Introduction: Item response theory (IRT) has received much attention in validation of assessment instrument because it allows the estimation of students' ability from any set of the items. Item response theory allows the difficulty and discrimination levels of each item on the test to be estimated. In the framework of IRT, item characteristics are…

Surveys with rating scales are often used in higher education research to measure student learning and development, yet testing and reporting on the longitudinal psychometric properties of these instruments is rare. Rasch techniques allow scholars to map item difficulty and individual aptitude on the same linear, continuous scale to compare…

The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…

As part of the Race to the Top initiative, the United States Department of Education made nearly 1 billion dollars available in State Educational Technology grants with the goal of ramping up school technology. One result of this effort is that states, districts, and schools across the country are using computerized assessments to measure their…

Andersen (1995, 2002) proves a theorem relating variances of parameter estimates from samples and subsamples and shows its use as an adjunct to standard statistical analyses. The authors show an application where the theorem is central to the hypothesis tested, namely, whether random guessing to multiple choice items affects their estimates in the…

Estimation of multidimensional item response theory (MIRT) model parameters can be carried out using the normal ogive with unweighted least squares estimation with the normal-ogive harmonic analysis robust method (NOHARM) software. Previous simulation research has demonstrated that this approach does yield accurate and efficient estimates of item…

In 2005, the ACS Examinations Institute released an exam for first-term general chemistry in which items are intentionally paired with one conceptual and one traditional item. A second-term, paired-questions exam was released in 2007. This paper presents an empirical study of student performances on these two exams based on national samples of…

It is known that the Rasch model is a special two-level hierarchical generalized linear model (HGLM). This article demonstrates that the many-faceted Rasch model (MFRM) is also a special case of the two-level HGLM, with a random intercept representing examinee ability on a test, and fixed effects for the test items, judges, and possibly other…

The linear logistic test model (LLTM) breaks down the item parameter of the Rasch model as a linear combination of some hypothesized elementary parameters. Although the original purpose of applying the LLTM was primarily to generate test items with specified item difficulty, there are still many other potential applications, which may be of use…

The popularity of intelligent tutoring systems (ITSs) is increasing rapidly. In order to make learning environments more efficient, researchers have been exploring the possibility of an automatic adaptation of the learning environment to the learner or the context. One of the possible adaptation techniques is adaptive item sequencing by matching…

Basic issues in understanding Item Response Theory (IRT), or Latent Trait Theory, measurement models are discussed. These theories have gained popularity because of their promise to provide greater precision and control in measurement involving both achievement and attitude instruments. IRT models implement probabilistic techniques that yield…

Proposes formulas for expected true-score measures and reliability of binary items as a function of their Rasch difficulty when the trait (ability) distribution is normal or logistic. Provides an illustrative example for using the proposed formulas. (SLD)

Describes an extension to the Rasch model for fundamental measurement in which there is parameterization not only for examinee ability and item difficulty but also for judge severity. Discusses variants of this model and judging plans, and explains its use in an empirical testing situation. (SLD)

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori…

Computer adaptive testing is the study of scoring tests and questions based on assumptions concerning the mathematical relationship between examinees' ability and the examinees' responses. Adaptive student tests, which are based on item response theory (IRT), have many advantages over conventional tests. We use the least square method, a…