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.