A Single Index Modeling for Longitudinal Data with an Application to a Blood Pressure Study

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jingwei Wu*+ and Wanzhu Tu
• Companies: Indiana University and Indiana University
• Keywords: Single index model ; Cubic-spline ; Penalized nonlinear least square

Abstract

Single index models are primarily used for dimension reduction while preserving the latent features of independent variables. In longitudinal studies, the construction and implementation of single index models are complicated by correlations that exist among repeatedly measured outcome and independent variables within a study subject. Model fitting remains a challenge as it has not been successfully incorporated to standard statistical software. In this presentation, we extend the partially linear single index mixed effect models (PLSIMEM) to a longitudinal data setting. Herein, we use a penalized spline (cubic-spline) with flexible knot selection to model the behavior of the single index component. P-splines are then fit directly by penalizing nonlinear least squares and can be implemented with existing software. To illustrate, we present a real data application that examines the independent and concurrent contributions of height and weight to blood pressure development in children. Monte Carlo simulations are used to examine the operating characteristics of the proposed procedure.