存在缺失响应和删失响应时间的潜变量建模: 一种脆弱比例风险方法
Latent Variable Modeling with Missing Responses and Censored Response Times: A Frailty Proportional Hazards Approach
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摘要: 在大规模教育测评中, 准确分析响应结果、响应时间、遗漏项和未到达项是评估考生能力和测试效度的关键.面对这一分析挑战, 本研究利用项目反应理论(Item Response Theory, IRT)与速度-准确性(Speed-Accuracy, SA)层次化框架, 并引入生存分析中的脆弱比例风险模型(Frailty Proportional Hazard Model).该模型不仅放宽了对时间分布的要求, 而且充分考虑了受访者群体的异质性, 并可有效利用协变量数据提升估计精度.为实现大规模数据的高效拟合, 我们开发了一种随机EM算法, 并通过理论分析确认了模型参数的渐近正态性, 确保其在大样本环境下的准确性.模拟数据的进一步分析显示, 相较于现有主流模型, 本模型在处理数据删失的复杂场景下展现出更优的估计效果.这些成果显著提升了对教育评估数据的解析能力, 同时为教育政策的制定和学术研究提供了一种有效的工具.Abstract: 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.
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