Robustness of fit indices to outliers and leverage observations in structural equation modeling

Normal-distribution-based maximum likelihood (NML) is the most widely used method in structural equation modeling (SEM), although practical data tend to be nonnormally distributed. The effect of nonnormally distributed data or data contamination on the normal-distribution-based likelihood ratio (LR) statistic is well understood due to many analytical and empirical studies. In SEM, fit indices are used as widely as the LR statistic. In addition to NML, robust procedures have been developed for more efficient and less biased parameter estimates with practical data. This article studies the effect of outliers and leverage observations on fit indices following NML and two robust methods. Analysis and empirical results indicate that good leverage observations following NML and one of the robust methods lead most fit indices to give more support to the substantive model. While outliers tend to make a good model superficially bad according to many fit indices following NML, they have little effect on those following the two robust procedures. Implications of the results to data analysis are discussed, and recommendations are provided regarding the use of estimation methods and interpretation of fit indices.