Abstract
This chapter discusses the robust procedures in structural equation models. The classical procedure for structural equation modeling was developed under the assumption of normally distributed data. In practice, data are seldom normally distributed, and often possess heavy tails. When the normality assumption is slightly violated, the normal distribution based maximum likelihood (ML) procedure still generates consistent parameter estimates. When data comes from a distribution with severe heavy tails, parameter estimates by ML may no longer be consistent. Standard errors and test statistics based on modeling the sample means and covariances may not be valid either. Three types of robust procedures are systematically introduced in the chapter. Statistical properties of each procedure are reviewed, and their strengths and weaknesses as well as scope of applicability are discussed. Examples are provided to contrast the properties of these procedures. While each of the robust procedures improves the ML procedure to a certain extent, only those that downweight the effect of outlying cases are really robust.
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