Anchors Aweigh: How the Choice of Anchor Items Affects the Vertical Scaling of 3PL Data with the Rasch Model

Abstract

ABSTRACT Vertical scaling is used to put tests of different difficulty onto a common metric. The Rasch model is often used to perform vertical scaling, despite its strict functional form. Few, if any, studies have examined anchor item choice when using the Rasch model to vertically scale data that do not fit the model. The purpose of this study was to investigate the implications of anchor item choice on bias in growth estimates when data do not fit the Rasch model. Data were generated with varying levels of true difference between grades and levels of the lower asymptote. When true growth or the lower asymptote were zero, estimates were unbiased and anchor item choice was not consequential. As true growth and the lower asymptote both increased, growth was underestimated and choice of anchor items had an impact. Easy anchor items led to less biased estimates of growth than hard anchor items.