Score-based measurement invariance checks for Bayesian maximum-a-posteriori estimates in item response theory

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2022-06-06 DOI:10.1111/bmsp.12275
Rudolf Debelak, Samuel Pawel, Carolin Strobl, Edgar C. Merkle
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Abstract

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

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项目反应理论中贝叶斯最大后验估计的基于分数的测量不变性检验
近年来,人们提出了一系列基于分数的测试来评估项目反应理论(IRT)中几个模型参数的不变性。这些测试最初是在最大似然框架中开发的。本研究讨论了贝叶斯最大后验估计和多组IRT模型的类似检验。我们提出了两类统计检验,它们基于使用混合方差方法的近似,或基于基于渐近结果的模拟方法。由此产生的测试通过模拟研究进行评估,该研究调查了它们对两参数和三参数逻辑模型中分类或连续人协变量的差异项目功能的敏感性。尽管基于混合方差的方法被发现在实践中对最大似然和最大后验估计是有用的,但基于模拟的方法被发现需要大样本量才能产生令人满意的结果。
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来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
期刊介绍: The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.
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