Applying Kaplan-Meier to Item Response Data

Some IRT models can be equivalently modeled in alternative frameworks such as logistic regression. Logistic regression can also model time-to-event data, which concerns the probability of an event occurring over time. Using the relation between time-to-event models and logistic regression and the relation between logistic regression and IRT, this article outlines how the nonparametric Kaplan-Meier estimator for time-to-event data can be applied to IRT data. Established Kaplan-Meier computational formulas are shown to aid in better approximating “parametric-type” item difficulty compared to methods from existing nonparametric methods, particularly for the less-well-defined scenario wherein the response function is monotonic but invariant item ordering is unreasonable. Limitations and the potential for Kaplan-Meier within differential item functioning are also discussed.