A comparison of linear and equipercentile equating and IRT equating with FIPC across multidimensional test forms for non-equivalent groups

The aim of this study was to compare linear equating (Levine and Tucker), equipercentile equating, and true and observed score IRT equating with fixed item parameter calibration methods when applied to non-equivalent groups taking forms which have various multidimensional structures: equal or unequal total test difficulty and similar or dissimilar difficulty within dimensions across forms. This situation may be common for large-scale test forms that are composed of multiple sub-content areas and are being administered to examinees of mixed abilities at different times. Within the specifications of this study, when forms differ in total difficulty but the difference in difficulty within dimensions is consistent across forms, the linear methods may be preferred. When forms differ in average item difficulty within dimensions, regardless of equal or unequal total test difficulty, the IRT method with fixed item parameter calibration is favoured when data are correlated.