DOI
https://doi.org/10.25772/JVH9-WP15
Defense Date
2014
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Biostatistics
First Advisor
Roy T. Sabo
Second Advisor
N. Rao Chaganty
Third Advisor
Ronald K. Elswick
Fourth Advisor
Robert A. Perera
Fifth Advisor
Wen Wan
Abstract
In the study of associated discrete variables, limitations on the range of the possible association measures (Pearson correlation, odds ratio, etc.) arise from the form of the joint probability function between the variables. These limitations are known as the Fréchet bounds. The bounds for cases involving associated binary variables are explored in the context of simulating datasets with a desired correlation and set of marginal probabilities. A new method for creating such datasets is compared to an existing method that uses the multivariate probit. A method for simulating associated binary variables using a desired odds ratio and known marginal probabilities is also presented. The Fréchet bounds for correlation between dependent binomial and negative binomial variables are determined as families of ranges in various cases. An example of a realistic analysis involving the Fréchet bounds in a dependent binomial setting is presented.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
12-8-2014