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A Penalized Spline Approach to Functional Mixed Effects Model Analysis

Authors

  • Huaihou Chen,

    1. Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 W168th Street, New York, New York 10032, U.S.A.
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  • Yuanjia Wang

    Corresponding author
    1. Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 W168th Street, New York, New York 10032, U.S.A.
      email: yw2016@columbia.edu
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email: yw2016@columbia.edu

Abstract

Summary 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.

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