The Polytomous Rasch Model and the Equating of Two Instruments
David Andrich · 2012
Equating different instruments that assess the same trait is an integral task of modern psychometrics. This chapter describes the application of the polytomous Rasch model (PRM) in equating two instruments intended to assess the same trait using only the total scores on the instruments. First, the chapter discusses the PRM and a reparameterization of each instrument's parameters. This reparameterization overcomes both estimation complications – it reduces the number of independent parameters that are to be estimated, and it can handle null scores provided there are not too many of them. Next, the chapter talks about the conditional statistical test of fit between the data and the model and two graphical tests of fit. Then, it summarizes two possible procedures for equating two instruments from a PRM analysis. Finally, the chapter provides an example describing which instruments have relatively large maximum scores and which have null scores.