A model-based approach to goodness-of-fit evaluation in item response theory

These authors congratulate Albert Maydeu-Olivares on his lucid and timely overview of goodness-of-fit assessment in IRT models, a field to which he himself has contributed considerably in the form of limited information statistics. In this commentary, Oberski and Vermunt focus on two aspects of model fit: (1) what causes there may be of misfit; and (2) what consequences misfit may have. They present their view on these topics in an integrated framework that is slightly different from that presented by Professor Maydeu-Olivares. They next provide a short illustration using an IRT analysis and, finally, draw some conclusions. This commentary expands on Maydeu-Olivares' overview of goodness-of-fit testing in item response theory by providing a model-based framework for GOF assessment. Oberski and Vermunt contend that many unresolved issues remain with the use of these measures, such as the problem of equivalent models, multiple testing, dealing with dependencies between parameters, and a shift of responsibility for deciding what may cause misfit and what is "of interest" toward the practitioner. These issues are, however, not absent in other goodness-of-fit assessment procedures, but merely less explicit. Therefore the model-based perspective appears to be a fruitful area of future research.