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首页> 外文期刊>Journal of applied statistics >A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework
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A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework

机译：贝叶斯框架下以偏态-正态潜在特征分布为中心的多组项目反应理论模型

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Very often, in psychometric research, as in educational assessment, it is necessary to analyze item response from clustered respondents. The multiple group item response theory (IRT) model proposed by Bock and Zimowski [12] provides a useful framework for analyzing such type of data. In this model, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The usual assumption for parameter estimation in this model, which is that the latent traits are random variables following different symmetric normal distributions, has been questioned in many works found in the IRT literature. Furthermore, when this assumption does not hold, misleading inference can result. In this paper, we consider that the latent traits for each group follow different skew-normal distributions, under the centered parameterization. We named it skew multiple group IRT model. This modeling extends the works of Azevedo et al. [4], Bazan el at. [11] and Bock and Zimowski [12] (concerning the latent trait distribution). Our approach ensures that the model is identifiable. We propose and compare, concerning convergence issues, two Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation. A simulation study was performed in order to evaluate parameter recovery for the proposed model and the selected algorithm concerning convergence issues. Results reveal that the proposed algorithm recovers properly all model parameters. Furthermore, we analyzed a real data set which presents asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of negative asymmetry for some latent trait distributions.
机译：在心理测量学研究中，就像在教育评估中一样，经常需要分析聚类受访者的项目反应。 Bock和Zimowski [12]提出的多组项目响应理论（IRT）模型为分析此类数据提供了有用的框架。在此模型中，选定的受访者组具有特定的兴趣，因此需要定义特定组的人口分布。在IRT文献中发现的许多著作中都质疑了该模型中参数估计的通常假设，即潜在特征是遵循不同对称正态分布的随机变量。此外，当该假设不成立时，可能导致误导性推断。在本文中，我们认为在中心参数化条件下，每组的潜在性状遵循不同的偏态正态分布。我们将其命名为“倾斜多组IRT模型”。这种建模扩展了Azevedo等人的工作。 [4]，巴赞尔。 [11]和博克和齐莫夫斯基[12]（关于潜在特征分布）。我们的方法可确保模型可识别。对于收敛问题，我们提出并比较了两种用于参数估计的蒙特卡洛马尔可夫链（MCMC）算法。为了评估所提出模型和所选算法的参数收敛性，进行了仿真研究。结果表明，该算法可以正确恢复所有模型参数。此外，我们分析了一个真实的数据集，该数据集表现出有关潜在特征分布的不对称性。通过使用我们的方法获得的结果证实了某些潜在性状分布存在负不对称性。

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