We introduce a new method for estimating the degree of nonadditivity in a one-facet generalizability theory design. One-facet G-theory designs have only one observation per cell, such as persons answering items in a test, and assume that there is no interaction between facets. When there is interaction, the model becomes nonadditive, and G-theory variance estimates and reliability coefficients are likely biased. We introduce a multidimensional method for detecting interaction and nonadditivity in G-theory that has less bias and smaller error variance than methods that use the one-degree of freedom method based on Tukey’s test for nonadditivity. The method we propose is more flexible and detects a greater variety of interactions than the formulation based on Tukey’s test. Further, the proposed method is descriptive and illustrates the nature of the facet interaction using profile analysis, giving insight into potential interaction like rater biases, DIF, threats to test security, and other possible sources of systematic construct-irrelevant variance. We demonstrate the accuracy of our method using a simulation study and illustrate its descriptive profile features with a real data analysis of neurocognitive test scores.

中文翻译：

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单面 g 理论设计中的多维非可加性：一种轮廓分析方法。

我们引入了一种新方法来估计单方面概括性理论设计中的非可加性程度。单方面 G 理论设计每个单元只有一个观察结果，例如人们在测试中回答项目，并假设各个方面之间没有相互作用。当存在交互作用时，模型变得非可加性，并且 G 理论方差估计和可靠性系数可能有偏差。我们引入了一种用于检测 G 理论中的相互作用和非加和性的多维方法，与使用基于 Tukey 的非加和性检验的单自由度方法的方法相比，该方法具有较小的偏差和较小的误差方差。我们提出的方法比基于 Tukey 测试的公式更灵活，并且可以检测更多种类的相互作用。更远，所提出的方法是描述性的，并使用配置文件分析说明了方面交互的本质，从而深入了解潜在的交互，例如评估者偏差、DIF、测试安全性威胁以及系统构造无关方差的其他可能来源。我们通过模拟研究证明了我们方法的准确性，并通过神经认知测试分数的真实数据分析来说明其描述性特征。