Study on the structural properties of the estimating equations arising in the fitting of models for binary longitudinal data

We investigate modeling issues for binary longitudinal data. Three nested marginal models are considered for describing a binary longitudinal data set arising out of a study done in Ohio observing the wheezing status of children over four years and grouped in those who suffered from maternal smoking and those who did not (Ware (1985)). We demonstrate that when the observations are uncorrelated, the estimating equations for these three models have a common set of equations with a special structure. We show that the same special structure is also present when the observations are correlated. Using this special structure in the estimating equations, we develop new methods to estimate the unknown parameters in these nested models. The initial solutions in these methods are determined naturally from the Estimating Equations and then improved to the final solutions through a series of steps described in the paper. We also study the joint probability models by Fitzmaurice and Laird (1993). We present methods that improve upon and avoid the computational complexity involved in drawing inference on parameters under the joint probability setup. Finally we consider the model selection problem for describing this data. The model selection problem is explored not only in terms of the number of covariates but also the most appropriate association structure between the observations that collected for each subject over a period of time.