Comparison of equating methods for multidimensional tests which contain items with differential item functioning

Differential item functioning (DIF) and test equating are two important subjects for fairness in reported test scores. However, they have been treated separately in the psychometric literature. Hence, studies investigating the relationship between DIF and equating are quite rare. Moreover, there is no study addressing this relationship in multidimensional perspective, yet. The purpose of this study is to reveal the relationship between DIF and equating in multidimensional perspective, and contribute to the literature. In order to reveal this relationship accurately and clearly, population invariance of equating was investigated. The data used in the study were generated in accordance with the simple structure multidimensional item response theory (SS-MIRT) model. Four different equating methods were used in the study: simple structure-multidimensional item response theory observed score, unidimensional item response theory observed score, unidimensional item response theory true score and equipercentile equating. The performances of the equating methods were compared according to their population invariance under various simulation conditions (differential form DIF, correlation between dimensions, group mean ability differences between two forms). According to the results, the method that most accurately reflects the relationship between DIF and equating is the multidimensional equating method for the 0.5 correlation condition. On the other hand, under 0.8 and 0.95 correlation conditions, all methods give similar results except the results of equipercentile equating method at scores with low frequencies. Also, group mean ability difference between two forms has no effect on the population invariance of the methods.