🤖 AI Summary
This study addresses the challenge of scale interference in operational latent variables during embedded pilot item calibration under few-shot adaptive routing. To mitigate this issue, the authors propose a Bayesian modular framework that severs feedback from pilot responses to operational latent variables, instead calibrating each pilot item independently via local logistic regression using fixed predictors derived from the posterior of operational traits. The approach innovatively incorporates an analytical debiasing mapping, enabling unbiased recovery of item parameters under a normal-ogive approximation. By integrating Firth’s penalized likelihood, multivariate delta-method covariance estimation, and Rubin’s pooling rules, the method achieves marginal likelihood calibration without per-item numerical integration while propagating parameter uncertainty into standard errors. Simulation results demonstrate substantially reduced attenuation bias and yield confidence interval coverage ranging from nominal to conservative under constrained conditions such as missing-at-random routing.
📝 Abstract
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.