The case of adaptive testing under a multidimensional response model with large numbers of constraints on the content of the test is addressed. The items in the test are selected using a shadow test approach. The 0–1 linear programming model that assembles the shadow tests maximizes posterior expected Kullback-Leibler information in the test. The procedure is illustrated for five different cases of multidimensionality. These cases differ in (a) the numbers of ability dimensions that are intentional or should be considered as “nuisance dimensions” and (b) whether the test should or should not display a simple structure with respect to the intentional ability dimensions.

Maximum likelihood and Bayesian procedures for item selection and scoring of multidimensional adaptive tests are presented. A demonstration using simulated response data illustrates that multidimensional adaptive testing (MAT) can provide equal or higher reliabilities with about one-third fewer items than are required by one-dimensional adaptive testing (OAT). Furthermore, holding test-length constant across the MAT and OAT approaches, substantial improvements in reliability can be obtained from multidimensional assessment. A number of issues relating to the operational use of multidimensional adaptive testing are discussed.

Two new methods for improving the measurement precision of a general test factor are proposed and evaluated. One new method provides a multidimensional item response theory estimate obtained from conventional administrations of multiple-choice test items that span general and nuisance dimensions. The other method chooses items adaptively to maximize the precision of the general ability score. Both methods display substantial increases in precision over alternative item selection and scoring procedures. Results suggest that the use of these new testing methods may significantly enhance the prediction of learning and performance in instances where standardized tests are currently used.