SelectedMethods for Correlated Binary Data: Model Selection and Homogeneity Tests
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Correlated bilateral data often arise in ophthalmological and otolaryngological studies, where responses of paired body parts of each subject are measured. A number of statistical models have been proposed to tackle this intra-class correlation problem. In practice, it is important to choose the most suitable model which fits the observed data well, then both asymptotic tests under large sample assumption and exact tests for small samples should be constructed to test the homogeneity of proportions in each group as well as some equality assumptions in each specific model. In this thesis, we compare different goodness-of-fit statistics for three popular models with correlated data including more than two groups. For the equal correlation coefficients model, we construct different asymptotic statistics for testing the equality of the correlation coefficients in each group. Moreover, we compare four exact procedures along with the asymptotic approach based on the score statistic in testing the homogeneity of proportions under the Rosner's model and the equal correlation coefficients model.