Using Paired Comparison Matrices to Estimate Parameters of the Partial Credit Rasch Measurement Model for Rater-Mediated Assessments

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)