AI 中文总结
该研究针对自适应路由下试点样本量小的问题，提出模块化局部校准（MLC）的贝叶斯框架，推导闭式去衰减映射，经模拟验证其可降低衰减偏差并保证区间覆盖率。
AI 中文摘要
当试点样本量较小且采用自适应路由时，嵌入在运行评估中的试点项目的连续校准颇具挑战性。我们提出一种用于局部项目校准的贝叶斯模块化框架，该框架阻断试点响应对运行潜在量表的反馈：从运行后验分布中抽取合理值，每个试点项目通过其自身的局部逻辑回归进行校准。该结构具有计算可扩展性，可保护运行特质估计值免受故障试点项目的影响，并允许对稀疏路由样本使用Firth惩罚似然。由于将估算特质视为固定预测变量会导致衰减偏差，我们推导了闭式去衰减映射，以在正态ogive、后验正态、同方差及联合正态近似下恢复生成的项目参数。所得的模块化局部校准（MLC）估计量无需逐项目数值积分即可达到边际似然校准目标。结合Rubin规则池化的多元delta方法协方差，将运行项目参数不确定性传播至焦点项目标准误。针对单维2PL的蒙特卡洛模拟显示，在研究条件下，包括受限范围MAR路由场景中，经校正的MLC大幅降低了衰减偏差，并产生了名义到保守的区间覆盖率。
英文摘要
The continuous calibration of pilot items embedded in operational assessments is challenging when pilot samples are small and adaptively routed. We formalize a Bayesian modularization framework for local item calibration that blocks feedback from pilot responses to the operational latent scale: Plausible Values are drawn from the operational posterior, and each pilot item is calibrated by its own local logistic regression. This construction is computationally scalable, protects operational trait estimates from malfunctioning pilot items, and admits Firth's penalized likelihood for sparse routed samples. Because treating imputed traits as fixed predictors induces attenuation, we derive closed-form disattenuation mappings that recover the generating item parameters under normal-ogive, posterior-normality, homoscedasticity, and joint-normality approximations. The resulting Modular Local Calibration (MLC) estimator reaches the target of marginal-likelihood calibration without per-item numerical integration. A multivariate delta-method covariance combined with Rubin's-rules pooling propagates operational item-parameter uncertainty into the focal item standard errors. Monte Carlo simulations for the unidimensional 2PL show that corrected MLC substantially reduces attenuation bias and yields nominal-to-conservative interval coverage in the studied conditions, including under restricted-range MAR routing.
