title: Using paired comparison matrices to estimate parameters of the partial credit Rasch measurement model for rater-mediated assessments.
abstract: The purpose of this paper is to describe a technique for estimating the parameters of a Rasch model that accommodates ordered categories and rater severity. The technique builds on the conditional pairwise algorithm described by Choppin (1968, 1985) and represents an extension of a conditional algorithm described by Garner and Engelhard (2000, 2002) in which parameters appear as the eigenvector of a matrix derived from paired comparisons. The algorithm is used successfully to recover parameters from a simulated data set. No one has previously described such an extension of the pairwise algorithm to a Rasch model that includes both ordered categories and rater effects. The paired comparisons technique has importance for several reasons: it relies on the separability of parameters that is true only for the Rasch measurement model; it works in the presence of missing data; it makes transparent the connectivity needed for parameter estimation; and it is very simple. The technique also shares the mathematical framework of a very popular technique in the social sciences called the Analytic Hierarchy Process (Saaty, 1996).
authors.affiliation: Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144-5591, USA. mgarner@kennesaw.edu
authors.forename: Mary
authors.initials: M
authors.lastname: Garner
authors.forename: George
authors.initials: G
authors.lastname: Engelhard
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D016555:Matched-Pair Analysis; D015233:Models, Statistical; D011594:Psychometrics / Q000379:methods*