Maximum Clique Algorithm and Its Approximation for Uniform Test Form Assembly

Abstract

Educational assessments occasionally require uniform test forms for which each test form comprises a different set of items, but the forms meet equivalent test specifications (i.e., qualities indicated by test information functions based on item response theory). We propose two maximum clique algorithms (MCA) for uniform test form assembly. The proposed methods can assemble uniform test forms with allowance of overlapping items among uniform test forms. First, we propose an exact method that maximizes the number of uniform test forms from an item pool. However, the exact method presents computational cost problems. To relax those problems, we propose an approximate method that maximizes the number of uniform test forms asymptotically. Accordingly, the proposed methods can use the item pool more efficiently than traditional methods can. We demonstrate the efficiency of the proposed methods using simulated and actual data.