HUD Colloquium Fall 2024 Presents: Dr. Jay Verkuilen & Peter J. Johnson

The Department of Human Development Colloquium Series Presents:

Dr. Jay Verkuilen & Peter J. Johnson

Program in Educational Psychology

Graduate Center, City University of New York

Abstract

Heywood cases and other improper solutions occur frequently in latent variable models. They have important consequences for scoring with the latent variable model and are indicative of issues in a model such as poor identification or model misspecification. In the context of the 2PL and 3PL models in IRT, they are more frequently known as Guttman items and are identified by having a discrimination parameter that is deemed excessively large. Asymmetric item response theory (AsymIRT) models often have parameters that are not easy to interpret directly, so scanning parameter estimates are not necessarily indicative of the presence of problematic values. Graphical examination of the IRF can be useful as well, but is necessarily subjective and highly dependent on choices of graphical defaults. We propose using the derivatives of the IRF and the item Fisher information functions to bypass the parameters, allowing for more concrete and consistent identification of Heywood cases. We illustrate the approach using several AsymIRT models and an empirical example.