Constrained regression models

Anita van der Kooij
Data Theory Group
Department of Education
Faculty of Social and Behavioral Sciences
Leiden University
P.O. Box 9555, 2300 RB Leiden
Phone: +31 71 527 3827 / 4105 (secretary)
E-mail: Anita Van der Kooij

Supervisors: Prof. dr J.J. Meulman

Project running from: 1 November 1996 – 1 November 2007

Summary:
The objective of the project is to develop various models for categorical data that will be derived from the general linear regression model by applying various kinds of constraints. Algorithms to fit these models will be developed, implemented, and applied to data from the field of social sciences. Also, the models will be evaluated in terms of performance and compared to existing models. The proposed constrained models can be divided into three classes.The first class of models concerns multivariate analysis of variance models, with additivity constraints and special attention to the modeling of interaction.The second class of models concerns particularly restricted pathmodels, resulting in (quasi) redundancy analysis, PLS-models, and forms of neural nets.

In the third class of models equality constraints will be applied to the regression weights to deal with instability due to multi-collinearity.In all cases the techniques will be appropiate for the analysis of categorical data, notably by allowing monotonic or completely nonlinear splinetransformations. Special attention will be given to suitable representations of the subjects in the analysis.

Date of defence: 27 June 2007

Title of thesis: Prediction accuracy and stability of regression with optimal scaling transformations. Leiden: Mostert en van Onderen. ISBN 978-90-9021936-3.