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Abstract Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon can also easily occur within individual tests. Measures of reading proficiency, for example, often use different task types within a single assessment, a feature that may not only lead to multidimensionality, but also an association between item difficulty and dimensionality. Using a latent regression strategy, we demonstrate through simulations and empirical analysis how associations between dimensionality and difficulty yield a nonlinear reference composite where the weights of the underlying dimensionschangeacross the scale continuum according to the difficulties of the items associated with the dimensions. We further show how this form of curvilinearity produces systematic forms of misspecification in traditional unidimensional IRT models (e.g., 2PL) and can be better accommodated by models such as monotone‐polynomial or asymmetric IRT models. Simulations and a real‐data example from the Early Childhood Longitudinal Study—Kindergarten are provided for demonstration. Some implications for measurement modeling and for understanding the effects of 2PL misspecification on measurement metrics are discussed. 

Abstract Traditional approaches to the modeling of multiple‐choice item response data (e.g., 3PL, 4PL models) emphasize slips and guesses as random events. In this paper, an item response model is presented that characterizes both disjunctively interacting guessing and conjunctively interacting slipping processes as proficiency‐related phenomena. We show how evidence for this perspective is seen in the systematic form of invariance violations for item slip and guess parameters under four‐parameter IRT models when compared across populations of different mean proficiency levels. Specifically, higher proficiency populations tend to show higher guess and lower slip probabilities than lower proficiency populations. The results undermine the use of traditional models for IRT applications that require invariance and would suggest greater attention to alternatives.