Abstract

This chapter describes a measurement approach for scaling individuals on a single dimension in the presence of multidimensionality. The approach, which we call the projective item response model, uses a unidimensional model for assessing multidimensional response data that contain a dominant dimension of interest. The novel approach is motivated by several observations: (1) that while scale development efforts always strive for unidimensional constructs (e.g., mathematical ability, anxiety, or botherness due to a disease and its treatment), tests require content validity and such a requirement often leads to a conflation of constructs from multiple dimensions; (2) that while multidimensional models are, logically, tools of choice for handling multidimensional data, they are not well equipped for the purpose of direct comparison of specific latent constructs across studies; and (3) that while complex multidimensional models are now computationally feasible, estimations for high dimensions using generally available sample sizes—especially in psychological and health sciences—are often sensitive to model misspecification and that some components of the estimated model could exhibit a high level of error. The most “vulnerable” parts are dimensions that are relatively weak and not well represented across items.