Accurate item parameters and standard errors (SEs) are crucial for many multidimensional item response theory (MIRT) applications. A recent study proposed the Gaussian Variational Expectation Maximization (GVEM) algorithm to improve computational efficiency and estimation accuracy (Cho et al., 2021). However, the SE estimation procedure has yet to…

The property of item parameter invariance in item response theory (IRT) plays a pivotal role in the applications of IRT such as test equating. The scope of parameter invariance when using estimates from finite biased samples in the applications of IRT does not appear to be clearly documented in the IRT literature. This article provides information…

In this article, we have suggested a new modified mixed randomized response (RR) model and studied its properties. It is shown that the proposed mixed RR model is always more efficient than the Kim and Warde's mixed RR model. The proposed mixed RR model has also been extended to stratified sampling. Numerical illustrations and graphical…

Multiple matrix designs are commonly used in large-scale assessments to distribute test items to students. These designs comprise several booklets, each containing a subset of the complete item pool. Besides reducing the test burden of individual students, using various booklets allows aligning the difficulty of the presented items to the assumed…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

An automated item selection procedure in Mokken scale analysis partitions a set of items into one or more Mokken scales, if the data allow. Two algorithms are available that pursue the same goal of selecting Mokken scales of maximum length: Mokken's original automated item selection procedure (AISP) and a genetic algorithm (GA). Minimum…

Ramsay-curve item response theory (RC-IRT) is a nonparametric procedure that estimates the latent trait using splines, and no distributional assumption about the latent trait is required. For item parameters of the two-parameter logistic (2-PL), three-parameter logistic (3-PL), and polytomous IRT models, RC-IRT can provide more accurate estimates…

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 study investigates measurement decision theory (MDT) as an underlying model for computer adaptive testing when the goal is to classify examinees into one of a finite number of groups. The first analysis compares MDT with a popular item response theory model and finds little difference in terms of the percentage of correct classifications. The…

This research examines the utility of the s-x[superscript 2] statistic proposed by Orlando and Thissen (2000) in evaluating item fit for multidimensional item response models. Monte Carlo simulation was conducted to investigate both the Type I error and statistical power of this fit statistic in analyzing two kinds of multidimensional test…

Measurement error is a common theme in classical measurement models used in testing and assessment. In classical measurement models, the definition of measurement error and the subsequent reliability coefficients differ on the basis of the test administration design. Internal consistency reliability specifies error due primarily to poor item…

The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of "Item Response Theory (IRT) models". The present paper provides an expository account of the DA-T Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs…

Coefficient "H" is used as an index of scalability in nonparametric item response theory (NIRT). It indicates the degree to which a set of items rank orders examinees. Theoretical sampling distributions, however, have only been derived asymptotically and only under restrictive conditions. Bootstrap methods offer an alternative possibility to…

Problems in selection of optimal designs in item-response theory (IRT) models are resolved through a sequential design procedure that is a modification of the D-optimality procedure proposed by Wynn (1970). This algorithm leads to consistent estimates, and the errors in selecting the abilities generally do not greatly affect optimality. (SLD)

RESGEN is a computer program designed to generate simulated latent trait distributions and then dichotomous or polytomous item responses based on item response models. The latent trait distributions can be univariate or multivariate normal, log-normal, uniform, or gamma. The item response models utilized in this program may have characteristics…