A Bayesian Approach to Fitting Mixed Models Using Shape-Restricted Regression Splines

• Activity Number: 306
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Amber Hackstadt*+ and Mary Meyer and Jennifer A. Hoeting
• Companies: Colorado State University and Colorado State University and Colorado State University
• Keywords: Bayesian Inference ; Nonparametric ; Semiparametric ; Mixed Models ; Constrained Regression ; Isotonic

Abstract

We propose a Bayesian approach to fit mixed models using shape-restricted regression splines. Linear mixed-effects models are often used to analyze repeated measure and longitudinal data but a-priori knowledge about the regression functions is often limited to smoothness and shape (monotone or convex). Shape-restricted splines are used to model regression functions in mixed-effects models and have the advantage of being robust to the number of knots while maintaining good statistical properties. They are flexible but retain a-priori information about the shape and smoothness of the relationships between variables. Simulation studies and examples demonstrate that a Bayesian framework along with vague priors gives function estimates that are similar to maximum likelihood estimates while providing posterior distributions to facilitate inference.