Partial linear models for longitudinal data based on quadratic inference functions

Abstract

In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non-parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper. © Board of the Foundation of the Scandinavian Journal of Statistics 2007.