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.

中文翻译：

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计算项目响应理论模型的边际可能性的蒙特卡洛方法的比较。

如今，贝叶斯方法通常用于估计项目响应理论（IRT）模型的参数。但是，由于IRT模型的复杂性和模型参数的相对较高维度，因此边缘可能性仍然很少用于比较IRT模型。在本文中，我们回顾了近年来文献中开发的蒙特卡洛（MC）方法，并提供了有关如何将这些方法应用于IRT模型的详细信息。特别是，我们将重点放在针对IRT模型的这些MC方法的“最佳可能”实施上。这些MC方法用于计算真实英语考试数据集的带逻辑链接（1PL模型）和两参数逻辑IRT模型（2PL模型）的一参数IRT模型下的边际可能性。我们进一步使用广泛适用的信息标准（WAIC）和偏差信息标准（DIC）来比较1PL模型和2PL模型。对于英语考试数据，所有这三个贝叶斯模型比较标准都赞成使用2PL模型。