Examining the effects of multidimensionality on vertical equating with the three-parameter logistic model /

Abstract

Results indicated that both the poorest item parameter estimation and the poorest equating occurred for the situation in which one test was unidimensional and one was multidimensional. When both tests were unidimensional or both were multidimensional the equatings were comparable to the unidimensional criterion equatings. There appeared to be a very slight advantage when both tests were unidimensional over equating tests that were both multidimensional when considering local equating bias (local equating consistency). However, the advantage appeared only at the extremes of the ability distribution, particularly at the lower end.

Equatings were examined in terms of standardized root mean squared differences, standardized differences between means, the ratio of standard deviations, correlations, and tau equivalence. The strength of the correlation between the two true (generating) traits appeared to have little effect on the quality of the equating. In general, the horizontal equatings were better than the vertical equatings.

Ten multidimensional data configurations and one unidimensional data configuration for thirty item tests were simulated for 6000 examinees. Each condition consisted of specific item parameter configurations and a specific correlation between traits on two dimensions. Three differences in mean difficulty between the two tests to be equated were simulated.