Model-Based Sufficient Dimension Reduction for Longitudinal Data Analysis

• Activity Number: 75
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Shanshan Ding*+ and Dennis Cook
• Companies: University of Minnesota-Twin Cities and University of Minnesota
• Keywords: Sufficient dimension reduction ; central subspace ; inverse regression ; partial central subspace

Abstract

Principal components analysis (PCA) and principal fitted components (PFC) are two major dimension reduction methods in regression. In current literature, these two methods are only applied to data with simple structure, where all observations are independently and identically distributed. In many real applications, however, one often needs to deal with data that contain dependent observations, such as repeated measured or longitudinal data. In this paper, we extend classical PCA and PFC and develop sufficient dimension reduction methods for this type of data. The proposed methods can reduce predictors' dimension and preserve full information in the conditional distribution of Y|X. Both methods are built on normal inverse models of the predictors. Thus, they inherit the asymptotic properties from maximum likelihood estimation. Furthermore, the extended PFC models are formed as inverse models of the predictors on the response, which can gain further efficiency by effective use of the response information without slicing. We demonstrate that our proposed methods outperform the existing dimension reduction approaches in both simulation study and real data analysis.