Latent Variable Modeling with Missing Responses and Censored Response Times: A Frailty Proportional Hazards Approach

In large-scale educational assessments, the accurate analysis of item responses, response times, omitted items, and not-reached items is crucial for evaluating examinees’ latent abilities and ensuring test validity. To address these analytical challenges, this study proposes a joint modeling approach that integrates Item Response Theory (IRT) within a hierarchical Speed-Accuracy (SA) framework, and incorporates a frailty proportional hazards model from survival analysis. This model not only relaxes the stringent distributional assumptions conventionally imposed on response times but also explicitly accounts for unobserved heterogeneity within the examinee population, while effectively leveraging covariate information to enhance estimation precision. To facilitate efficient model fitting for large-scale data, we develop a Stochastic Expectation-Maximization (StEM) algorithm and rigorously establish the asymptotic normality of the parameter estimators through theoretical analysis, thereby guaranteeing valid statistical inference in large-sample settings. Extensive simulation studies demonstrate that the proposed model yields superior estimation performance in complex scenarios involving data censoring compared to prevailing mainstream models. These advancements significantly enhance the analytical capacity for educational assessment data, providing a robust methodological tool for both academic research and educational policymaking.