R. Bairakdar - MSc Thesis Defence in Mathematics
Speaker: Ms. Roba Bairakdar (MSc)
Abstract: A flexible approach for modeling longitudinal data is proposed. The model consists of nested bivariate copulas with Generalized Linear Mixed Models (GLMM) marginals, which are tested and validated by means of likelihood ratio tests and compared via their AICc and BIC values. The copulas are joined together through a vine structure. Rank-based methods are used for the estimation of the copula parameters, and appropriate model validation methods are used such as the Cramér Von Mises goodness-of-fit test. This model allows flexibility in the choice of the marginal distributions, provided by the family of the GLMM. Additionally, a wide variety of copula families can be fitted to the tree structure, allowing different nested dependence structures. This methodology is tested by an application on real data in a biostatistics study.