Physical Sciences and Mathematics Commons^™

Modeling And Analysis Of Repeated Ordinal Data Using Copula Based Likelihoods And Estimating Equation Methods, Raghavendra Rao Kurada

Mathematics & Statistics Theses & Dissertations

Repeated or longitudinal ordinal data occur in many fields such as biology, epidemiology, and finance. These data normally are analyzed using both likelihood and non-likelihood methods. The first part of this dissertation discusses the multivariate ordered probit model which is a likelihood method based on latent variables. We show that this latent variable model belong to a very general class of Copula models. We use the copula representation for the multivariate ordered probit model to obtain maximum likelihood estimates of the parameters. We apply the methodology in the analysis of real life data examples.

Though likelihood methods are preferable, there …

The Doubly Inflated Poisson And Related Regression Models, Manasi Sheth-Chandra

Mathematics & Statistics Theses & Dissertations

Most real life count data consists of some values that are more frequent than allowed by the common parametric families of distributions. For data consisting of only excess zeros, in a seminal paper Lambert (1992) introduced Zero-Inflated Poisson (ZIP) model, which is a mixture model that accounts for the inflated zeros. In this thesis, two Doubly Inflated Poisson (DIP) probability models, DIP (p, λ) and DIP ( p1, p2, λ), are discussed for situations where there is another inflated value k > 0 besides the inflated zeros. The distributional properties such as identifiability, moments, and conditional probabilities …