Equating methods are designed to adjust between alternate versions of assessments targeting the same content at the same level, with the aim that scores from the different versions can be used interchangeably. The statistical processes used in equating have, however, been extended to statistically "link" assessments that differ, such as…

The nonequivalent-groups anchor-test (NEAT) data-collection design is commonly used in large-scale assessments. Under this design, different test groups take different test forms. Each test form has its own unique items and all test forms share a set of common items. If item response theory (IRT) models are applied to analyze the test data, the…

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items,…

The last series of Raven's standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization…

Rasch common-item equating is often used in high-stakes testing to maintain equivalent passing standards across test administrations. If unaddressed, item parameter drift poses a major threat to the accuracy of Rasch common-item equating. We compared the performance of well-established and newly developed drift detection methods in small and large…

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of…

In applications of item response theory (IRT) models, it is known that empirical violations of the local independence (LI) assumption can significantly bias parameter estimates. To address this issue, we propose a threshold-autoregressive item response theory (TAR-IRT) model that additionally accounts for order dependence among the item responses…

Examples of the impact of statistical theory on assessment practice are provided from the perspective of a statistician trained in theoretical statistics who began to work on assessments. Goodness of fit of item-response models is examined in terms of restricted likelihood-ratio tests and generalized residuals. Minimum discriminant information…

Massive Open Online Courses (MOOCs) have become a popular tool for worldwide learners. However, a lack of emotional interaction and support is an important reason for learners to abandon their learning and eventually results in poor learning performance. This study applied an integrative framework of achievement emotions to uncover their holistic…

Mixture models have been developed to enable detection of within-subject differences in responses and response times to psychometric test items. To enable mixture modeling of both responses and response times, a distributional assumption is needed for the within-state response time distribution. Since violations of the assumed response time…

Purpose: This study aims to compare the performances of Item Response Theory (IRT) equating and kernel equating (KE) methods based on equating errors (RMSD) and standard error of equating (SEE) using the anchor item nonequivalent groups design. Method: Within this scope, a set of conditions, including ability distribution, type of anchor items…

In this article, alternative randomized response models are proposed, which make use of sum of quantitative scores generated from two decks of cards being used in a survey. The proposed methods are compared to the Odumade and Singh and Singh and Grewal models through a simulation study. It is shown that the modified methods can be used more…

The four-parameter logistic (4PL) Item Response Theory (IRT) model has recently been reconsidered in the literature due to the advances in the statistical modeling software and the recent developments in the estimation of the 4PL IRT model parameters. The current simulation study evaluated the performance of expectation-maximization (EM),…

This note is concerned with evaluation of location parameters for polytomous items in multiple-component measuring instruments. A point and interval estimation procedure for these parameters is outlined that is developed within the framework of latent variable modeling. The method permits educational, behavioral, biomedical, and marketing…

Count responses with grouping and right censoring have long been used in surveys to study a variety of behaviors, status, and attitudes. Yet grouping or right-censoring decisions of count responses still rely on arbitrary choices made by researchers. We develop a new method for evaluating grouping and right-censoring decisions of count responses…