Fisher Information-Based Item Difficulty and Discrimination Indices for Binary Item Response Models

While difficulty and discrimination parameters have appealing and intuitive meanings in the 2PL model, the parameters in IRT models outside of the 2PL are much harder to interpret. For example, even adding the pseudo-guessing parameter with the 3PL model makes the difficulty and discrimination parameters no longer have the meaning they have in the 2PL, and they are not directly comparable when the pseudo-guessing parameter differs. Increasingly, models even more complicated than the 3PL, such as the 4PL or various asymmetric IRF models, e.g., the Logistic Positive Exponent (LPE), Heteroscedastic Residuals (HR), Complimentary Log–Log (CLL), etc., have been considered. These models help resolve some issues encountered in IRT, but unfortunately, they sacrifice the interpretable nature of difficulty and discrimination that the 2PL provides. We propose to use two properties of Fisher information—the maximizer and a transformation of the information at the maximum—in analogy to the 2PL model, for which the model parameters and the Fisher information function are in close correspondence, as measures of effective difficulty and discrimination, respectively.