Nonparametric Mixed-Effects Density Regression for Repeated Measures Data

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chi-yang Chiu*+ and Yuedong Wang
• Companies: and University of California, Santa Barbara
• Keywords: Densitiy Estimation ; Mixed-Effects Models ; Smoothing Spline ; MCMC

Abstract

Conditional density provides the most informative summary of the relationship between independent and dependent variable. It enables us to examine the overall shapes of densities as well as summary characteristics such as quantiles and modes. Repeated measures designs are widely used in many area such as agriculture, education and pharmaceutical sciences. The data from repeated measures designs are correlated. We develop a nonparametric method for conditional density estimation for repeated measures data. Specifically we propose nonparametric mixed-effects density regression (NMDR) models. The NMDR models allow us to estimate conditional densities with less restraints on the form of densities when data are correlated. The models may be constructed through using Smoothing Spline ANOVA (SS ANOVA) method. Penalized marginal likelihood is used to estimate the density function as well as parameters. We incorporate stochastic approximation algorithm (SAA) with Newton-Raphson method for stochastic optimization and Markov chain Monte Carlo (MCMC) for approximating integral. An example from speech science is provided to illustrate the utility of our model.