Using Projective IRT to Evaluate the Effects of Multidimensionality on Unidimensional IRT Model Parameters

The application of unidimensional IRT models requires item response data to be unidimensional. Often, however, item response data contain a dominant dimension, as well as one or more nuisance dimensions caused by content clusters. Applying a unidimensional IRT model to multidimensional data causes violations of local independence, which can vitiate IRT applications. To evaluate and, possibly, remedy the problems caused by forcing unidimensional models onto multidimensional data, we consider the creation of a projected unidimensional IRT model, where the multidimensionality caused by nuisance dimensions is controlled for by integrating them out from the model. Specifically, when item response data have a bifactor structure, one can create a unidimensional model based on projecting to the general factor. Importantly, the projected unidimensional IRT model can be used as a benchmark for comparison to a unidimensional model to judge the practical consequences of multidimensionality. Limitations of the proposed approach are detailed.