A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors
A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors
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DOI：
10.1007/s11336-008-9108-6
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发表时间：
2009-09-01
期刊：
影响因子：
3
通讯作者：
Hoshino, Takahiro
中科院分区：
文献类型：
--
作者：
Miyazaki, Kei;Hoshino, Takahiro
在项目反应理论(IRT)中，项目特征曲线(ICCs)是通过Logistic模型或正态卵形模型来描述的，考生给出正确答案的概率通常是其能力参数的单调递增函数。然而，由于从Logistic模型或普通卵形模型只能获得有限的形状模式，所以应用的模型有可能不符合数据。针对这些问题，提出了一种新的基于Dirichlet过程混合Logistic分布的半参数IRT模型。我们的方法不依赖于假设，只要求ICCs是单调非减函数，也就是说，我们的方法可以处理比现有方法更多类型的项目反应模式，如单参数正态卵形模型和两参数或三参数Logistic模型。我们进行了两个仿真研究，结果表明，该方法可以表达更多的ICCs形状模式，并且比现有的参数和非参数方法更准确地估计能力参数。该方法也被应用于人脸表情识别数据中，取得了显著的效果。
In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models or normal ogive models, there is a possibility that the model applied does not fit the data. As a result, the existing method can be rejected because it cannot deal with various item response patterns.To overcome these problems, we propose a new semiparametric IRT model using a Dirichlet process mixture logistic distribution. Our method does not rely on assumptions but only requires that the ICCs be a monotonically nondecreasing function; that is, our method can deal with more types of item response patterns than the existing methods, such as the one-parameter normal ogive models or the two- or three-parameter logistic models.We conducted two simulation studies whose results indicate that the proposed method can express more patterns of shapes for ICCs and can estimate the ability parameters more accurately than the existing parametric and nonparametric methods. The proposed method has also been applied to Facial Expression Recognition data with noteworthy results.