Analysis of models for longitudinal and clustered binary data

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.;The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the models we obtain maximum likelihood estimates for the regression and correlation parameters, and study both asymptotic and small-sample properties of the estimates. Through simulations we compare the efficiency of the two methods and demonstrate that neither is uniformly superior over the other.;The second part of this dissertation deals with marginal models, an alternative to multivariate probability models. We discuss the generalized estimating equations and the quadratic inference function methods for estimating the regression parameter in marginal models. Relative efficiency calculations show these methods when compared to the likelihood estimates could result in significant loss in efficiency for highly correlated data. We also propose a modified quadratic inference function method and demonstrate through efficiency calculations this is an improvement of the original quadratic inference function approach. The final part of this dissertation deals with methods for constructing higher order Markov chain models using copulas.