The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

By D. Powell, William D. Schafer. 2001

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Reporting practices in confirmatory factor analysis: an overview and some recommendations. (2009, background): “…of MVN can lead to an overestimation of the chi-square statistic and, hence, to an inflated Type 1 error (e.g., Curran, West, & Finch, 1996; Powell & Schafer, 2001) and downward biased standard errors (Bandalos, 2002; Kaplan, 2000; Nevitt & Hancock, 2001), and may undermine the assumptions…”
Assessing Goodness of Fit: Simple Rules of Thumb Simply Do Not Work (2011, background): “, see Vernon & Eysenck, 2007). For example, Marsh et al. (2004) cautioned against treating ‘‘currently available ‘rules of thumb’ as if they were golden rules’’ (p.”
LATENT GROWTH MIXTURE MODELING: A SIMULATION STUDY (2007, background): “Two meta-analyses (Hoogland & Boomsma, 1998; Powell & Schafer, 2001) conclude results from about 50 simulation studies, where the focus has been in the robustness of estimators and the likelihood ratio chi-square test.”
Is the ML Chi-Square Ever Robust to Nonnormality? A Cautionary Note With Missing Data (2008, background): “Its performance in this case can be severely affected, usually leading to high rejection rates (Curran, West, & Finch, 1996; Henly, 1993; Hu, Bentler, & Kano, 1992; Powell & Schafer, 2001 ).”