Item response theory (IRT) models the relationship between the possible scores on a test item against a test taker's attainment of the latent trait that the item is intended to measure. In this study, we compare two models for tests with polytomously scored items: the optimal scoring (OS) model, a nonparametric IRT model based on the principles of…

Any time examinees have had access to items and/or answers prior to taking a test, the fairness of the test and validity of test score interpretations are threatened. Therefore, there is a high demand for procedures to detect both compromised items (CI) and examinees with preknowledge (EWP). In this article, we develop a procedure that uses item…

Clinical, medical, and health psychologists use difference scores obtained from pretest--posttest designs employing the same test to assess intraindividual change possibly caused by an intervention addressing, for example, anxiety, depression, eating disorder, or addiction. Reliability of difference scores is important for interpreting observed…

Topic models are mathematical and statistical models used to analyze textual data. The objective of topic models is to gain information about the latent semantic space of a set of related textual data. The semantic space of a set of textual data contains the relationship between documents and words and how they are used. Topic models are becoming…

Despite common operationalization, measurement efficiency of computerized adaptive testing should not only be assessed in terms of the number of items administered but also the time it takes to complete the test. To this end, a recent study introduced a novel item selection criterion that maximizes Fisher information per unit of expected response…

This research proposes a new statistic for testing latent variable distribution fit for unidimensional item response theory (IRT) models. If the typical assumption of normality is violated, then item parameter estimates will be biased, and dependent quantities such as IRT score estimates will be adversely affected. The proposed statistic compares…

Questionnaires that include items eliciting count responses are becoming increasingly common in psychology. This study proposes methodological techniques to overcome some of the challenges associated with analyzing multivariate item response data that exhibit zero inflation, maximum inflation, and heaping at preferred digits. The modeling…

The purpose of this article is to introduce and review the capability and performance of the Stata item response theory (IRT) package that is available from Stata v.14, 2015. Using a simulated data set and a publicly available item response data set extracted from Programme of International Student Assessment, we review the IRT package from…

Calibration of new items online has been an important topic in item replenishment for multidimensional computerized adaptive testing (MCAT). Several online calibration methods have been proposed for MCAT, such as multidimensional "one expectation-maximization (EM) cycle" (M-OEM) and multidimensional "multiple EM cycles"…

In this article, a latent trait model is proposed for the response times in psychological tests. The latent trait model is based on the linear transformation model and subsumes popular models from survival analysis, like the proportional hazards model and the proportional odds model. Core of the model is the assumption that an unspecified monotone…

For mixed-type tests composed of both dichotomous and polytomous items, polytomous items often yield more information than dichotomous ones. To reflect the difference between the two types of items, polytomous items are usually pre-assigned with larger weights. We propose an item-weighted likelihood method to better assess examinees' ability…

A method for medical screening is adapted to differential item functioning (DIF). Its essential elements are explicit declarations of the level of DIF that is acceptable and of the loss function that quantifies the consequences of the two kinds of inappropriate classification of an item. Instead of a single level and a single function, sets of…

Because of response disturbances such as guessing, cheating, or carelessness, item response models often can only approximate the "true" individual response probabilities. As a consequence, maximum-likelihood estimates of ability will be biased. Typically, the nature and extent to which response disturbances are present is unknown, and, therefore,…

In the course of screening a form of a medical licensing exam for items that function differentially (DIF) between men and women, the authors used the traditional Mantel-Haenszel (MH) statistic for initial screening and a Bayesian method for deeper analysis. For very easy items, the MH statistic unexpectedly often found DIF where there was none.…

Studied a method for flagging differential item functioning (DIF) based on loss functions. Builds on earlier research that led to the development of an empirical Bayes enhancement to the Mantel-Haenszel DIF analysis. Tested the method through simulation and found its performance better than some commonly used DIF classification systems. (SLD)