ABSTRACT Multilevel structural equation models (MSEM) are typically evaluated on the basis of goodness of fit indices. A problem with these indices is that they pertain to the entire model, reflecting simultaneously the degree of fit for all levels in the model. Consequently, in cases that lack model fit, it is unclear which level model is misspecified. Although some researchers have suggested that model fit be assessed separately at all levels, this is not always ideal as it depends on the choice of fit indices, cutoff points, and magnitude of the intraclass correlation. Equivalence testing has recently been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been heralded as a way to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this paper is to illustrate the use of equivalence testing for assessing multilevel model fit in educational research. Although the described procedures can be easily generalized to models with more than two levels, for simplicity we explicitly consider only two-level models.

中文翻译：

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使用等效测试评估多层结构方程模型的拟合优度

摘要多级结构方程模型（MSEM）通常根据拟合指标的优劣进行评估。这些索引的问题在于它们与整个模型有关，同时反映了模型中所有级别的拟合程度。因此，在缺乏模型拟合的情况下，不清楚哪个级别的模型指定不正确。尽管一些研究人员建议对模型拟合进行各个级别的单独评估，但这并不总是理想的，因为它取决于拟合指数，临界点和类内相关程度的选择。最近推荐使用等效测试作为评估模型拟合优度的一种较好方法。该方法还被认为是一种改进结构方程建模的推论性质的方法，可以作为一种确认工具。本文的目的是说明等效性测试在评估教育研究中的多层次模型拟合中的使用。尽管所描述的过程可以轻松地推广到具有两个以上级别的模型，但为简单起见，我们仅明确考虑了两个级别的模型。