Estimation with improved efficiency in semi-parametric linear longitudinal models

Abstract

In this article, we revisit the semi-parametric linear models with auto-correlated errors, where the means of the repeated responses of an individual consist of a specified regression function in time dependent covariates as well as a time dependent nonparametric function. The estimation of the regression parameters involved in the specified regression function is of main interest, and most of the existing studies estimate these parameters by using the so-called semi-parametric generalized estimating equations (SGEEs) approach. We offer two main contributions. First, we demonstrate that the existing SGEEs are partly standardized. Second, as opposed to this partly standardized SGEE (PSSGEE) approach, we suggest a fully standardized semi-parametric generalized quasi-likelihood (FSSGQL) approach that provides more efficient regression estimates. This efficiency gain by the FSSGQL approach over the PSSGEE approach is also demonstrated through an empirical study.