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…

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…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

Because of concerns about test security, different test forms are typically used across different testing occasions. As a result, equating is necessary in order to get scores from the different test forms that can be used interchangeably. In order to assure the quality of equating, multiple equating methods are often examined. Various equity…

Raju, van der Linden, and Fleer (1995) introduced a framework for differential functioning of items and tests (DFIT) for unidimensional dichotomous models. Since then, DFIT has been shown to be a quite versatile framework as it can handle polytomous as well as multidimensional models both at the item and test levels. However, DFIT is still limited…

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

Item response theory (IRT) uses a family of statistical models for estimating stable characteristics of items and examinees and defining how these characteristics interact in describing item and test performance. With a focus on the three-parameter logistic IRT (Birnbaum, 1968; Lord, 1980) model, the current study examines the accuracy and…

This paper investigates four methods of linear equating under the common item nonequivalent groups design. Three of the methods are well known: Tucker, Angoff-Levine, and Congeneric-Levine. A fourth method is presented as a variant of the Congeneric-Levine method. Using simulation data generated from the three-parameter logistic IRT model we…

Two sampling-and-classification-based procedures were developed for automated test assembly: the Cell Only and the Cell and Cube methods. A simulation study based on a 540-item bank was conducted to compare the performance of the procedures with the performance of a mixed-integer programming (MIP) method for assembling multiple parallel test…

Several factors could cause variability in item response theory (IRT) linking and equating procedures, such as the variability across examinee samples and/or test items, seasonality, regional differences, native language diversity, gender, and other demographic variables. Hence, the following question arises: Is it possible to select optimal…

Problem Statement: Learning-teaching activities bring along the need to determine whether they achieve their goals. Thus, multiple choice tests addressing the same set of questions to all are frequently used. However, this traditional assessment and evaluation form contrasts with modern education, where individual learning characteristics are…

Since 2010, the whole national cohort Key Stage 2 (KS2) National Curriculum test in science in England has been replaced with a sampling test taken by pupils at the age of 11 from a nationally representative sample of schools annually. The study reported in this paper compares the performance of different subgroups of the samples (classified by…

Small sample equating remains a largely unexplored area of research. This study attempts to fill in some of the research gaps via a large-scale, IRT-based simulation study that evaluates the performance of seven small-sample equating methods under various test characteristic and sampling conditions. The equating methods considered are typically…

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

All differential item functioning (DIF) methods require at least a moderate sample size for effective DIF detection. Samples that are less than 200 pose a challenge for DIF analysis. Smoothing can improve upon the estimation of the population distribution by preserving major features of an observed frequency distribution while eliminating the…