Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach

Abstract

In educational measurement, building multiple alternate test forms is usually highly desirable in practice. Test assembly problems are classified as NP-hard (Non-deterministic Polynomial-time hard) problems, and their computation time increases exponentially as the problem size grows. The purpose of this study was to construct parallel forms item-by-item based on a seed test, using two proposed item selection heuristic methods (random item sequence assigned to maximum distance form with content balance [R-MD-B] and random item sequence assigned to random form with content balancing [R-R-B]) incorporating a flexible content balancing method. The results were compared with two modified versions of the Armstrong, Jones, and Wu heuristics (random item sequence assigned to maximum distance form with Armstrong\'s replacement [R-MD-R] and random item sequence assigned to random form with Armstrong\'s replacement [R-R-R]) and two models incorporating mixed integer programming (MIP) methods. The results showed that the R-MD-B and R-R-B methods yielded results comparable with the two MIP methods with less computation time in terms of the item information functions, test characteristic curves, and content coverage. The results also showed that R-MD-B and R-R-B can be extended to handle test assembly constraints in practical settings.