Profile-kernel versus backfitting in the partially linear models for longitudinal clustered data

• Published in: Biometrika Vol. 91; no. 2; pp. 251 - 262
• Main Author: Hu, Zonghui
• Format: Journal Article
• Language: English
• Published: Oxford University Press for Biometrika Trust 01.06.2004
• Series: Biometrika
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/91.2.251

We study the profile-kernel and backfitting methods in partially linear models for clustered longitudinal data. For independent data, despite the potential root-n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profile-kernel method; that is, for clustered data, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profile-kernel estimator. Consequently, the common practice of using the backfitting method to compute profile-kernel estimates is no longer advised. We illustrate this in detail by following Zeger & Diggle (1994) and Lin & Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described. Copyright Biometrika Trust 2004, Oxford University Press.