Structural Equation Modeling: Applications Using Mplus

2.3 CFA Model with Non-Normal and Censored Continuous Indicators

In Section 2.2 we have discussed and demonstrated CFA with continuous indicators. The default estimator ML requires multivariate normally distributed data for model estimation. Very often, such an assumption is violated in data for social science studies. Under the condition of non- normality, ML parameter estimates are less likely to be biased; however, when non- normality increases the standard errors of ML parameter estimates and model fit indices tend to be underestimated, and model χ ² statistics would be inflated (Browne, 1982; Satorra, 1992; West, Finch, and Curran, 1995; Finch, West, and MacKinnon, 1997). As such, dealing with non- normality is an important issue in SEM. Non- normal data violates the multivariate normality assumption mainly due to skewness, kurtosis, censoring, outlier and influential cases. In this section, we will discuss and demonstrate how to conduct CFA with non- normal and censored data. We start with testing non- normality.

2.3.1 Testing Non-Normality

Mplus allows data screening for outliers and influential cases by checking the Mahalanobis distance (Rousseeuw and Van Zomeren, 1990), log- likelihood distance influence measure (Cook and Weisberg, 1982), and Cook' s D (Cook, 1977), as well as histograms or scatterplots. However, the current version of Mplus does not provide a case- robust estimator to deal with outliers and influential cases. Once outliers and influential cases are identified, ...