Generalized linear longitudinal semi-parametic models with time dependent covariates

Abstract

Longitudinal data analysis is challenging because of the difficulties in modelling the correlations among the repeated responses, especially when the associated covariates are time dependent. Recent studies have examined correlations for both linear and discrete unbalanced longitudinal data, which are modelled following a Gaussian-type auto-regressive moving average (ARMA) class of auto-correlations. However, these studies were confined to a regression setup where the regression function is completely specified. In t his thesis, we consider a semi-parametric regression setup in which the regression function involves a specified as well as an unspecified function over time. Under the ARMA type correlation structure, we provide a semi-parametric generalized quasi-likelihood (SGQL) approach for the estimation of the main regression parameters. The proposed inference approach is compared with some existing generalized estimating equation (GEE) approaches mainly through simulation studies. The linear longitudinal semi-parametric model, for its foundational nature, is discussed in detail. Theoretical details on semi-parametric estimation for longitudinal count and binary data are also provided