An application of a hierarchical IRT model for items in families generated through the application of different combinations of design rules is discussed. Within the families, the items are assumed to differ only in surface features. The parameters of the model are estimated in a Bayesian framework, using a data-augmented Gibbs sampler. An obvious…

Cognitive ability tests are widely used in organizations around the world because they have high predictive validity in selection contexts. Although these tests typically measure several subdomains, testing is usually carried out for a single subdomain at a time. This can be ineffective when the subdomains assessed are highly correlated. This…

An accurately calibrated item bank is essential for a valid computerized adaptive test. However, in some settings, such as occupational testing, there is limited access to test takers for calibration. As a result of the limited access to possible test takers, collecting data to accurately calibrate an item bank in an occupational setting is…

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

The effect of person misfit to an item response theory (IRT) model on a mastery/nonmastery decision was investigated. Also investigated was whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

Developed a multilevel item response (IRT) model that allows for differences between the distributions of item parameters of families of item clones. Results from simulation studies based on an item pool from the Law School Admission Test illustrate the accuracy of the item pool calibration and adaptive testing procedures based on the model. (SLD)

Imposed a two-level regression model on the ability parameters in an item response theory (IRT) model. Uses a simulation study and an empirical data set to show that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. (SLD)

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple…

A version of sequential mastery testing is studied in which response behavior is modeled by an item response theory (IRT) model. First, a general theoretical framework is sketched that is based on a combination of Bayesian sequential decision theory and item response theory. A discussion follows on how IRT based sequential mastery testing can be…

The effect of person misfit to an item response theory model on a mastery/nonmastery decision was investigated. Furthermore, it was investigated whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

In this paper it is shown that differential item functioning can be evaluated using the Lagrange multiplier test or C. R. Rao's efficient score test. The test is presented in the framework of a number of item response theory (IRT) models such as the Rasch model, the one-parameter logistic model, the two-parameter logistic model, the generalized…

A two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that this offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and…

In computerized adaptive testing, updating parameter estimates using adaptive testing data is often called online calibration. In this paper, how to evaluate whether the adaptive testing model used for online calibration fits the item response model used sufficiently is studied. Three approaches are investigated, based on a Lagrange multiplier…