Assembling a Computerized Adaptive Testing Item Pool as a Set of Linear Tests

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.