One of the primary goals of international large-scale assessments in education is the comparison of country means in student achievement. This article introduces a framework for discussing differential item functioning (DIF) for such mean comparisons. We compare three different linking methods: concurrent scaling based on full invariance, concurrent scaling based on partial invariance using the RMSD statistic, and robust and nonrobust linking approaches based on separate scaling. Furthermore, we analytically derive the bias in the country means of different linking methods in the presence of DIF. In a simulation study, we show that the partial invariance and robust linking approaches provide less biased country means than the full invariance approach in the case of biased items.

国际大规模教育评估的主要目标之一是比较各国在学生成绩方面的平均水平。本文介绍了一个框架，用于讨论用于此类均值比较的差分项目功能 (DIF)。我们比较了三种不同的链接方法：基于完全不变性的并发扩展，使用 RMSD 统计基于部分不变性的并发扩展，以及基于单独扩展的鲁棒和非鲁棒链接方法。此外，我们分析得出在存在 DIF 的情况下不同链接方法的国家手段的偏差。在模拟研究中，我们表明，在有偏差的项目的情况下，部分不变性和稳健链接方法比完全不变性方法提供的国家均值偏差更小。