Prediction accuracy and stability of regression with optimal scaling transformations

Abstract

The central topic of this thesis is the CATREG approach to nonlinear regression. This approach finds optimal quantifications for categorical variables and/or nonlinear transformations for numerical variables in regression analysis. (CATREG is implemented in SPSS Categories by the author of the thesis; the relevant parts of the Categories manual are included in the appendix.) The first chapter of the thesis provides a non-technical introduction to the CATREG approach, illustrated with graphs. The more technical part of the thesis includes (1) a solution to the local minima problem for monotone transformations, as well as a study of the effect of several data conditions on the incidence and severeness of local minima, (2) the incorporation into CATREG of a particular resampling method (the .632 bootstrap) for assessing prediction accuracy, and (3) the incorporation into CATREG of several regularization methods (Ridge Regression, the Lasso, and the Elastic Net) for stabilizing the estimates of the regression coefficients and transformations. The technical part is followed by a chapter describing a bulimia nervosa study in which the CATREG-Lasso and the .632 bootstrap are applied.