The Rasch facets model was developed to account for facet data, such as student essays graded by raters, but it accounts for only one kind of rater effect (severity). In practice, raters may exhibit various tendencies such as using middle or extreme scores in their ratings, which is referred to as the rater centrality/extremity response style. To…

The examinee-selected-item (ESI) design, in which examinees are required to respond to a fixed number of items in a given set of items (e.g., choose one item to respond from a pair of items), always yields incomplete data (i.e., only the selected items are answered and the others have missing data) that are likely nonignorable. Therefore, using…

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are…

The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

The random-threshold generalized unfolding model (RTGUM) was developed by treating the thresholds in the generalized unfolding model as random effects rather than fixed effects to account for the subjective nature of the selection of categories in Likert items. The parameters of the new model can be estimated with the JAGS (Just Another Gibbs…

In some tests, examinees are required to choose a fixed number of items from a set of given items to answer. This practice creates a challenge to standard item response models, because more capable examinees may have an advantage by making wiser choices. In this study, we developed a new class of item response models to account for the choice…

Rating scale items have been widely used in educational and psychological tests. These items require people to make subjective judgments, and these subjective judgments usually involve randomness. To account for this randomness, Wang, Wilson, and Shih proposed the random-effect rating scale model in which the threshold parameters are treated as…

Both testlet design and hierarchical latent traits are fairly common in educational and psychological measurements. This study aimed to develop a new class of higher order testlet response models that consider both local item dependence within testlets and a hierarchy of latent traits. Due to high dimensionality, the authors adopted the Bayesian…

Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

The generalized graded unfolding model (GGUM) has been recently developed to describe item responses to Likert items (agree-disagree) in attitude measurement. In this study, the authors (a) developed two item selection methods in computerized classification testing under the GGUM, the current estimate/ability confidence interval method and the cut…

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…