TY - JOUR
T1 - Marginal longitudinal nonparametric regression
T2 - Locality and efficiency of spline and kernel methods
AU - Welsh, A. H.
AU - Lin, X.
AU - Carroll, R. J.
PY - 2002
Y1 - 2002
N2 - We consider nonparametric regression in a longitudinal marginal model of generalized estimating equation (GEE) type with a time-varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large. In such models, the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations. Two methods of estimating the nonparametric function can be considered: kernel methods and spline methods. Recently, surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature, it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent, that is, working independence in the GEE jargon. As seen through equivalent kernel results, in univariate independent data problems splines and kernels have similar behavior; smoothing splines are equivalent to kernel regression with a specific higher-order kernel, and hence smoothing splines are local. This equivalence suggests that in our marginal model, working independence might be preferable for spline methods. Our results suggest the opposite; via theoretical and numerical calculations, we provide evidence suggesting that for our marginal model, marginal smoothing and penalized regression splines are not local in their behavior. In contrast to the kernel results, our evidence suggests that when using spline methods, it is worthwhile to account for the correlation structure. Our results also suggest that spline methods appear to be more efficient than the previously proposed kernel methods for our marginal model.
AB - We consider nonparametric regression in a longitudinal marginal model of generalized estimating equation (GEE) type with a time-varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large. In such models, the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations. Two methods of estimating the nonparametric function can be considered: kernel methods and spline methods. Recently, surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature, it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent, that is, working independence in the GEE jargon. As seen through equivalent kernel results, in univariate independent data problems splines and kernels have similar behavior; smoothing splines are equivalent to kernel regression with a specific higher-order kernel, and hence smoothing splines are local. This equivalence suggests that in our marginal model, working independence might be preferable for spline methods. Our results suggest the opposite; via theoretical and numerical calculations, we provide evidence suggesting that for our marginal model, marginal smoothing and penalized regression splines are not local in their behavior. In contrast to the kernel results, our evidence suggests that when using spline methods, it is worthwhile to account for the correlation structure. Our results also suggest that spline methods appear to be more efficient than the previously proposed kernel methods for our marginal model.
KW - Clustered data
KW - Equivalent kernel
KW - Generalized estimating equation
KW - Generalized least squares
KW - Kernel regression
KW - Longitudinal model
KW - Nonparametric regression
KW - P-spline
KW - Regression spline
KW - Repeated measures
KW - Smoothing spline
KW - Weighted least squares
UR - http://www.scopus.com/inward/record.url?scp=0035998825&partnerID=8YFLogxK
U2 - 10.1198/016214502760047014
DO - 10.1198/016214502760047014
M3 - Article
SN - 0162-1459
VL - 97
SP - 482
EP - 493
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 458
ER -