Three new corrections for standardized person-fit statistics for tests with polytomous items

Abstract

Recent years have seen a growing interest in the development of person-fit statistics for tests with polytomous items. Some of the most popular person-fit statistics for such tests belong to the class of standardized person-fit statistics, $T$, that is assumed to have a standard normal null distribution. However, this distribution only holds when (a) the true ability parameter is known and (b) an infinite number of items are available. In practice, both conditions are violated, and the quality of person-fit results is expected to deteriorate. In this paper, we propose three new corrections for $T$ that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The three new corrections are direct extensions of those that were developed by Gorney et al. (Psychometrika, 2024, https://doi.org/10.1007/s11336-024-09960-x) for tests with only dichotomous items. Our simulation study reveals that the three new corrections tend to outperform not only the original statistic $T$ but also an existing correction for $T$ proposed by Sinharay (Psychometrika, 2016, 81, 992). Therefore, the new corrections appear to be promising tools for assessing person fit in tests with polytomous items.