Incorporating Information Functions in IRT Scaling

Abstract

Item response theory (IRT) scaling via a set of items common to two test forms assumes that those item’s parameters are invariant with respect to a linear transformation. Characteristic curve methods rely on this assumption; scale transformations are conducted by minimizing a loss function between item characteristic curves (ICCs), as in the case of Haebara (1980), or test characteristic curves (TCCs), as in the case of Stocking and Lord (1983). However, minimizing the loss function between characteristic curves does not guarantee that the same will hold for information functions. This study introduces two new scaling methodologies: one combines the ICC methodology of Haebara (1980) with item information functions (IIFs); the other combines the TCC methodology of Stocking and Lord (1983) with test information functions (TIFs). In a simulation experiment, Haebara’s (1980) and Stocking and Lord’s (1983) methodologies as well as the two new scaling methodologies were applied to simulated administrations of a fixed form under different latent trait distributions. Results suggest that IRT scaling by combining TCCs with TIFs yields some benefits over the existing characteristic curve methodologies; however, combining ICCs with IIFs did not perform as well as the other three scaling methodologies.