贝叶斯分层项目反应理论模型奇异行为的益处--深入调查与偏差校正

IF 1 4区 心理学 Q4 PSYCHOLOGY, MATHEMATICAL
Christoph König, Rainer W. Alexandrowicz
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引用次数: 0

摘要

贝叶斯层次模型是项目反应理论(IRT)模型的一种流行方法,研究人员在使用贝叶斯层次模型时,通常需要在项目参数估计的精确度和准确度之间做出权衡。考虑到集合原理和方差收缩,贝叶斯分层 IRT 模型的预期行为是,与非分层模型相比,提供更精确但有偏差的项目参数估计。然而,以往的研究指出,在双参数逻辑 IRT 模型中,可能不需要做出上述权衡。通过全面的模拟研究,我们对这种可能性进行了深入调查。结果表明,与非分层模型相比,分层模型在偏差、均方根误差和精度方面都有更出色的表现。在某些条件下,项目参数估计的偏差与方差成分的偏差无关。此外,我们还为项目区分度参数估计提供了一个偏差修正程序。总之,我们证明了 IRT 模型创造了一种独特的情况,即贝叶斯分层方法与非分层方法相比,不仅能获得更精确的参数估计,而且能获得更准确的参数估计。我们将从理论和应用两个角度讨论这种有益的行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Benefits of the Curious Behavior of Bayesian Hierarchical Item Response Theory Models—An in-Depth Investigation and Bias Correction
When using Bayesian hierarchical modeling, a popular approach for Item Response Theory (IRT) models, researchers typically face a tradeoff between the precision and accuracy of the item parameter estimates. Given the pooling principle and variance-dependent shrinkage, the expected behavior of Bayesian hierarchical IRT models is to deliver more precise but biased item parameter estimates, compared to those obtained in nonhierarchical models. Previous research, however, points out the possibility that, in the context of the two-parameter logistic IRT model, the aforementioned tradeoff has not to be made. With a comprehensive simulation study, we provide an in-depth investigation into this possibility. The results show a superior performance, in terms of bias, RMSE and precision, of the hierarchical specifications compared to the nonhierarchical counterpart. Under certain conditions, the bias in the item parameter estimates is independent of the bias in the variance components. Moreover, we provide a bias correction procedure for item discrimination parameter estimates. In sum, we show that IRT models create a unique situation where the Bayesian hierarchical approach indeed yields parameter estimates that are not only more precise, but also more accurate, compared to nonhierarchical approaches. We discuss this beneficial behavior from both theoretical and applied point of views.
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来源期刊
CiteScore
2.30
自引率
8.30%
发文量
50
期刊介绍: Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.
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