Mean and Variance Corrected Test Statistics for Structural Equation Modeling with Many Variables

Data in social and behavioral sciences are routinely collected using questionnaires, and each domain of interest is tapped by multiple indicators. Structural equation modeling (SEM) is one of the most widely used methods to analyze such data. However, conventional methods for SEM face difficulty when the number of variables ((Formula presented.)) is large even when the sample size ((Formula presented.)) is also rather large. This article addresses the issue of model inference with the likelihood ratio statistic (Formula presented.). Using the method of empirical modeling, mean-and-variance corrected statistics for SEM with many variables are developed. Results show that the new statistics not only perform much better than (Formula presented.) but also are substantial improvements over other corrections to (Formula presented.). When combined with a robust transformation, the new statistics also perform well with non-normally distributed data.