A Penalized Spline Approach to Functional Mixed-Effects Model Analysis

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Huaihou Chen*+
• Companies: Columbia University
• Keywords: Multi-level functional data ; Functional random effects ; Semiparametric longitudinal data analysis

Abstract

In this work, we decompose longitudinal outcomes as a sum of several terms: a baseline function, covariates with time-varying coefficients, random subject-specific curves and residual measurement error processes. Using penalized splines, we propose nonparametric estimation of the baseline function, varying-coefficient, subject-specific curves and the associated covariance function which represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Decomposing variability of the outcomes as a between-subject source and a within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights.