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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 select the items. Thanks to extremely rapid convergence of the Markov chain and simple posterior calculations, the algorithm is ready for use in real-world adaptive testing with running times fully comparable with algorithms that fix all parameters at point estimates during testing.

One of the methods of controlling test security in adaptive testing is imposing random item-ineligibility constraints on the selection of the items with probabilities automatically updated to maintain a predetermined upper bound on the exposure rates. Three major improvements of the method are presented. First, a few modifications to improve the initialization of the method and accelerate the impact of its feedback mechanism on the observed item-exposure rates are introduced. Second, the case of conditional item-exposure control given the uncertainty of examinee's ability parameter is addressed. Third, although rare for a well-designed item pool, when applied in combination with the shadow-test approach to adaptive testing the method may meet occasional infeasibility of the shadow-test model. A big "M" method is proposed that resolves the issue. The practical advantages of the improvements are illustrated using simulated adaptive testing from a real-world item pool under a variety of conditions.

Two simple constraints on the item parameters in a response--time model are proposed to control the speededness of an adaptive test. As the constraints are additive, they can easily be included in the constraint set for a shadow-test approach (STA) to adaptive testing. Alternatively, a simple heuristic is presented to control speededness in plain adaptive testing without any constraints. Both types of control are easy to implement and do not require any other real-time parameter estimation during the test than the regular update of the test taker's ability estimate. Evaluation of the two approaches using simulated adaptive testing showed that the STA was especially effective. It guaranteed testing times that differed less than 10 seconds from a reference test across a variety of conditions. (Contains 4 figures and 3 tables.)

This article reviews the use of the software program lp_solve version 5.5 for solving mixed-integer automated test assembly (ATA) problems. The program is freely available under Lesser General Public License 2 (LGPL2). It can be called from the statistical language R using the lpSolveAPI interface. Three empirical problems are presented to demonstrate how to use the program and interface to (a) simultaneously assemble multiple test forms with absolute targets for their test information functions, (b) assemble shadow tests for computerized adaptive testing, and (c) assemble multistage tests using relative targets for their test information functions, all subject to various quantitative and categorical constraints. The results of this study indicate that it is now possible for researchers and testing organizations to implement ATA for small to moderately sized test assembly problems using free software. (Contains 3 tables and 4 figures.)

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of A [subscript s] -optimality (or D [subscript s] -optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters.

An adaptive testing method is presented that controls the speededness of a test using predictions of the test takers' response times on the candidate items in the pool. Two different types of predictions are investigated: posterior predictions given the actual response times on the items already administered and posterior predictions that use the responses on these items as an additional source of information. In a simulation study with an adaptive test modeled after a test from the Armed Services Vocational Aptitude Battery, the effectiveness of the methods in removing differential speededness from the test was evaluated. (Contains 6 figures.)

In order to identify aberrant response-time patterns on educational and psychological tests, it is important to be able to separate the speed at which the test taker operates from the time the items require. A lognormal model for response times with this feature was used to derive a Bayesian procedure for detecting aberrant response times. Besides, a combination of the response-time model with a regular response model in an hierarchical framework was used in an alternative procedure for the detection of aberrant response times, in which collateral information on the test takers' speed is derived from their response vectors. The procedures are illustrated using a data set for the Graduate Management Admission Test[R] (GMAT[R]). In addition, a power study was conducted using simulated cheating behavior on an adaptive test.

In most operational computerized adaptive testing (CAT) programs, the Sympson-Hetter (SH) method is used to control the exposure of the items. Several modifications and improvements of the original method have been proposed. The Stocking and Lewis (1998) version of the method uses a multinomial experiment to select items. For severely constrained CAT, the list on which this experiment is conducted not only has to be of appropriate length but also needs to balance the composition of the test with respect to its specifications. In this article it is shown how the SH method of exposure control can be implemented in the shadow test approach. The method was applied to an adaptive test with 433 constraints on various attributes. Both a single and a multiple shadow-test approach were used to compare different list lengths for the SH method. (Contains 2 tables and 3 figures.)

Response times on items can be used to improve item selection in adaptive testing provided that a probabilistic model for their distribution is available. In this research, the author used a hierarchical modeling framework with separate first-level models for the responses and response times and a second-level model for the distribution of the ability and speed parameters in the population of test takers. The framework allows the author to retrofit an empirical prior distribution for the ability parameter on each occurrence of a new response time. In an example with an adaptive version of the Law School Admission Test (LSAT), the author shows how this additional update of the posterior distribution of the ability leads to a substantial improvement of the ability estimator. Two ways of applying the procedure in real-world adaptive testing are discussed. (Contains 6 figures.)

Two conditional versions of the exposure-control method with item-ineligibility constraints for adaptive testing in van der Linden and Veldkamp (2004) are presented. The first version is for unconstrained item selection, the second for item selection with content constraints imposed by the shadow-test approach. In both versions, the exposure rates of the items are controlled using probabilities of item ineligibility given [theta] that adapt the exposure rates automatically to a goal value for the items in the pool. In an extensive empirical study with an adaptive version of the Law School Admission Test, the authors show how the method can be used to drive conditional exposure rates below goal values as low as 0.025. Obviously, the price to be paid for minimal exposure rates is a decrease in the accuracy of the ability estimates. This trend is illustrated with empirical data. (Contains 6 figures and 1 table.)

A potential undesirable effect of multistage testing is differential speededness, which happens if some of the test takers run out of time because they receive subtests with items that are more time intensive than others. This article shows how a probabilistic response-time model can be used for estimating differences in time intensities and speed between subtests and test takers and detecting differential speededness. An empirical data set for a multistage test in the computerized CPA Exam was used to demonstrate the procedures. Although the more difficult subtests appeared to have items that were more time intensive than the easier subtests, an analysis of the residual response times did not reveal any significant differential speededness because the time limit appeared to be appropriate. In a separate analysis, within each of the subtests, we found minor but consistent patterns of residual times that are believed to be due to a warm-up effect, that is, use of more time on the initial items than they actually need.

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test for a population of test takers. The two local methods were generally best. Surprisingly, the TCF method performed slightly worse than the equipercentile method. Both methods showed strong bias and uniformly large inaccuracy, but the TCF method suffered from extra error due to the lower asymptote of the test characteristic function. It is argued that the worse performances of the two methods are a consequence of the fact that they use a single equating transformation for an entire population of test takers and therefore have to compromise between the individual score distributions. (Contains 4 figures.)

Test-item writing efforts typically results in item pools with an undesirable correlational structure between the content attributes of the items and their statistical information. If such pools are used in computerized adaptive testing (CAT), the algorithm may be forced to select items with less than optimal information, that violate the content constraints, and/or have unfavorable exposure rates. Although at first sight somewhat counterintuitive, it is shown that if the CAT pool is assembled as a set of linear test forms, undesirable correlations can be broken down effectively. It is proposed to assemble such pools using a mixed integer programming model with constraints that guarantee that each test meets all content specifications and an objective function that requires them to have maximal information at a well-chosen set of ability values. An empirical example with a previous master pool from the Law School Admission Test (LSAT) yielded a CAT with nearly uniform bias and mean-squared error functions for the ability estimator and item-exposure rates that satisfied the target for all items in the pool. (Contains 6 figures.)

Preventing items in adaptive testing from being over- or underexposed is one of the main problems in computerized adaptive testing. Though the problem of overexposed items can be solved using a probabilistic item-exposure control method, such methods are unable to deal with the problem of underexposed items. Using a system of rotating item pools, on the other hand, is a method that potentially solves both problems. In this method, a master pool is divided into (possibly overlapping) smaller item pools, which are required to have similar distributions of content and statistical attributes. These pools are rotated among the testing sites to realize desirable exposure rates for the items. A test assembly model, motivated by Gulliksen's matched random subtests method, was explored to help solve the problem of dividing a master pool into a set of smaller pools. Different methods to solve the model are proposed. An item pool from the Law School Admission Test was used to evaluate the performances of computerized adaptive tests from systems of rotating item pools constructed using these methods.

Item-exposure control in computerized adaptive testing is implemented by imposing item-ineligibility constraints on the assembly process of the shadow tests. The method resembles Sympson and Hetter's (1985) method of item-exposure control in that the decisions to impose the constraints are probabilistic. The method does not, however, require time-consuming simulation studies to set values for control parameters before the operational use of the test. Instead, it can set the probabilities of item ineligibility adaptively during the test using the actual item-exposure rates. An empirical study using an item pool from the Law School Admission Test showed that application of the method yielded perfect control of the item-exposure rates and had negligible impact on the bias and mean-squared error functions of the ability estimator.

The Hetter and Sympson (1997; 1985) method is a method of probabilistic item-exposure control in computerized adaptive testing. Setting its control parameters to admissible values requires an iterative process of computer simulations that has been found to be time consuming, particularly if the parameters have to be set conditional on a realistic set of values for the examinees' ability parameter. Formal properties of the method are identified that help us explain why this iterative process can be slow and does not guarantee admissibility. In addition, some alternatives to the SH method are introduced. The behavior of these alternatives was estimated for an adaptive test from an item pool from the Law School Admission Test (LSAT). Two of the alternatives showed attractive behavior and converged smoothly to admissibility for all items in a relatively small number of iteration steps. (Contains 3 figures.)

Combined the methods of alpha-stratified adaptive testing and constrained adaptive testing with shadow tests. Outlines the advantages of this approach in reducing overexposure and underexposure of items in an item pool and illustrates these advantages with an example from the Law School Admission Test. (SLD)

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)

Developed a method based on 0-1 linear programming to stratify an item pool optimally for use in alpha-stratified adaptive testing. Applied the method to a previous item pool from the computerized adaptive test of the Graduate Record Examinations. Results show the new method performs well in practical situations. (SLD)

Examined the case of adaptive testing under a multidimensional response model with large numbers of constraints on the content of the test and items selected using a shadow test approach. Illustrated the procedure with five different cases of multidimensionality that differ in the numbers of ability dimensions and test structure with respect of intentional ability dimensions. (SLD)

Presents a constrained computerized adaptive testing (CAT) algorithm that can be used to equate CAT number-correct scores to a reference test. Used an item bank from the Law School Admission Test to compare results of the algorithm with those for equipercentile observed-score equating. Discusses advantages of the approach. (SLD)

Performed a simulation study to demonstrate the dramatic impact of capitalization on estimation errors on ability estimation in adaptive testing. Discusses four different strategies to minimize the likelihood of capitalization in computerized adaptive testing. (SLD)

Proposes a procedure for empirical initialization of the trait (theta) estimator in adaptive testing that is based on the statistical relation between theta and background variables known prior to test administration. Illustrates the procedure for an adaptive version of a test from the Dutch General Aptitude Battery. (SLD)

Proposes an item-selection algorithm for neutralizing the differential effects of time limits on computerized adaptive test scores. Uses a statistical model for distributions of examinees' response times on items in a bank that is updated each time an item is administered. Demonstrates the method using an item bank from the Armed Services Vocational Aptitude Battery. (SLD)

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure." (SLD)

Proposes a model for constrained computerized adaptive testing in which the information in the test at the trait level (theta) estimate is maximized subject to the number of possible constraints on the content of the test. Test assembly relies on a linear-programming approach. Illustrates the approach through simulation with items from the Law School Admission Test. (SLD)

This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the ability estimators produced by these criteria are discussed and empirically criticized. (SLD)

New theory and practice in testing is replacing the standard test by the test item bank and classical test theory by item response theory. Eight papers and a commentary are presented in this special issue concerning test item banking. (SLD)