Nonparametric inference in multivariate categorical data analysis

Mariëlle Linting PhD

Project: Leiden University

Supervisors: Prof. dr J.J. Meulman, prof. dr P.J.F. Groenen

Project running from: 1 January 2000 – 1 September 2007

Summary:
In behavioral sciences most researchers use well known data analysis techniques, like multple regression analysis or analysis of variance. Other (multivariate) analysis techniques are much less often used. The purpose of this project is to shed new light on the many possibilities of multivariate categorical anlysis, with special application to educational data. In particular, categorical principal components analysis (CATPCA) and categorical regression analysis (CATREG) will be of interest. One reason why these techniques are not very often used, is that no immediate statistical inferences can be made. Therfore, this project will be focused specifically on establishing stability and statistical significance of solutions obtained from these techniques. Stability issues will be considered by means of bootstrap and jackknife procedures. By using permutation tests, statistical significance of the solutions will be established. Grphical representation of analysis results will receive special attention. Through its focus on the variety of ways ub which inferences can be made from advanced multivariate techniques, this study aims to a wider use of these techniques in the behavioral sciences.

Date of defence: 16 October 2007

Title of thesis: Nonparametric inference in nonlinear Prinicpal Components Analysis. ISBN: 978-90-9022232-5