D-Vine Pair-Copula Models for Longitudinal Binary Data

Dependent longitudinal binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. A popular method for analyzing such data is the multivariate probit (MP) model. The motivation for this dissertation stems from the fact that the MP model fails even the binary correlations are within the feasible range. The reason being the underlying correlation matrix of the latent variables in the MP model may not be positive definite. In this dissertation, we study alternatives that are based on D-vine pair-copula models. We consider both the serial dependence modeled by the first order autoregressive (AR(1)) and the equicorrelated correlation structures. Simulation results show that our model is more effective than MP model. Some real life data analysis are presented to show usefulness of our models. We also consider a general situation where the marginal distributions are ordered multinomial. We extend the D-vine pair-copula model to handle multinomial longitudinal data, and compare the generated probability distributions with other methods that are available in R packages