Effect of examinee ability on test equating invariance

Previous research on the application of IRT methodology to vertical test equating has demonstrated conflicting results about the degree of invariance shown by these methods with respect to examinee ability. The purpose of this study was to examine IRT equating invariance by simulating the vertical equating of two tests under varying conditions. Rasch, three-parameter, and equipercentile equating methods were compared. Six equating cases, using different sets of item parameters, were replicated based on examinee samples of low, medium, or high ability or where ability was matched to the difficulty level of the test. The results showed that all three methods were reasonably invariant to examinee ability level under all conditions imposed. This suggests that multidimensionality is likely to be the cause of the lack of invariance found in real datasets. Index terms: Examinee ability; Invariance in item response theory; Item response theory, equating; Item response theory, invariance; Test equating; Vertical equating