This manuscript consists of three papers which formulate novel generalized linear model methodologies.
In Chapter 1, we introduce a variant of the traditional concordance statistic that is associated with logistic regression. This adjusted c − statistic as we call it utilizes the differences in predicted probabilities as weights for each event/non- event observation pair. We highlight an extensive comparison of the adjusted and traditional c-statistics using simulations and apply these measures in a modeling application.
In Chapter 2, we feature the development and investigation of three model selection criteria based on cross-validatory c-statistics: Model Misspecification Pre- diction Error, Fitting Sample Prediction Error, and Sum of Prediction Errors. We examine the properties of the corresponding selection criteria based on the cross- validatory analogues of the traditional and adjusted c-statistics via simulation and illustrate these criteria in a modeling application.
In Chapter 3, we propose and investigate an alternate approach to pseudo- likelihood model selection in the generalized linear mixed model framework. After outlining the problem with the pseudo-likelihood model selection criteria found using the natural approach to generalized linear mixed modeling, we feature an alternate approach, implemented using a SAS macro, that obtains and applies the pseudo-data from the full model for fitting all candidate models. We justify the propriety of the resulting pseudo-likelihood selection criteria using simulations and implement this new method in a modeling application.