Model assessment: Bayes assisted tests and tests for discrete data
In this thesis, two areas of goodness-of fit are discussed and new methodology proposed. In the first, Bayesian methods are introduced to provide a narrow band of alternative continuous distributions when the distribution tested is uniform or normal A particular use of Bayesian methods allows consideration of the problem of testing the distribution of latent (unobserved) variables when these are connected by a known relationship to a set of observed variables. The technique is used to advance an interesting procedure introduced in Geology by Krumbein and for a modern example, to test the distribution of the frailty term (random effects) in a Cox Proportional Hazards (PH) model.
The second part of the thesis deals with discrete data with particular emphasis on applying Cramér-von Mises statistics. Tests are proposed for K samples in an ordered contingency table. Finally, the K sample procedure is applied to testing the fit of the binary regression model to longitudinal (correlated) data using Generalized estimating equations. A common thread throughout the thesis is the use of the Cramér-von Mises statistics or closely related statistics for testing.