Conditional Item-Exposure Control in Adaptive Testing Using Item-Ineligibility Probabilities Wim J. van der Linden Bernard P. Veldkamp University of Twente Two conditional versions of the exposure-control method with item-ineligibility constraints for adaptive testing in van der Linden and Veldkamp (2004) are pre- sented. 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 y 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. Keywords: adaptive testing; conditional item-exposure control; item eligibility method; uniform exposure rates Items in adaptive tests are selected as a solution to an optimization problem in which an objective function is maximized over the item pool. If the test has to meet a set of content specifications, the optimization becomes an instance of a more complicated constrained combinatorial optimization problem. A popular choice for the objective function in these problems is the value of the informa- tion function at the current ability estimate for the items in the pool. Suppose the items have been calibrated using the three-parameter logistic (3-PL) model p i ðyÞ ≡ PrfU ij ¼ 1g ≡ c i þð1  c i Þ exp½a i ðy  b i Þ 1 þ exp½a i ðy  b i Þ ; ð1Þ where y ∈ ð∞; ∞Þ is a parameter representing the ability of the test taker and b i ∈ ð∞; ∞Þ, a i > 0, and c i ∈ ½0; 1 are the difficulty, discriminating power, The authors are grateful to Wim M. M. Tielen for his computational assistance. 398 Journal of Educational and Behavioral Statistics December 2007, Vol. 32, No. 4, pp. 398–418 DOI: 10.3102/1076998606298044 Ó 2007 AERA and ASA. http://jebs.aera.net