Approximating multidimensionality with asymmetric unidimensional IRT models

Unidimensional item response theory (IRT) models are widely used even in settings where assessment data exhibit subtle forms of multidimensionality. Recent empirical evidence suggests that when item difficulty is associated with dimensionality, asymmetric item characteristic curves (ICCs) emerge in the unidimensional approximation. Through theoretical derivation and extensive simulation, this paper develops a framework for understanding the emergence and the degree of ICC asymmetry in UIRT models when applied to multidimensional data with difficulty-dimensionality associations. An empirical analysis of the Virginia Language & Literacy Screener (VALLSS) confirms the predicted patterns. These results highlight ICC asymmetry as an anticipated consequence of unidimensional approximation and underscore its relevance for applications such as vertical scaling and test linking.