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…

In large-scale educational assessment data consistent with a simple-structure multidimensional item response theory (MIRT) model, where every item measures only one latent variable, separate unidimensional item response theory (UIRT) models for each latent variable are often calibrated for practical reasons. While this approach can be valid for…

On August 7th, 2013, the New York State Education Commissioner, John King, announced the initial results of the state's new assessment, which was designed to measure college and career readiness relative to the Common Core Learning Standards. Commissioner King noted that the proficiency rates on these assessments were significantly lower than…

This paper first discusses the relationship between Kullback-Leibler information (KL) and Fisher information in the context of multi-dimensional item response theory and is further interpreted for the two-dimensional case, from a geometric perspective. This explication should allow for a better understanding of the various item selection methods…

In a selected response test, aberrant responses such as careless errors and lucky guesses might cause error in ability estimation because these responses do not actually reflect the knowledge that examinees possess. In a computerized adaptive test (CAT), these aberrant responses could further cause serious estimation error due to dynamic item…

The generalized graded unfolding model (GGUM) has been recently developed to describe item responses to Likert items (agree-disagree) in attitude measurement. In this study, the authors (a) developed two item selection methods in computerized classification testing under the GGUM, the current estimate/ability confidence interval method and the cut…

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,…

In sequential mastery testing (SMT), assessment via computer is used to classify examinees into one of two mutually exclusive categories. Unlike paper-and-pencil tests, SMT has the capability to use variable-length stopping rules. One approach to shortening variable-length tests is stochastic curtailment, which halts examination if the probability…

It has been widely reported that in computerized adaptive testing some examinees may get much lower scores than they would normally if an alternative paper-and-pencil version were given. The main purpose of this investigation is to quantitatively reveal the cause for the underestimation phenomenon. The logistic models, including the 1PL, 2PL, and…

The standard error of the maximum likelihood ability estimator is commonly estimated by evaluating the test information function at an examinee's current maximum likelihood estimate (a point estimate) of ability. Because the test information function evaluated at the point estimate may differ from the test information function evaluated at an…

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (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…

Under a multidimensional item response theory (MIRT) computerized adaptive testing (CAT) testing scenario, a trait estimate (theta) in one dimension will provide clues for subsequently seeking a solution in other dimensions. This feature may enhance the efficiency of MIRT CAT's item selection and its scoring algorithms compared with its…