An Evaluation of the Accuracy of Multidimensional IRT Linking

Abstract

Most multidimensional item response theory (MIRT) parameter estimation programs solve the identification problem by requiring that multidimensional traits be distributed as multivariate normal, MVN(0, I). Three types of MIRT linking methods were evaluated, which are based on a composite transformation that changes the linked group’s reference system into the base group’s reference system: an orthogonal Procrustes rotation, a translation transformation, and a single dilation. The results indicate that the best MIRT linking method was an unbiased, effective, and consistent estimator that produced accurate estimates of transformation parameters when errors in estimation of item parameters were purposely manipulated. This method was capable of successfully recovering item parameters under model-fitting conditions.