The Estimation Of Semiparametric Model For Longitudinal Data Basing On Quadratic Inference Functions

Longitudinal data is referred to data in which individuals are messured repeatedly through time, so it combines elements of cross-sectional data and time-series data. The prominent advantage of longitudinal data is that it can analyze effectively the change of individuals over time. However, it is complicated by repeated messurement within individuals and variation among individuals.Liang & Zeger(1986) introduced the ingenious idea of using a working correlation matrix with a small set of nuisance parameters. The generalised estimating equation(GEE) estimators of the regression parameters are consistent even when the true correlation matrix is not an element of the class of working correlation matrices, and are efficient when the working correlation is correctly specified. When the working correlation is mis-specified, however, the GEE no longer results in the optimal estimation. Qu et al.(2000) introduced a different strategy for estimating the working correlation so that the estimator always existed, and, even if the correlation was misspecified, the regression estimator remained optimal within the assumed family. Their idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices. Then use the quadratic inference functions(QIF) to constract the estimating equation.The purpose of this paper is to apply the quadratic inference functions to the semi-parametric model for longitudinal data and improve the estimator of the parametric part in the model. We succeed in proving the consistent and asymptotic normality of the QIF estimator. Last, we compare the QIF and GEE methods by simulations and apply the QIF estimator to the CD4 data.