Best Predictor Methods for Correlated Data

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ABSTRACT 0103792This project proposes to develop statistical methods useful for the analysis of correlated, non-normally distributed data. Such data arises commonly in clinical trials, in familial genetic studies, in ecological studies, and in a variety of other contexts when binary or count data is gathered on the same subject, on the same family, at the same site, or from the plot of land. Failure to account for correlations in the analysis of such data can readily lead to misleading conclusions.The methods will be based on deriving unbiased estimating equations for both variance components and regression parameters within the context of a generalized linear mixed model. The goal is to derive methods of wide utility with good small sample performance. The performance of the newly developed methods will be assessed on their own with regard to ease of computation, lack of bias, smallness of mean square error, the ease with which accurate standard errors can be computed, and the ease of calculating accurate confidence intervals and performing hypothesis tests. The methods will also be compared to extant methods (maximum likelihood, higher order Laplace approximations, penalized quasi-likelihood and generalized estimating equations) using the same criteria.