Modeling Sums of Correlated Binary Data: A Simulation Study 
Travis J. Atkinson
Master's Candidate
Department of Statistics
Colorado State University
Tuesday, June 27, 2006
3:00 p.m.
006 Statistics Building
ABSTRACT
A simulation study is conducted to compare four distributions used to model sums of correlated binary data as applied primarily to developmental toxicology studies. Specifically, we investigate which model estimates the marginal response probability p = P[X i = 1] and the firstorder correlation coefficient _ = corr[X i ,X j ], i ? j most accurately; where X i = 0, 1. The four models of interest in this study are the betabinomial, the folded logistic, the Laplace transform of the gamma distribution, and the qpower model. Each of the models is introduced, including discourse of the emergence of each model in the statistical literature. We also include thorough discussions of the NewtonRaphson algorithm and application of this algorithm to each of the models as a means of finding maximum likelihood estimates of the model parameters.
