Ordering properties of homogeneity analysis, when applied to data from IRT models

Matthijs Warrens PhD

Project: Leiden University

Project running from: 1 July 2003 – 1 July 2007

Supervisors: Prof. dr W.J. Heiser, dr D.N.M. de Gruijter

Summary:
When applied to data generated by some Item Response Theory (IRT) model, homogeneity analysis (including simple and multiple correspondence analysis) seems to recover the ordering of the person and item parameters quite well. The current project aims at a full theoretical expla-nation for this phenomenon, and at a rigorous description of the conditions under which these ordering properties hold. Heiser’s (1981) work on the consecutive ones property in correspon-dence analysis will be generalized to the probabilistic case along the lines of what Schriever (1985) has done for multiple correspondence analysis. Both dichotomous and polytomous items will be considered. If possible, stronger properties than ordering of parameter values are of inter-est as well. Another question is whether the results can be extended to the multidimensional case. Finally, the effect of sample size on recovery will be studied in some simulation studies.

Date of defence: 25 June 2008

Title of thesis: Similarity coefficients for binary data: Properties of coefficients, coefficient matrices, multi-way metrics and mutlivariate coeffiicents

ISBN: 978-90-8891-0524