项目反应理论模型边际似然计算的蒙特卡罗方法比较
A Comparison of Monte Carlo Methods for Computing Marginal Likelihoods of Item Response Theory Models.
作者信息
Liu Yang, Hu Guanyu, Cao Lei, Wang Xiaojing, Chen Ming-Hui
机构信息
Department of Statistics, University of Connecticut, Storrs, Connecticut, U.S.A.
School of Basic Science, Changchun University of Technology, Changchun, China.
出版信息
J Korean Stat Soc. 2019 Dec;48(4):503-512. doi: 10.1016/j.jkss.2019.04.001. Epub 2019 May 17.
Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development of how these methods are applied to the IRT models. In particular, we focus on the "best possible" implementation of these MC methods for the IRT models. These MC methods are used to compute the marginal likelihoods under the one-parameter IRT model with the logistic link (1PL model) and the two-parameter logistic IRT model (2PL model) for a real English Examination dataset. We further use the widely applicable information criterion (WAIC) and deviance information criterion (DIC) to compare the 1PL model and the 2PL model. The 2PL model is favored by all of these three Bayesian model comparison criteria for the English Examination data.
如今，贝叶斯方法经常用于估计项目反应理论（IRT）模型的参数。然而，由于边际似然的复杂性和模型参数的相对高维度，它们仍然很少用于比较IRT模型。在本文中，我们回顾了近年来文献中开发的蒙特卡罗（MC）方法，并详细阐述了这些方法如何应用于IRT模型。特别是，我们专注于这些MC方法在IRT模型中的“最佳可能”实现。这些MC方法用于计算具有逻辑链接的单参数IRT模型（1PL模型）和双参数逻辑IRT模型（2PL模型）下针对真实英语考试数据集的边际似然。我们进一步使用广泛适用的信息准则（WAIC）和偏差信息准则（DIC）来比较1PL模型和2PL模型。对于英语考试数据，2PL模型受到所有这三个贝叶斯模型比较准则的青睐。
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