Partial sufficient dimension reduction in regression.

Abstract

In this thesis we propose a new model-based reduction method to reduce the dimension of one set of predictors while maintaining another set of predictors and a response if the response is present. Based on the probabilistic PCA model (Tipping and Bishop 1999) and the PFC model (Cook 2007), we develop new models in the partial dimension reduction context: partial probabilistic PCA models, partial PFC models, and combining models. We estimate the parameters of interest for the partial sufficient reduction using the maximum likelihood method. Methods are also proposed for prediction in partial PFC models.