Structural equation modeling with heavy tailed distributions

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Observations on the Use of Growth Mixture Models in Psychological Research (2007, background): “Note that the ML estimates are robust to certain forms of non-normality (Browne, 1984; Browne & Shapiro, 1988; Satorra, 1990; Satorra & Bentler, 1990).2 Other estimators for these models also exist that forgo the normality assumption (Browne, 1984; Yuan, Bentler, & Chan, 2004 ).”
8. Outliers, Leverage Observations, and Influential Cases in Factor Analysis: Using Robust Procedures to Minimize Their Effect (2008, methodology): “To segregate the confounding effect in dsi or dci in controlling outliers and leverage observations, Yuan et al. (2004) introduced a residualbased M-distance dri for the one-factor model.”
Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models. (2003, methodology): “Actually, Yuan et al. (2001) found that the sample x (.10) i leads to the most efcient parameter estimates in (18) among various procedures.”
Bayesian Inference and Application of Robust Growth Curve Models Using Student's t Distribution (2013, background): “Failing to account for the longer-than-normal tails or outliers in data may result in unreliable parameter estimates, incorrect standard errors and confidence intervals, and misleading statistical tests and inference (Maronna et al., 2006; Yuan et al., 2004; Zu & Yuan, 2010).”