Dimensionality in Compensatory MIRT When Complex Structure Exists: Evaluation of DETECT and NOHARM

This study investigated the effect of complex structure on dimensionality assessment in compensatory multidimensional item response models using DETECT- and NOHARM-based methods. The performance was evaluated via the accuracy of identifying the correct number of dimensions and the ability to accurately recover item groupings using a simple matching similarity (SM) coefficient. The DETECT-based methods yielded higher proportion correct than the NOHARM-based methods in two- and three-dimensional conditions, especially when correlations were ≤.60, data exhibited ≤30% complexity, and sample size was 1,000. As the complexity increased and the sample size decreased, the performance of the methods typically diminished. The NOHARM-based methods were either equally successful or better in recovering item groupings than the DETECT-based methods and were mostly affected by complexity levels. The DETECT-based methods were affected largely by the test length, such that with the increase of the number of items, SM coefficients would decrease substantially.