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…

Newer statistical procedures are typically introduced to help address the limitations of those already in practice or to deal with emerging research needs. Quantile regression (QR) is introduced in this paper as a relatively new methodology, which is intended to overcome some of the limitations of least squares mean regression (LMR). QR is more…