Latent Variable Modeling with Missing and Deleting Response Times: A Fragile Proportional Hazard Approach

In large-scale educational assessments, accurately analyzing response results, response times, omissions, and unreached items is crucial for evaluating student abilities and test validity. To address this analytical challenge, this study utilizes Item Response Theory (IRT) and a Speed-Accuracy (SA) hierarchical framework, incorporating the frailty proportional hazard model from survival analysis. This model not only relaxes the requirements for time distribution but also considers the heterogeneity of the test-taker population and can effectively use covariate data to enhance estimation precision. To efficiently fit large-scale data, we developed a stochastic EM algorithm and confirmed the asymptotic normality of the model parameters through theoretical analysis, ensuring accuracy in a large-sample environment. Further analysis with simulated data demonstrates that, compared to existing mainstream models, our model shows superior estimation performance in complex scenarios of data omission. These results significantly enhance our ability to interpret educational assessment data and provide an effective tool for educational policy formulation and academic research.