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Tree-Based Global Model Tests for Polytomous Rasch Models

机译：基于树的多层Rasch模型的全球模型试验

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摘要

Psychometric measurement models are only valid if measurement invariance holds between test takers of different groups. Global model tests, such as the well-established likelihood ratio (LR) test, are sensitive to violations of measurement invariance, such as differential item functioning and differential step functioning. However, these traditional approaches are only applicable when comparing previously specified reference and focal groups, such as males and females. Here, we propose a new framework for global model tests for polytomous Rasch models based on a model-based recursive partitioning algorithm. With this approach, a priori specification of reference and focal groups is no longer necessary, because they are automatically detected in a data-driven way. The statistical background of the new framework is introduced along with an instructive example. A series of simulation studies illustrates and compares its statistical properties to the well-established LR test. While both the LR test and the new framework are sensitive to differential item functioning and differential step functioning and respect a given significance level regardless of true differences in the ability distributions, the new data-driven approach is more powerful when the group structure is not known a priorias will usually be the case in practical applications. The usage and interpretation of the new method are illustrated in an empirical application example. A software implementation is freely available in the R system for statistical computing.
机译：如果在不同组的测试接收器之间存在测量不变性，则心理测量模型仅适用于有效。全球模型测试，例如既有良好的似然比（LR）测试，对违反测量不变性的敏感性，例如差分项目功能和差分步长功能。然而，这些传统方法仅适用于比较先前指定的参考和焦点群体，例如男性和女性。在这里，我们为基于模型的递归分区算法提出了一种新的全局模型测试框架，用于多组织RASCH模型。通过这种方法，不再需要先验的参考和焦点组规范，因为它们被自动以数据驱动方式检测到。新框架的统计背景与一个有效的例子一起引入。一系列仿真研究说明并比较了其统治性质对良好的LR测试。虽然LR测试和新框架都对差分项目功能和差异阶段功能敏感并尊重给定的重要性水平，但无论能力分布的真实差异如何，当组结构未知时，新的数据驱动方法更强大实际应用中通常情况下，通常是这种情况。在经验应用示例中说明了新方法的使用和解释。用于统计计算的R系统可以自由地提供软件实现。

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