Yunhang Yin

Date of Award

Fall 2023

Document Type

Open Access Thesis



First Advisor

Dexin Shi

Second Advisor

Amanda Fairchild


This study aimed to understand the effect of model size on the Root Mean Square Error of Approximation (RMSEA) under nonnormal data. We considered three methods for computing the sample RMSEA and the associated confidence intervals (i.e., the normal theory method [Browne & Cudeck, 1993], the BSL method [Brosseau-Liard, Savalei & Li, 2012], and the Lai method [Lai, 2020]). The performance of the three methods was compared across various model sizes, sample sizes, levels of misspecification, and levels of nonnormality. Results indicated that the normal theory RMSEA should not be used under nonnormal data unless the model size is very small. In the presence of nonnormal data, researchers should consider using either the BSL or the Lai method to estimate RMSEA and its confidence intervals. The Lai method is recommended when very large models are fit under nonnormal data.


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