Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the multidimensional item response theory (MIRT) framework. Three equating procedures—two observed score procedures and one true score procedure—were created and described in detail. One observed score procedure was presented as a direct extension of unidimensional IRT (UIRT) observed score equating and is referred to as the “Full MIRT Observed Score Equating Procedure.” The true score procedure and the second observed score procedure incorporated unidimensional approximation procedures to equate exams using UIRT equating principles. These procedures are referred to as the “Unidimensional Approximation of MIRT True Score Equating Procedure” and the “Unidimensional Approximation of MIRT Observed Score Equating Procedure,” respectively. Three exams were used to conduct UIRT observed score and true score equating, MIRT observed score and true score equating, and equipercentile equating. The equipercentile equating procedure was conducted for the purpose of comparison because this procedure does not explicitly violate the IRT assumption of unidimensionality. Results indicated that the MIRT equating procedures performed more similarly to the equipercentile equating procedure than the UIRT equating procedures, presumably due to the violation of the unidimensionality assumption under the UIRT equating procedures.