Nonparametric Regression Analysis of Longitudinal Data

Staniswalis, Joan G.; Lee, J. Jack

doi:10.2307/2670055

Cited by 94 publications

(134 citation statements)

References 19 publications

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“…Our approach can be seen as an extension of functional principal component analysis for multilevel functional data [7]. Our methods apply to longitudinal data where each observation is functional, and should thus not be confused with nonparametric methods for the longitudinal profiles of scalar variables [17,30,31,37,41,48,50,51]. For good introductions to functional data analysis in general, please see [10,34].…”

Section: Introductionmentioning

confidence: 99%

Longitudinal Functional Principal Component Analysis

Greven

Crainiceanu

Caffo

et al. 2011

Contributions to Statistics

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We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The model can be viewed as the functional analog of the classical longitudinal mixed effects model where random effects are replaced by random processes. Methods have wide applicability and are computationally feasible for moderate and large data sets. Computational feasibility is assured by using principal component bases for the functional processes. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study designed to analyze differences and changes in brain connectivity in healthy volunteers and multiple sclerosis (MS) patients. An R implementation is provided. 87

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Section: Introductionmentioning

confidence: 99%

Longitudinal Functional Principal Component Analysis

Greven

Crainiceanu

Caffo

et al. 2011

Contributions to Statistics

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“…These raw covariances are smoothed with a surface smoother and the smooth covariance surface is then discretized in order to obtain eigenvalues/eigenvectors of the resulting covariance matrix. The resulting eigenvectors are smoothed to obtain the eigenfunction estimatesψ k (see Rice and Silverman, 1991;Staniswalis and Lee, 1998) for residual processes R(·).…”

Section: Fitting Functional Response Modelsmentioning

confidence: 99%

Functional Response Models

Kowalski

2007

Modern Applied U‐Statistics

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We review functional regression models and discuss in more detail the situation where the predictor is a vector or scalar such as a dose and the response is a random trajectory. These models incorporate the influence of the predictor either through the mean response function, through the random components of a Karhunen-Loève or functional principal components expansion, or by means of a combination of both. In a case study, we analyze dose-response data with functional responses from an experiment on the age-specific reproduction of medflies. Daily egg-laying was recorded for a sample of 874 medflies in response to dietary dose provided to the flies. We compare several functional response models for these data. A useful criterion to evaluate models is a model's ability to predict the response at a new dose. We quantify this notion by means of a conditional prediction error that is obtained through a leave-one-dose-out technique.

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“…Therefore the diagonal of the raw covariances should be removed, i.e., only C i (t ij , t il ), j = l, should be included as predictors in the smoothing step (Staniswalis and Lee, 1998). We again use one-curve-leave-out cross-validation,…”

Section: Estimation Of the Mean And Covariance Functionsmentioning

confidence: 99%

“…Our approach is related to that of Staniswalis and Lee (1998), who also used scatter-plot smoothing to obtain mean and covariance functions, and proposed modifications to allow for additional measurement errors. We also propose an improved estimate for the variance of these errors through improved estimation in the neighborhood of and at the diagonal of the covariance surface, by fitting local quadratic components along the direction perpendicular to the diagonal.…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate

et al. 2003

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We present the application of a nonparametric method to perform functional principal components analysis for functional curve data that consist of measurements of a random trajectory for a sample of subjects. This design typically consists of an irregular grid of time points on which repeated measurements are taken for a number of subjects. We introduce shrinkage estimates for the functional principal component scores that serve as the random effects in the model. Scatterplot smoothing methods are used to estimate the mean function and covariance surface of this model. We propose improved estimation in the neighborhood of and at the diagonal of the covariance surface, where the measurement errors are reflected. The presence of additive measurement errors motivates shrinkage estimates for the functional principal components scores. Shrinkage estimates are developed through best linear prediction and in a generalized version, aiming at minimizing one-curve-leave-out prediction error. The estimation of individual trajectories combines data obtained from that individual as well as all other individuals. We apply our methods to new data regarding the analysis of the level of 14 C -folate in plasma as a function of time since dosing healthy adults with a small tracer dose of 14 C -folic acid. A time transformation was incorporated to handle design irregularity concerning the time points on which the measurements were taken.The proposed methodology incorporating shrinkage and data-adaptive features is seen to be well suited for describing population kinetics of 14 C -folate specific activity and random effects, and can also be applied to other functional data analysis problems.

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Nonparametric Regression Analysis of Longitudinal Data

Cited by 94 publications

References 19 publications

Longitudinal Functional Principal Component Analysis

Longitudinal Functional Principal Component Analysis

Functional Response Models

Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate

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