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Title: Local polynomial mixed-effects models for longitudinal data
Authors: Wu, H.
Zhang, J.-T. 
Keywords: Bandwidth selection
Leave-one-point-out cross-validation
Leave-one-subject-out cross-validation
Linear mixed-effects model
Local polynomial smoothing
Longitudinal data
Nonparametric mixed-effects model
Issue Date: Sep-2002
Citation: Wu, H., Zhang, J.-T. (2002-09). Local polynomial mixed-effects models for longitudinal data. Journal of the American Statistical Association 97 (459) : 883-897. ScholarBank@NUS Repository.
Abstract: We consider a nonparametric mixed-effects model yi(tij) = η(tij) + νi(tij) + εi(tij), j = 1, 2,..., ni = 1, 2,..., n for longitudinal data. We propose combining local polynomial kernel regression and linear mixed-effects (LME) model techniques to estimate both fixed-effects (population) curve η(t) and random-effects curves vi(t). The resulting estimator, called the local polynomial LME (LLME) estimator, takes the local correlation structure of the longitudinal data into account naturally. We also propose new bandwidth selection strategies for estimating η(t) and νi(t). Simulation studies show that our estimator for η(t) is superior to the existing estimators in the sense of mean squared errors. The asymptotic bias, variance, mean squared errors, and asymptotic normality are established for the LLME estimators of η(t). When ni is bounded and n tends to infinity, our LLME estimator converges in a standard nonparametric rate, and the asymptotic bias and variance are essentially the same as those of the kernel generalized estimating equation estimator proposed by Lin and Carroll. But when both ni and n tend to infinity, the LLME estimator is consistent with a slower rate of n1/2 compared to the standard nonparametric rate, due to the existence of within-subject correlations of longitudinal data. We illustrate our methods with an application to a longitudinal dataset.
Source Title: Journal of the American Statistical Association
ISSN: 01621459
DOI: 10.1198/016214502388618672
Appears in Collections:Staff Publications

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