The Impact of Levels of Discrimination on Vertical Equating in the Rasch Model.

Aligning scales in vertical equating carries a number of challenges for practitioners in contexts such as large-scale testing. This paper examines the impact of high and low discrimination on the results of vertical equating when the Rasch model is applied. A simulation study is used to show that different levels of discrimination introduce systematic error into estimates. A second simulation study shows that for the purpose of vertical equating, items with high or low discrimination contain information about translation constants that contains systematic error. The impact of differential item discrimination on vertical equating is examined and subsequently illustrated in terms of a real data set from a large-scale testing program, with vertical links between grade 3 and 5 numeracy tests. Implications of the results for practitioners conducting vertical equating with the Rasch model are identified, including monitoring progress over time. Implications for other item response models are also discussed.