关键词: 项目反应理论, 异常作答, 稳健项目参数估计

Abstract: Item Response Theory (IRT) models are widely used in psychological and educational measurement. Their effectiveness, however, can be undermined by data quality issues, particularly aberrant responding, such as cheating, careless errors, rapid guessing, and hybrid forms involving multiple aberrant response behaviors. Such responses are especially prevalent in online assessments, where the absence of supervision, external distractions, and low participant motivation can introduce substantial measurement noise. Empirical evidence indicates that even 10~15% proportion of aberrant responses can meaningfully distort parameter estimates, while higher proportions (20~30% or more) can lead to severe bias in item and ability parameter estimates, reduce reliability, distort factor structures, and compromise measurement invariance test.
Person-fit statistics (PFS) are widely used to identify aberrant respondents. However, their dependence on full-sample parameter estimates makes them susceptible to the masking effect, in which aberrant responses bias item parameter estimation and, in turn, obscure person misfit, particularly when the proportion of aberrant responses is high. To overcome this limitation, a robust marginal maximum likelihood method has been proposed that incorporates PFS-derived weights into the likelihood function, thereby down-weighting aberrant respondents during parameter estimation. Using the $ l^*_z$ statistic, this method can effectively reduce bias while retaining all response data.
Building on this framework, the present study introduces a new robust weighting method, namely Residual-Based Robust Weighting (RRW), which replaces $ l^*_z$ with a residual-based person-fit statistic (PFS). Residual-based statistics quantify item-level deviations between observed and expected responses, standardized by their variances and aggregated across items. This finer-grained approach improves sensitivity to subtle and heterogeneous aberrant patterns compared to the aggregated likelihood ratio underlying $ l^*_z$. As a result, RRW assigns lower weights to respondents whose residual patterns deviate substantially from model expectations, while preserving the full contribution of respondents whose responses are consistent with the model.
We evaluated the proposed RRW method through simulation studies and an empirical example, comparing its performance with unweighted estimation and the $ l^*_z$-based RMML approach. Results showed that aberrant responding substantially distorts item parameter estimation, with the unweighted method exhibiting the largest increases in RMSE and bias as aberrance levels rise. The $ l^*_z$-based method improved discrimination estimates to some extent but showed limited effectiveness for threshold parameters. In contrast, RRW consistently achieved lower estimation errors for both discrimination and threshold parameters across most conditions, with its advantages becoming more pronounced under higher aberrance levels. Moreover, RRW maintained stable performance as test length increased, demonstrating strong robustness and applicability in complex testing scenarios.
Empirical results further validated RRW's superiority: it reduced item parameter estimation error to a certain extent and enhanced ability estimates for non-aberrant respondents, demonstrating its effectiveness in mitigating the adverse impact of aberrant responses in real testing contexts. By improving item parameter accuracy, RRW indirectly increases the precision of ability estimation, providing a practical and robust alternative for IRT applications in complex testing environments. Overall, evidence from both simulation and empirical analyses indicates that the RRW weighted estimation method effectively reduces the negative effects of complex aberrant response patterns on item parameter estimation and shows strong potential for practical implementation.

Key words: item response theory, aberrant responding, robust item parameter estimation