The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee's ability and optimally…

Through simulated data, five multidimensional computerized adaptive testing (MCAT) selection procedures with varying test lengths are examined and compared using different stopping rules. Fixed item exposure rates are used for all the items, and the Priority Index (PI) method is used for the content constraints. Two stopping rules, standard error…

This chapter addresses the psychometric challenges in assessing English language learners (ELLs) and students with disabilities (SWDs). The first section addresses some general considerations in the assessment of ELLs and SWDs, including the prevalence of ELLs and SWDs in the student population, federal and state legislation that requires the…

Item response theory (IRT) and related latent variable models represent modern psychometric theory, the successor to classical test theory in psychological assessment. Although IRT has become prevalent in the measurement of ability and achievement, its contributions to clinical domains have been less extensive. Applications of IRT to clinical…

Item calibration is an essential issue in modern item response theory based psychological or educational testing. Due to the popularity of computerized adaptive testing, methods to efficiently calibrate new items have become more important than that in the time when paper and pencil test administration is the norm. There are many calibration…

Imposed time limits on computer adaptive tests (CATs) can result in examinees having difficulty completing all items, thus compromising the validity and reliability of ability estimates. In this study, the effects of speededness were explored in a simulated CAT environment by varying examinee response patterns to end-of-test items. Expectedly,…

Two IRT-based procedures to estimate test reliability for a certification exam that used both adaptive (via a MST model) and non-adaptive design were considered in this study. Both procedures rely on calibrated item parameters to estimate error variance. In terms of score variance, one procedure (Method 1) uses the empirical ability distribution…

The reliability coefficient is predicted from the test information function (TIF) or two modified TIF formulas and a specific trait distribution. Examples illustrate the variability of the reliability coefficient across different trait distributions, and results are compared with empirical reliability coefficients. (SLD)

Evaluated the distribution of person fit within the computerized-adaptive testing (CAT) environment through simulation. Found that, within the CAT environment, these indexes tend not to follow a standard normal distribution. Person fit indexes had means and standard deviations that were quite different from the expected. (SLD)

Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the…

In a variable-length adaptive test with a stopping rule that relied on the asymptotic standard error of measurement of the examinee's estimated true score, M. S. Stocking (1987) discovered that it was sufficient to know the examinee's true score and the number of items administered to predict with some accuracy whether an examinee's true score was…

An item selection procedure for computerized adaptive testing based on average global information is proposed. Results from simulation studies comparing the approach with the usual maximum item information item selection indicate that the new method leads to improvement in terms of bias and mean squared error reduction under many circumstances.…

Error indices (bias, standard error of estimation, and root mean square error) obtained on different scales of measurement under different test termination rules in a computerized adaptive test (CAT) context were examined. Four ability estimation methods were studied: (1) maximum likelihood estimation (MLE); (2) weighted likelihood estimation…

Simulated data were used to investigate the performance of modified versions of the Mantel-Haenszel method of differential item functioning (DIF) analysis in computerized adaptive tests (CAT). Results indicate that CAT-based DIF procedures perform well and support the use of item response theory-based matching variables in DIF analysis. (SLD)

R. J. Owen (1975) proposed an approximate empirical Bayes procedure for item selection in adaptive testing. The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach, but…