A New Person-Fit Statistic for the Lognormal Model for Response Times

Response-time models are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular response-time models, and suggests a simple person-fit statistic for the model. The distribution of the statistic under the null hypothesis of no misfit is proved to be χ² distribution. A simulation study and a real data example demonstrate the usefulness of the suggested statistic.