Vertical equating of educational tests: A simulation study using a two-dimensional compensatory model with Yen's Q(3) statistic and Bejar's procedure to assess commensurability

In the assessment of educational progress, it is sometimes desirable to find a common scale of measurement for scores on tests at different levels of achievement such as grade levels. Research on this process, known as vertical equating, has shown that current methods of equating using unidimensional item response models tend to produce poor results. The researchers attributed the findings to guessing by the lower-ability examinees and to multidimensionality of the two tests.;There is evidence that if all of the items of a test measure approximately the same combination of traits, and if these traits may be assumed to compensate for each other in determining the probability of a correct response to each item, then the test will fit a unidimensional model. It may be that an appropriate method of assessing commensurability could predict whether two tests at different levels could be validly equated.;The current study was designed to examine the dimensionality conditions under which vertical equating may be appropriate, using item response data generated to simulate various conditions of multidimensionality across tests. Yen's Q;It was found that Yen's Q...