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…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

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…

A simulation study was conducted to investigate the application of expected a posteriori (EAP) trait estimation in computerized adaptive tests (CAT) based on the partial credit model and compare it with maximum likelihood estimation (MLE). Results show the conditions under which EAP and MLE provide relatively accurate estimation in CAT. (SLD)

The case of adaptive testing under a multidimensional logistic response model is addressed. An adaptive algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The item selection criterion is a simple expression in closed form. In addition, it is…

General guidelines are developed to assist practitioners in devising operational computerized adaptive testing systems based on the graded response model. The effects of the following major variables were examined: item pool size; stepsize used along the trait continuum until maximum likelihood estimation could be calculated; and stopping rule…

Used simulations of computerized adaptive tests to evaluate results yielded by four commonly used ability estimation methods: maximum likelihood estimation (MLE) and three Bayesian approaches. Results show clear distinctions between MLE and Bayesian methods. (SLD)

Derives three reliability estimates for the Bayes modal estimate (BME) and the maximum-likelihood estimate (MLE) of theta in computerized adaptive tests (CATs). Computes the three reliability estimates and the true reliabilities of both BME and MLE for seven simulated CATs. Results show the true reliabilities for BME and MLE to be nearly identical…

A simulation study explored the effect of population distribution on maximum likelihood estimation (MLE) and expected a posteriori (EAP) estimation in computerized adaptive testing based on the rating scale model of D. Andrich (1978). The choice between EAP and MLE for particular situations is discussed. (SLD)

Evaluated the relative accuracy of the weighted likelihood estimate (WLE) of T. Warm (1989) compared to the maximum likelihood estimate (MLE), expected a posteriori estimate, and maximum a posteriori estimate. Results of the Monte Carlo study, which show the relative advantages of each approach, suggest that the test termination rule has more…

Extended the use of a beta prior in trait estimation to the maximum expected a posteriori (MAP) method of Bayesian estimation. This new method, essentially unbiased MAP, was compared with MAP, essentially unbiased expected a posteriori, weighted likelihood, and maximum-likelihood estimation methods. The new method significantly reduced bias in…

Using the constant information model, constant amounts of test information, and a finite interval of ability, simulated data were produced for 8 ability levels and 20 numbers of test items. Analyses suggest that it is desirable to consider modifying test information functions when they measure accuracy in ability estimation. (SLD)

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…

Computerized adaptive testing procedures (CATPs) based on the graded response method (GRM) of F. Samejima (1969) and the partial credit model (PCM) of G. Masters (1982) were developed and compared. Both programs used maximum likelihood estimation of ability, and item selection was conducted on the basis of information. Two simulated data sets, one…

Two new methods have been proposed to determine unexpected sum scores on sub-tests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted p, was compared with a method where the probability for each score combination was calculated using a…