Simple-Structure Multidimensional Item Response Theory Equating for Multidimensional Tests

A theoretical and conceptual framework for true-score equating using a simple-structure multidimensional item response theory (SS-MIRT) model is developed. A true-score equating method, referred to as the SS-MIRT true-score equating (SMT) procedure, also is developed. SS-MIRT has several advantages over other complex multidimensional item response theory models including improved efficiency in estimation and straightforward interpretability. The performance of the SMT procedure was examined and evaluated through four studies using different data types. In these studies, results from the SMT procedure were compared with results from four other equating methods to assess the relative benefits of SMT compared with the other procedures. In general, SMT showed more accurate equating results compared with the traditional unidimensional IRT (UIRT) equating when the data were multidimensional. More accurate performance of SMT over UIRT true-score equating was consistently observed across the studies, which supports the benefits of a multidimensional approach in equating for multidimensional data. Also, SMT performed similarly to a SS-MIRT observed score method across all studies.