Modeling and Analysis of Repeated Ordinal Data Using Copula Based Likelihoods and Estimating Equation Methods

<p>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 <em>Copula</em> 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.</p> <p>Though likelihood methods are preferable, there are computational challenges implementing them. Alternatives are the non-likelihood models. These are partially specified models, that is, in these models only the functional forms of the marginals are known but joint distributions are unknown. In addition, the dependence among the observations is modeled using an appropriate correlation structure. The second part of the dissertation outlines the estimating equations approach for the analysis of longitudinal ordinal data for these non-likelihood models. We study the asymptotic properties of the estimates for both likelihood and non-likelihood methods. Comparisons based on simulations show that the maximum likelihood estimates arising from copula models are more efficient than the estimates obtained from estimating equations.</p> <p>The third part of this dissertation describes how ordinal data can be viewed as multinomial random vectors and points out the theoretical challenges in finding restrictions on the correlation parameters for dependent multinomial random vectors.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2011

Author dc:creator

• Kurada, Raghavendra Rao

Contributors dc:contributor

• N. Rao Chaganty
• Dayanand N. Naik
• Nak-Kyeong Kim
• Larry Filer

• Copula-based likelihoods
• Estimating equations
• Ordered probits
• Ordinal data
• Statistics and Probability

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9781267112583

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1028