In real-world situations, multidimensional data may appear on large-scale tests or psychological surveys. The purpose of this study was to investigate the effects of the quantity and magnitude of cross-loadings and model specification on item parameter recovery in multidimensional Item Response Theory (MIRT) models, especially when the model was…

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…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

Many large-scale educational surveys have moved from linear form design to multistage testing (MST) design. One advantage of MST is that it can provide more accurate latent trait [theta] estimates using fewer items than required by linear tests. However, MST generates incomplete response data by design; hence, questions remain as to how to…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

In confirmatory factor analysis quite similar models of measurement serve the detection of the difficulty factor and the factor due to the item-position effect. The item-position effect refers to the increasing dependency among the responses to successively presented items of a test whereas the difficulty factor is ascribed to the wide range of…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

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 item-position effect describes how an item's position within a test, that is, the number of previous completed items, affects the response to this item. Previously, this effect was represented by constraints reflecting simple courses, for example, a linear increase. Due to the inflexibility of these representations our aim was to examine…

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test…

Cross-level invariance in a multilevel item response model can be investigated by testing whether the within-level item discriminations are equal to the between-level item discriminations. Testing the cross-level invariance assumption is important to understand constructs in multilevel data. However, in most multilevel item response model…

In recent years, the computerised adaptive test (CAT) has gained popularity over conventional exams in evaluating student capabilities with desired accuracy. However, the key limitation of CAT is that it requires a large pool of pre-calibrated questions. In the absence of such a pre-calibrated question bank, offline exams with uncalibrated…

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…

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…