title: A penalized spline approach to functional mixed effects model analysis.
abstract: In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject-specific curves, and the associated covariance function that represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population- and subject-level curves. In addition, decomposing variability of the outcomes as a between- and within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood-based method to select multiple smoothing parameters. 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. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 W168th Street, New York, New York 10032, USA.
authors.forename: Huaihou
authors.initials: H
authors.lastname: Chen
authors.forename: Yuanjia
authors.initials: Y
authors.lastname: Wang
mesh_terms: D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D006321:Heart / Q000502:physiology; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D015233:Models, Statistical