A generalized many-facet Rasch model and its Bayesian estimation using Hamiltonian Monte Carlo
A generalized many-facet Rasch model and its Bayesian estimation using Hamiltonian Monte Carlo
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DOI：
10.1007/s41237-020-00115-7
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发表时间：
2020-05
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影响因子：
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通讯作者：
Masaki Uto;M. Ueno
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文献类型：
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作者：
Masaki Uto;M. Ueno
成绩评估，其中评分员评估考生的表现为给定的任务，有一个持久的困难，能力测量的准确性取决于评分员的特点。为了解决这个问题，已经提出了各种项目反应理论（IRT）模型，将评分员特征参数。传统的模型部分考虑了三个典型的评分者特征：严重性，一致性和范围限制。每一个都是重要的，以提高模型拟合和能力测量的准确性，特别是当评分员的多样性增加。然而，没有模型能够同时代表每一个已经提出。开发这样一个复杂的模型的一个障碍是参数估计的困难。在复杂模型中，最大似然估计通常会导致参数估计不稳定和不准确。贝叶斯估计有望提供更稳健的估计。虽然它会产生很高的计算成本，最近增加的计算能力和有效的马尔可夫链蒙特卡罗（MCMC）算法的发展，使其使用可行的。因此，我们提出了一个新的IRT模型，可以代表所有三个典型的评分员特征。该模型被制定为一个推广的多方面的Rasch模型。我们还开发了一个贝叶斯估计方法，该模型使用No-U-Turn哈密顿蒙特卡罗，一个国家的最先进的MCMC算法。我们通过仿真和实际数据实验证明了所提出的方法的有效性。
Performance assessments, in which raters assess examinee performance for given tasks, have a persistent difficulty in that ability measurement accuracy depends on rater characteristics. To address this problem, various item response theory (IRT) models that incorporate rater characteristic parameters have been proposed. Conventional models partially consider three typical rater characteristics: severity, consistency, and range restriction. Each are important to improve model fitting and ability measurement accuracy, especially when the diversity of raters increases. However, no models capable of simultaneously representing each have been proposed. One obstacle for developing such a complex model is the difficulty of parameter estimation. Maximum likelihood estimation, which is used in most conventional models, generally leads to unstable and inaccurate parameter estimations in complex models. Bayesian estimation is expected to provide more robust estimations. Although it incurs high computational costs, recent increases in computational capabilities and the development of efficient Markov chain Monte Carlo (MCMC) algorithms make its use feasible. We thus propose a new IRT model that can represent all three typical rater characteristics. The model is formulated as a generalization of the many-facet Rasch model. We also develop a Bayesian estimation method for the proposed model using No-U-Turn Hamiltonian Monte Carlo, a state-of-the-art MCMC algorithm. We demonstrate the effectiveness of the proposed method through simulation and actual data experiments.