In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

In this article, we systematically introduce the just another Gibbs sampler (JAGS) software program to fit common Bayesian cognitive diagnosis models (CDMs) including the deterministic inputs, noisy "and" gate model; the deterministic inputs, noisy "or" gate model; the linear logistic model; the reduced reparameterized unified…

The recent literature on computerized adaptive testing (CAT) has developed methods for creating CAT item pools from a large master pool. Each CAT pool is designed as a set of nonoverlapping forms reflecting the skill levels of an assumed population of test takers. This article presents a Monte Carlo method to obtain these CAT pools and discusses…

This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…

When constructed response test items are scored by more than one rater, the repeated ratings allow for the consideration of individual rater bias and variability in estimating student proficiency. Several hierarchical models based on item response theory have been introduced to model such effects. In this article, the authors demonstrate how these…

Outlines an approach to differential item functioning (DIF) analysis using hierarchical linear regression that makes it possible to combine results of logistic regression analyses across items to identify consistent sources of DIF, to quantify the proportion of explained variation in DIF coefficients, and to compare the predictive accuracy of…

Describes a goodness-of-fit statistic that considers the imprecision with which ability is estimated and involves constructing item fit tables based on each examinee's posterior distribution of ability, given the likelihood of the response pattern and an assumed marginal ability distribution. Also describes a Monte Carlo resampling procedure to…

For complex educational assessments, there is an increasing use of "item families," which are groups of related items. However, calibration or scoring for such an assessment requires fitting models that take into account the dependence structure inherent among the items that belong to the same item family. C. Glas and W. van der Linden…