Multidimensional Test Assembly Using Mixed-Integer Linear Programming: An Application of Kullback–Leibler Information

Many educational testing programs require different test forms with minimal or no item overlap. At the same time, the test forms should be parallel in terms of their statistical and content-related properties. A well-established method to assemble parallel test forms is to apply combinatorial optimization using mixed-integer linear programming (MILP). Using this approach, in the unidimensional case, Fisher information (FI) is commonly used as the statistical target to obtain parallelism. In the multidimensional case, however, FI is a multidimensional matrix, which complicates its use as a statistical target. Previous research addressing this problem focused on item selection criteria for multidimensional computerized adaptive testing (MCAT). Yet these selection criteria are not directly transferable to the assembly of linear parallel test forms. To bridge this gap the authors derive different statistical targets, based on either FI or the Kullback–Leibler (KL) divergence, that can be applied in MILP models to assemble multidimensional parallel test forms. Using simulated item pools and an item pool based on empirical items, the proposed statistical targets are compared and evaluated. Promising results with respect to the KL-based statistical targets are presented and discussed.