项目反应理论中潜在心理特质“填补”的参数估计方法及其演变

The Data-augmentation Techniques in Item Response Modeling: Current Approaches and New Developments

在心理与教育测量中,项目反应理论(Item Response Theory,IRT)模型的参数估计方法是理论研究与实践应用的基本工具。最近,由于IRT模型的不断扩展与EM(expectation-maximization)算法自身的固有问题,参数估计方法的改进与发展显得尤为重要。这里介绍了IRT模型中边际极大似然估计的发展,提出了它的阶段性特征,即联合极大似然估计阶段、确定性潜在心理特质"填补"阶段、随机潜在心理特质"填补"阶段,重点阐述了它的潜在心理特质"填补"(data augmentation)思想。EM算法与Metropolis-Hastings Robbins-Monro(MH-RM)算法作为不同的潜在心理特质"填补"方法,都是边际极大似然估计的思想跨越。目前,潜在心理特质"填补"的参数估计方法仍在不断发展与完善。

Abstract： The parameter estimation techniques in item response theory modeling are indispensable to theoretical researches and real applications. This paper focused on its data augmentation techniques and described its historical development from the Bock and Aitkin＇s （1981） deterministic EM algorithm to the Cai＇s （2010） Metropolis-Hastings Robbins-Monro （MH-RM） algorithm （the integration of Markov Chain Monte Carlo and maximum marginal likelihood estimation, known as the stochastic data augmentation）. Currently, the statistical computing still needs to be developed in new applications. Key words： item response theory; latent trait; data augmentation; maximum marginal likelihood estimation; EM algorithm; MH-RM algorithm