IRT Goodness-of-Fit Using Approaches from Logistic Regression
We present an IRT goodness-of-ﬁt framework based on approaches from logistic regression. We brieﬂy elaborate the formal relation of IRT models and logistic regression modeling. Subsequently, we examine which model tests and goodness-of-ﬁt indices from logistic regression can be meaningfully used for IRT. The performance of the casewise deviance, a collapsed deviance, and the Hosmer- Lemeshow test is studied by means of a simulation that compares their power to well known IRT model tests. Next, various R2 measures are discussed in terms of interpretability and appropriateness within an IRT context. By treating IRT models as classiﬁers, several additional indices such as hit rate, sensitivity, speciﬁcity, and area under the ROC curve are deﬁned. Data stemming from a social discomfort scale are used to demonstrate the application of these statistics.