Date of Award
Spring 2026
Document Type
Open Access Dissertation
Department
Psychology
First Advisor
Dexin Shi
Abstract
Evaluating model fit is an important topic of structural equation modeling (SEM), with the Root Mean Square Error of Approximation (RMSEA) and the Comparative Fit Index (CFI) serving as two of the most used fit indices. Although RMSEA and CFI can be estimated accurately under ideal scenarios (e.g., complete data and multivariate normality), such conditions are often unattainable in psychological research or practice. The presence of non-normality and incompleteness particularly poses difficulties for SEM model fit estimation. Despite advances in handling each difficulty separately, limited attention has been given to this joint challenge. This dissertation addresses this gap by evaluating several methods for estimating RMSEA and CFI in this double trouble context.
A Monte Carlo simulation study was conducted to assess the performance of those methods under conditions involving non-normal data and varying rates of missing data generated under a Missing at Random (MAR) mechanism. The simulation design included varying sample sizes, degrees of model misspecification, and different missing data patterns to better reflect real-world research complexity. Results found that under non- normal complete data, both BSL and Lai yielded unbiased estimates of RMSEA and CFI, with Lai’s interval estimation slightly outperforming the BSL.
Under conditions involving non-normal data and missingness, FIMLZS2, TSZS, TSLai, MIBSL, and MILai generally yielded unbiased RMSEA estimates and accurate confidence intervals for population RMSEA when the missing data rate was low to moderate (15% to 25%) and sample sizes were large (e.g., N > 500). However, under conditions with a substantial missing data rate (i.e., 50%), performance varied depending on the non-normal data generation algorithms and missing data patterns. Across many conditions, FIMLBSL underestimated RMSEA.
Across conditions with low to moderate missingness, all methods yielded unbiased and/or consistent estimates of the CFI. At 50% missingness, FIMLZS2 and TSZS showed modestly better performance than competing methods, with relative bias typically within 10%. MI-based methods also met the relative-bias criterion, but acceptable performance generally required larger sample sizes. FIMLBSL performed acceptably overall; however, its CFI estimates became increasingly larger as N increased, indicating more favorable fit irrespective of the true extent of model misfit.
This work concludes that the SEM model fit estimation under the double trouble condition requires methods that explicitly account for both distributional violations and missing data patterns. Practical recommendations are provided to guide applied researchers in choosing viable estimation methods. This work contributes to a principled framework for SEM model fit estimation in a joint challenge data scenario and highlights directions for future methodological development.
Rights
© 2026, Yunhang Yin
Recommended Citation
Yin, Y.(2026). Double Trouble: Assessing Model Fit in Structural Equation Modeling (SEM) When Jointly Handling Non- Normality and Missing Data. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8866