| Analysis of longitudinal data becomes quite challenging when dealing with non-Gaussian outcome variables due to lack of well developed multivariate distributions. Liang and Zeger (1986) developed the generalized estimating equations (GEE) approach for responses from the exponential family by using a multivariate form of the quasi-likelihood. These models assume that the effect of each covariate may be defined explicitly via parametric, mostly linear, functions.;In this thesis, we develop non-parametric modeling techniques that relax this parametric assumption. We let the data decide on what functional form the covariate effect follows via smoothing. To this end, generalized additive models (Hastie and Tibshirani, 1986) and varying-coefficient models (Hastie and Tibshirani, 1993) are developed for GEE based models. Theoretical justifications are given for the algorithms by following the penalized (quasi) likelihood approach. Informal testing procedures are proposed for the models by following Rotnitzky and Jewell (1990) and their validity is assessed via simulation. The consistency of the appropriate systems of equations, conditions for non-degeneracy of the solutions and convergence of the Gauss-Seidel type procedures are discussed in detail.;Finally, the new non-parametric models are illustrated and compared to their parametric counterparts through real data examples. |
