Identifying Item Preknowledge Through Convergence Iteration Count Analysis in Ability Estimation

Item preknowledge (IP) is a severe form of cheating that fundamentally undermines the fairness and score interpretability of educational assessments. Existing detection methods for IP are predominantly constructed under the item response theory (IRT) framework, but these conventional indicators are inherently static: they rely solely on the final converged estimates of item parameters and examinee ability, while completely overlooking the rich dynamic information embedded in the iterative convergence process of ability estimation. To address this core limitation, this paper proposes a novel dynamic detection indicator—the convergence iteration count (CIC)—defined as the number of iterations required for the IRT model to converge to a stable ability estimate for each examinee. We validate the effectiveness of the CIC indicator through Monte Carlo simulated experiments across diverse scenarios, with varying proportions of compromised items and levels of misclassification uncertainty of compromised items, covering both known and unknown compromised item range conditions. Results show that the CIC indicator significantly outperforms traditional static indicators (including the TW, KL, and SR indicators) in identifying IP examinees. Notably, even in the extreme complex scenario with a 60% high proportion of compromised items and 50% high misclassification uncertainty, the area under the curve of the CIC indicator remains approaching or exceeding 0.8. The CIC indicator also exhibits strong robustness in scenarios where the range of compromised items is unknown, with detection performance surpassing most conventional non-prior-information based indicators.