Evaluating Fit Indices for Multivariate t-Based Structural Equation Modeling with Data Contamination

Mark H. C. Lai, Jiaqi Zhang

In conventional structural equation modeling (SEM), with the presence of even a tiny amount of data contamination due to outliers or influential observations, normal-theory maximum likelihood (ML-Normal) is not efficient and can be severely biased. The multivariate-t-based SEM, which recently got implemented in Mplus as an approach for mixture modeling, represents a robust estimation alternative to downweigh the impact of outliers and influential observations. To our knowledge, the use of maximum likelihood estimation with a multivariate-t model (ML-t) to handle outliers has not been shown in SEM literature. In this paper we demonstrate the use of ML-t using the classic Holzinger and Swineford (1939) data set with a few observations modified as outliers or influential observations. A simulation study is then conducted to examine the performance of fit indices and information criteria under ML-Normal and ML-t in the presence of outliers. Results showed that whereas all fit indices got worse for ML-Normal with increasing amount of outliers and influential observations, their values were relatively stable with ML-t, and the use of information criteria was effective in selecting ML-normal without data contamination and selecting ML-t with data contamination, especially when the sample size was at least 200.