An eigenvector method for estimating item parameters of the dichotomous and polytomous Rasch models.
The purpose of this paper is to describe a technique for obtaining item parameters of the Rasch model, a technique in which the item parameters are extracted from the eigenvector of a matrix derived from comparisons between pairs of items. The technique can be applied to both dichotomous and polytomous data. In application to a previously published data set, it is shown that the technique provides item parameter estimates comparable to those produced by joint maximum likelihood estimation, and for the most difficult items, the technique appears to produce superior estimates. This method has several advantages. It easily accommodates missing data, and makes transparent the basis for item parameter estimation in the presence of missing data. Furthermore, the method provides a link to other methods in the social sciences and, in particular, provides the framework for application of graph theory to the analysis of assessment networks. Finally, it exploits several characteristics that are unique to the Rasch model.
Garner
Mary
M
Kennesaw State University, Department of Mathematics, 1000 Chastain Roads, Kennesaw, GA 30144, USA. mgarner@kennesaw.edu
D000465:Algorithms; D006801:Humans; D015233:Models, Statistical; D011594:Psychometrics / Q000706:statistics & numerical data; D015203:Reproducibility of Results; D012942:Social Sciences / Q000706:statistics & numerical data*