Non-normal data require robust maximum likelihood estimation to avoid biased model fit

Evidence

Because the data violated the assumption of multivariate normality by displaying excessive multivariate kurtosis, traditional maximum likelihood estimation (MLM) could not be used for the CFA. Instead, the covariance matrices, which were calculated with PRELIS, were analyzed using robust MLM (Satorra & Bentler, 1994) using LISREL 8.72 (statistical software; Jöreskog & Sörbom, 2005). The MLM compensates for non-normal data by adjusting the chi-square statistic, standard errors, and fit indexes in order to yield less biased estimates of model fit and provide more robust standard errors (Brown, 2006; Finney & DiStefano, 2006; West, Finch, & Curran, 1995; for an application of this method using psychology of religion measures, see Dy-Liacco, Piedmont, Murray-Swank, Rodgerson, & Sherman, 2009). — Sherman A. Lee, Chelsea A. Reid, Stephen D. Short, Jeffrey A. Gibbons, Ruth Yeh, and Matthew L. Campbell, Fear of Muslims, 50

Categorization

• XREF: Connects to any structural equation modeling or psychometrics work using Satorra-Bentler corrections.
• SHARE: Worth sending to a colleague doing CFA on skewed survey data who is still defaulting to standard ML.