Assessing measurement invariance is an important step in establishing a meaningful comparison of measurements of a latent construct across individuals or groups. Most recently, moderated nonlinear factor analysis (MNLFA) has been proposed as a method to assess measurement invariance. In MNLFA models, measurement invariance is examined in a single-group confirmatory factor analysis model by means of parameter moderation. The advantages of MNLFA over other methods is that it (a) accommodates the assessment of measurement invariance across multiple continuous and categorical background variables and (b) accounts for heteroskedasticity by allowing the factor and residual variances to differ as a function of the background variables. In this article, we aim to make MNLFA more accessible to researchers without access to commercial structural equation modeling software by demonstrating how this method can be applied with the open-source R package OpenMx.

中文翻译：

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使用 R 包 OpenMx 通过缓和的非线性因子分析评估测量不变性。

评估测量不变性是在个体或群体之间建立潜在构造测量的有意义比较的重要步骤。最近，已提出缓和非线性因子分析（MNLFA）作为评估测量不变性的方法。在 MNLFA 模型中，测量不变性通过参数调节在单组验证性因子分析模型中进行检查。与其他方法相比，MNLFA 的优势在于它 (a) 可以评估跨多个连续和分类背景变量的测量不变性，以及 (b) 通过允许因子和残差方差作为背景变量的函数而不同来解释异方差性。在本文中，