Measurement invariance research has focused on identifying biases in test indicators measuring a latent trait across two or more groups. However, relatively little attention has been devoted to the practical implications of noninvariance. An important question is whether noninvariance in indicators or items results in differences in observed composite scores across groups. The current study introduces the Bayesian region of measurement equivalence (ROME) as a framework for visualizing and testing the combined impact of partial invariance on the group difference in observed scores. Under the proposed framework, researchers first compute the highest posterior density intervals (HPDIs)—which contain the most plausible values—for the expected group difference in observed test scores over a range of latent trait levels. By comparing the HPDIs with a predetermined range of values that is practically equivalent to zero (i.e., region of measurement equivalence), researchers can determine whether a test instrument is practically invariant. The proposed ROME method can be used for both continuous indicators and ordinal items. We illustrated ROME using five items measuring mathematics-specific self-efficacy from a nationally representative sample of 10th graders. Whereas conventional invariance testing identifies a partial strict invariance model across gender, the statistically significant noninvariant items were found to have a negligible impact on the comparison of the observed scores. This empirical example demonstrates the utility of the ROME method for assessing practical significance when statistically significant item noninvariance is found.

中文翻译：

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用于建立测量不变性的贝叶斯测量等效区域 (ROME) 方法。

测量不变性研究的重点是确定测量两个或多个群体的潜在特征的测试指标的偏差。然而，人们对非不变性的实际影响的关注相对较少。一个重要的问题是指标或项目的非不变性是否会导致观察到的各组综合得分的差异。当前的研究引入了贝叶斯测量等效区域（ROME）作为可视化和测试部分不变性对观察到的分数的组差异的综合影响的框架。在提出的框架下，研究人员首先计算最高后验密度区间（HPDI）——其中包含最合理的值——以预测一系列潜在特质水平上观察到的测试分数的预期群体差异。通过将 HPDI 与实际上等于零的预定值范围（即测量等效区域）进行比较，研究人员可以确定测试仪器是否实际上是不变的。所提出的 ROME 方法可用于连续指标和序数项。我们使用五个项目来说明罗马，这些项目来自全国代表性的十年级学生样本，用于衡量数学特定的自我效能感。尽管传统的不变性测试确定了跨性别的部分严格不变性模型，但发现统计显着的非不变项对观察到的分数的比较的影响可以忽略不计。这个经验例子证明了当发现统计显着的项目非不变性时，ROME 方法在评估实际意义方面的实用性。