A popular method to assess measurement invariance of a particular item is based on likelihood ratio tests with all other items as anchor items. The results of this method are often only reported in terms of statistical significance, and researchers proposed different methods to empirically select anchor items. It is unclear, however, how many…

We extend a recent didactic by Magis, Raiche, and Beland on the use of the l[subscript z] and l[subscript z]* person-fit statistics. We discuss a number of possibly confusing details and show that it is important to first investigate item response theory model fit before assessing person fit. Furthermore, it is argued that appropriate…

This article extends the work by Armstrong and Shi on CUmulative SUM (CUSUM) person-fit methodology. The authors present new theoretical considerations concerning the use of CUSUM person-fit statistics based on likelihood ratios for the purpose of detecting cheating and random guessing by individual test takers. According to the Neyman-Pearson…

The authors discuss a new method that combines the randomized response technique with item response theory. This method allows the researcher to obtain information at the individual person level without knowing the true responses. With this new method, it is possible to compare groups of individuals by means of analysis of variance or regression…

Mokken models of monotone homogeneity and double monotonicity and the Rasch model are compared using data from 990 young adult examinees taking a Dutch verbal intelligence test--the Verbal Analogies Test. The model of monotone homogeneity was found suitable for basic testing; more sophisticated applications appear to require parametric models.…