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Biometrika 2001 88(4):1179-1185; doi:10.1093/biomet/88.4.1179
© 2001 by Biometrika Trust
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Miscellaneous

Semiparametric regression for clustered data

Xihong Lin1 and Raymond J.Carroll2

1 Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.Axlin{at}sph.umich.edu 2 Department of Statistics, Texas A&M University, College Station, Texas 77843-3143, U.S.A.carroll{at}stat.tamu.edu

We consider estimation in a semiparametric partially generalised linear model for clustered data using estimating equations. A marginal model is assumed where the mean of the outcome variable depends on some covariates parametrically and a cluster-level covariate nonparametrically.A profile-kernel method allowing for working correlation matrices is developed. We show that the nonparametric part of the model can be estimated using standard nonparametric methods, including smoothing-parameter estimation, and the parametric part of the model can be estimated in a profile fashion. The asymptotic distributions of the parameter estimators are derived, and the optimal estimators of both the nonparametric and parametric parts are shown to be obtained when the working correlation matrix equals the actual correlation matrix. The asymptotic covariance matrix of the parameter estimator is consistently estimated by the sandwich estimator. We show that the semiparametric ecient score takes on a simple form and our profile-kernel method is semiparametric ecient. The results for the case where the nonparametric part of the model is an observation-level covariate are noted to be dramatically dierent.

Key Words: Clustered data; Generalised estimation equation; Kernel method; Longitudinal data; Nonparametric regression; Partially linear model; Profile method; Sandwich estimator; Semiparametric eciency bound; Semiparametric ecient score

Received July 2000. Revised March 2001


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