Efficient Corrections for Standardized Person-Fit Statistics.

Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331-342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191-199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75-106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and 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 new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.

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

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 $$ T $$ , 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 $$ T $$ 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 $$ T $$ but also an existing correction for T $$ T $$ 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.

Using item scores and response times in person-fit assessment.

The use of joint models for item scores and response times is becoming increasingly popular in educational and psychological testing. In this paper, we propose two new person-fit statistics for such models in order to detect aberrant behaviour. The first statistic is computed by combining two existing person-fit statistics: one for the item scores, and one for the item response times. The second statistic is computed directly using the likelihood function of the joint model. Using detailed simulations, we show that the empirical null distributions of the new statistics are very close to the theoretical null distributions, and that the new statistics tend to be more powerful than several existing statistics for item scores and/or response times. A real data example is also provided using data from a licensure examination.

Using Item Scores and Distractors to Detect Test Speededness.

Test speededness refers to a situation in which examinee performance is inadvertently affected by the time limit of the test. Because speededness has the potential to severely bias both person and item parameter estimates, it is crucial that speeded examinees are detected. In this article, we develop a change-point analysis (CPA) procedure for detecting test speededness. Our procedure distinguishes itself from existing CPA procedures by using information from both item scores and distractors. Using detailed simulations, we show that under most conditions, the new CPA procedure improves the detection of speeded examinees and produces more accurate change-point estimates. It therefore seems there is a considerable amount of information to be gained from the item distractors, which, quite notably are available in all multiple-choice data. A real data example is also provided.

Two New Models for Item Preknowledge.

To evaluate preknowledge detection methods, researchers often conduct simulation studies in which they use models to generate the data. In this article, we propose two new models to represent item preknowledge. Contrary to existing models, we allow the impact of preknowledge to vary across persons and items in order to better represent situations that are encountered in practice. We use three real data sets to evaluate the fit of the new models with respect to two types of preknowledge: items only, and items and the correct answer key. Results show that the two new models provide the best fit compared to several other existing preknowledge models. Furthermore, model parameter estimates were found to vary substantially depending on the type of preknowledge being considered, indicating that answer key disclosure has a profound impact on testing behavior.