Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

To address response style or bias in rating scales, forced-choice items are often used to request that respondents rank their attitudes or preferences among a limited set of options. The rating scales used by raters to render judgments on ratees' performance also contribute to rater bias or errors; consequently, forced-choice items have recently…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures (DPMs) offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT…

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…

Item compromise has long posed challenges in educational measurement, jeopardizing both test validity and test security of continuous tests. Detecting compromised items is therefore crucial to address this concern. The present literature on compromised item detection reveals two notable gaps: First, the majority of existing methods are based upon…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

Lord's (1980) equity theorem claims observed-score equating to be possible only when two test forms are perfectly reliable or strictly parallel. An analysis of its proof reveals use of an incorrect statistical assumption. The assumption does not invalidate the theorem itself though, which can be shown to follow directly from the discrete nature of…

Extreme response set, the tendency to prefer the lowest or highest response option when confronted with a Likert-type response scale, can lead to misfit of item response models such as the generalized partial credit model. Recently, a series of intrinsically multidimensional item response models have been hypothesized, wherein tendency toward…

It is common practice to log-transform response times before analyzing them with standard factor analytical methods. However, sometimes the log-transformation is not capable of linearizing the relation between the response times and the latent traits. Therefore, a more general approach to response time analysis is proposed in the current…

Value-added models have been widely used to assess the contributions of individual teachers and schools to students' academic growth based on longitudinal student achievement outcomes. There is concern, however, that ignoring the presence of missing values, which are common in longitudinal studies, can bias teachers' value-added scores.…

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function…

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

Under item response theory, the characteristic curve methods (Haebara and Stocking-Lord methods) are used to link two ability scales from separate calibrations. The linking methods use their respective criterion functions that can be defined differently according to the symmetry- and distribution-related schemes. The symmetry-related scheme…

An analytical approach was employed to compare sensitivity of causal effect estimates with different assumptions on treatment noncompliance and non-response behaviors. The core of this approach is to fully clarify bias mechanisms of considered models and to connect these models based on common parameters. Focusing on intention-to-treat analysis,…

This article presents a psychometric model for estimating ability and item-selection strategies in self-adapted testing. In contrast to computer adaptive testing, in self-adapted testing the examinees are allowed to select the difficulty of the items. The item-selection strategy is defined as the distribution of difficulty conditional on the…