The performance of model fit measures by robust weighted least squares estimators in Confirmatory Factor Analysis

Open Access
Zhao, Yu
Graduate Program:
Educational Psychology
Doctor of Philosophy
Document Type:
Date of Defense:
December 17, 2014
Committee Members:
  • Pui Wa Lei, Dissertation Advisor
  • Pui Wa Lei, Committee Chair
  • Hoi Kin Suen, Committee Member
  • Jonna Marie Kulikowich, Committee Member
  • Aleksandra B Slavkovic, Committee Member
  • model fit
  • fit indices
  • model misspecification
  • model size
  • CFA
  • cut-off
  • small sample
  • DWLS
  • ordinal variables
Despite the prevalence of ordinal observed variables in applied structural equation modeling (SEM) research, limited attention has been given to model evaluation methods suitable for ordinal variables, thus providing practitioners in the field with few guidelines to follow. This dissertation represents a first attempt to thoroughly examine the performance of five fit measures—χ^2 statistic, Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR)—produced by the mean- and variance-corrected Weighted Least Squares (WLSMV) estimator from Mplus 7 and the Diagonally Weighted Least Squares (DWLS) estimator from LISREL 9.1, both of which are forms of Robust Weighted Least Squares (RWLS) estimator designed to accommodate ordinal and nonnormal observed variables, in Confirmatory Factor Analysis (CFA) model evaluation, under various realistic sample, data, and model conditions, especially when different types and degrees of model misspecification occur. This study also empirically examined the applicability of the most widely used cut-off criteria of the fit indices proposed by Hu and Bentler (1999) in RWLS estimation with ordinal variables. Results showed that in evaluating the goodness-of-fit of CFA models with ordinal variables, fit measures generated by Mplus WLSMV seemed to be more effective and reliable than those produced by LISREL DWLS across studied conditions. The WLSMV fit measures generally maintained good Type I error control and were powerful enough to detect moderate model misspecification, provided that the model was not too large. The DWLS fit measures, on the other hand, were susceptible to influences of small sample size and could be largely inflated or deflated when a small sample was used to evaluate a large model. In addition, Hu and Bentler’s (1999) cut-off criteria, despite of their popularity among applied SEM researchers, were not universally applicable in RWLS model evaluation, mainly because all of the fit indices examined varied systematically with the size of the proposed model. Recommendations are made by the end of the dissertation, based on the results of the current study, on practical issues pertaining to real-life CFA model evaluation with ordinal observed variables, such as minimum sample size required and how to use information provided by the RWLS fit measures to make model-data fit decisions, while taking into consideration the sample, data, and model characteristics specific to researchers’ own studies.