applications. [ABSTRACT FROM AUTHOR]

Given a high dimensional p -vector of continuous predictors X and a univariate response Y , principal fitted components (PFC) provide a sufficient reduction of X that retains all regression information about Y in X while reducing the dimensionality. The reduction is a set of linear combinations of all the p predictors, where with the use of a flexible set of basis functions, predictors related to Y via complex, nonlinear relationship can be detected. In the presence of possibly large number of irrelevant predictors, the accuracy of the sufficient reduction is hindered. The proposed method adapts a sequential test to the PFC to obtain a “pruned” sufficient reduction that shed off the irrelevant predictors. The sequential test is based on the likelihood ratio which expression is derived under different covariance structures of X | Y . The resulting reduction has an improved accuracy and also allows the identification of the relevant variables. [ABSTRACT FROM AUTHOR]