Polytomous attributes, particularly those defined as part of the test development process, can provide additional diagnostic information. The present research proposes the polytomous generalized deterministic inputs, noisy, "and" gate (pG-DINA) model to accommodate such attributes. The pG-DINA model allows input from substantive experts…

Optimal test-design methods are applied to rule-based item generation. Three different cases of automated test design are presented: (a) test assembly from a pool of pregenerated, calibrated items; (b) test generation on the fly from a pool of calibrated item families; and (c) test generation on the fly directly from calibrated features defining…

Interest in developing computerized adaptive testing (CAT) under cognitive diagnosis models (CDMs) has increased recently. CAT algorithms that use a fixed-length termination rule frequently lead to different degrees of measurement precision for different examinees. Fixed precision, in which the examinees receive the same degree of measurement…

A testlet is a cluster of items that share a common passage, scenario, or other context. These items might measure something in common beyond the trait measured by the test as a whole; if so, the model for the item responses should allow for this testlet trait. But modeling testlet effects that are negligible makes the model unnecessarily…

For mixed-type tests composed of dichotomous and polytomous items, polytomous items often yield more information than dichotomous items. To reflect the difference between the two types of items and to improve the precision of ability estimation, an adaptive weighted maximum-a-posteriori (WMAP) estimation is proposed. To evaluate the performance of…

Increasingly, researchers interested in identifying potentially biased test items are encouraged to use a confirmatory, rather than exploratory, approach. One such method for confirmatory testing is rooted in differential bundle functioning (DBF), where hypotheses regarding potential differential item functioning (DIF) for sets of items (bundles)…

When tests consist of multiple-choice and constructed-response items, researchers are confronted with the question of which item response theory (IRT) model combination will appropriately represent the data collected from these mixed-format tests. This simulation study examined the performance of six model selection criteria, including the…

In 2008, Penfield showed that measurement invariance across all response options of a multiple-choice item (correct option and the "J" distractors) can be modeled using a nominal response model that included a differential distractor functioning (DDF) effect for each of the "J" distractors. This article extends this concept to consider how the…

Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm…

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 testlet response model is designed for handling items that are clustered, such as those embedded within the same reading passage. Although the testlet is a powerful tool for handling item clusters in educational and psychological testing, the interpretations of its item parameters, the conditional correlation between item pairs, and the…

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…

The delta-plot method (Angoff, 1972) is a graphical technique used in the context of test equating for identifying common items with aberrant changes in their item difficulties across administrations or alternate forms. This brief research report explores the effects on equated aggregate scores when delta-plot outliers are either retained in or…

In this study, all the advantages of slope parameters, random weights, and latent regression are acknowledged when dealing with component and composite items by adding slope parameters and random weights into the standard item response model with internal restrictions on item difficulty and formulating this new model within a multilevel framework…

A latent transition analysis (LTA) model was described with a mixture Rasch model (MRM) as the measurement model. Unlike the LTA, which was developed with a latent class measurement model, the LTA-MRM permits within-class variability on the latent variable, making it more useful for measuring treatment effects within latent classes. A simulation…