Department of Human Development and Quantitative Methodology, University of Maryland, 1230B Benjamin Building, College Park, MD, 20742 , USA.
Psychometrika. 2018 Jun;83(2):333-354. doi: 10.1007/s11336-017-9582-9. Epub 2017 Sep 6.
In most item response theory applications, model parameters need to be first calibrated from sample data. Latent variable (LV) scores calculated using estimated parameters are thus subject to sampling error inherited from the calibration stage. In this article, we propose a resampling-based method, namely bootstrap calibration (BC), to reduce the impact of the carryover sampling error on the interval estimates of LV scores. BC modifies the quantile of the plug-in posterior, i.e., the posterior distribution of the LV evaluated at the estimated model parameters, to better match the corresponding quantile of the true posterior, i.e., the posterior distribution evaluated at the true model parameters, over repeated sampling of calibration data. Furthermore, to achieve better coverage of the fixed true LV score, we explore the use of BC in conjunction with Jeffreys' prior. We investigate the finite-sample performance of BC via Monte Carlo simulations and apply it to two empirical data examples.
在大多数项目反应理论应用中，需要首先从样本数据中校准模型参数。使用估计参数计算得到的潜在变量 (LV) 分数因此受到来自校准阶段的继承抽样误差的影响。在本文中，我们提出了一种基于重抽样的方法，即自举校准 (BC)，以降低 LV 分数的区间估计中携带的抽样误差的影响。BC 修正了插件后验的分位数，即在估计的模型参数处评估的 LV 的后验分布，以更好地匹配真实后验的相应分位数，即在真实模型参数处评估的后验分布，通过对校准数据的重复抽样。此外，为了更好地覆盖固定的真实 LV 分数，我们探索了将 BC 与杰弗里斯先验结合使用。我们通过蒙特卡罗模拟研究了 BC 的有限样本性能，并将其应用于两个实证数据示例。
