Target Rotations and Assessing the Impact of Model Violations on the Parameters of Unidimensional Item Response Theory Models

Abstract

Reise, Cook, and Moore proposed a “comparison modeling” approach to assess the distortion in item parameter estimates when a unidimensional item response theory (IRT) model is imposed on multidimensional data. Central to their approach is the comparison of item slope parameter estimates from a unidimensional IRT model (a restricted model), with the item slope parameter estimates from the general factor in an exploratory bifactor IRT model (the unrestricted comparison model). In turn, these authors suggested that the unrestricted comparison bifactor model be derived from a target factor rotation. The goal of this study was to provide further empirical support for the use of target rotations as a method for deriving a comparison model. Specifically, we conducted Monte Carlo analyses exploring (a) the use of the Schmid–Leiman orthogonalization to specify a viable initial target matrix and (b) the recovery of true bifactor pattern matrices using target rotations as implemented in Mplus. Results suggest that to the degree that item response data conform to independent cluster structure, target rotations can be used productively to establish a plausible comparison model.