ABSTRACT
In general, item preknowledge is hard to detect due to multiple unknowns involved: unknown subgroups of examinees accessing unknown compromised subsets of items prior to taking the test. This chapter aims to identify all three unknowns by methods of information theory and combinatorial optimization. It describes an algorithm to detect all three unknowns, leading to better detection of aberrant examinees and better identification of the specific items to which each had prior access. The advantages and limitations of the algorithm are demonstrated on simulated and real data. This algorithm extends the 3D Algorithm by Dmitry Belov. Two approaches to detect item preknowledge were compared. The first approach was to compute the LZ statistic, which was used as a baseline in all studies. The second approach was the Divergence Algorithm. The chapter also describes a combinatorial search for the compromised subset given a fixed suspicious subgroup. The convergence of simulated annealing can be analyzed by its reduction to a Markov chain.
