First Advisor

Schaffer, Jay Ryan, 1969-

Second Advisor

Lalonde, Trent L.

Document Type


Date Created



In practice, it is very common to have clustered binary responses, where binary data are naturally grouped by sampling technique or some property of the sampling units. Often these clusters are unbalanced. The preferred class of models for clustered binary data is the Hierarchical Generalized Linear Model (HGLM), where random effects are used to account for the overdispersion known to exist for clustered binary data. There are many methods to estimate the parameters in Hierarchical Generalized Linear Models, but none of the current methods allowed the overdispersion to vary from cluster to cluster. As clustered binary data led to overdispersion, it was reasonable to conclude that unbalanced clustered binary data may have been different overdispersion for different cluster sizes. By ignoring possible changes in overdispersion across clusters, test statistics tended to show innfatedType I error rates. In this research, two HGLM methods were adjusted to account for different overdispersion across different cluster sizes. The first new method was the Extended Restricted Pseudo Likelihood (EREPL), an adjustment of Restricted Pseudo Likelihood. Extended Restricted Pseudo Likelihood allowed for different dispersion adjustments for each cluster. The new second method was Adjusted Scale Binomial Beta (ASBB), an extension of the classical Binomial Beta model. This method allowed the Beta distributed random effect to have different scale parameters for each cluster. Through simulation, these extensions were compared to the original methods in terms of power, Type I error rate, and estimator standard errors. Adjusted Scale Binomial Beta h-likelihood was comparable to existing methods, as it gave us a low standard error and acceptable Type I error. Moreover, Binomial Beta h-likelihood had inflated Type I error. The Restricted Pseudo Likelihood could also be applied to unbalanced clustered binary data.


Linear models (Statistics); Correlation (Statistics)


118 pages

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Copyright is held by the author