Frick Hannah, Strobl Carolin, Zeileis Achim
Universität Innsbruck, Innsbruck, Austria.
Universität Zürich, Zürich, Switzerland.
Educ Psychol Meas. 2015 Apr;75(2):208-234. doi: 10.1177/0013164414536183. Epub 2014 Jun 22.
Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest differential item functioning (DIF) tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch mixture models is sensitive to the specification of the ability distribution even when the conditional maximum likelihood approach is used. It is demonstrated in a simulation study how differences in ability can influence the latent classes of a Rasch mixture model. If the aim is only DIF detection, it is not of interest to uncover such ability differences as one is only interested in a latent group structure regarding the item difficulties. To avoid any confounding effect of ability differences (or impact), a new score distribution for the Rasch mixture model is introduced here. It ensures the estimation of the Rasch mixture model to be independent of the ability distribution and thus restricts the mixture to be sensitive to latent structure in the item difficulties only. Its usefulness is demonstrated in a simulation study, and its application is illustrated in a study of verbal aggression.
当检验单个Rasch模型的测量不变性假设时，Rasch混合模型可能是一个有用的工具。当DIF组与可用的显性协变量仅有弱相关性时，与显性差异项目功能（DIF）检验相比，它们具有优势。与单个Rasch模型不同，即使使用条件最大似然法，Rasch混合模型的估计对能力分布的设定也很敏感。在一项模拟研究中证明了能力差异如何影响Rasch混合模型的潜在类别。如果目标仅仅是DIF检测，那么揭示这种能力差异并不重要，因为人们只对关于项目难度的潜在组结构感兴趣。为了避免能力差异（或影响）的任何混杂效应，这里引入了一种新的Rasch混合模型分数分布。它确保Rasch混合模型的估计独立于能力分布，从而使混合仅对项目难度中的潜在结构敏感。在一项模拟研究中证明了它的有用性，并在一项言语攻击研究中说明了它的应用。
