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


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 first-order correlation coefficient p = corr[X i ,X j ], i not equal to j most accurately; where X i = 0, 1. The four models of interest in this study are the beta-binomial, the folded logistic, the Laplace transform of the gamma distribution, and the q-power 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 Newton-Raphson algorithm and application of this algorithm to each of the models as a means of finding maximum likelihood estimates of the model parameters.



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