The focus of this paper is on the empirical relationship between item difficulty and item discrimination. Two studies--an empirical investigation and a simulation study--were conducted to examine the association between item difficulty and item discrimination under classical test theory and item response theory (IRT), and the effects of the…

In learning diagnostic assessments, the attribute hierarchy specifies a sequential network of interrelated attribute mastery processes, which makes a test blueprint consistent with the cognitive theory. One of the most important functions of attribute hierarchy is to guide or limit the developmental direction of students and then form a…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

Simulation studies are fundamental to psychometric discourse and play a crucial role in operational and academic research. Yet, resources for psychometricians interested in conducting simulations are scarce. This Instructional Topics in Educational Measurement Series (ITEMS) module is meant to address this deficiency by providing a comprehensive…

Simulation studies are extremely common in the item response theory (IRT) research literature. This article presents a didactic discussion of "truth" and "error" in IRT-based simulation studies. We ultimately recommend that future research focus less on the simple recovery of parameters from a convenient generating IRT model,…

Recent advances have enabled diagnostic classification models (DCMs) to accommodate longitudinal data. These longitudinal DCMs were developed to study how examinees change, or transition, between different attribute mastery statuses over time. This study examines using longitudinal DCMs as an approach to assessing growth and serves three purposes:…