Handbook of Latent Variable and Related Models

Handbook of Latent Variable and Related Models

Handbook of Computing and Statistics with Applications
2007, Pages 367-397
Handbook of Latent Variable and Related Models

17 - Robust Procedures in Structural Equation Modeling*

https://doi.org/10.1016/B978-044452044-9/50020-3Get rights and content

Abstract

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 come 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. This chapter systematically introduces three types of robust procedures. 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 certain extent, only those that downweight the effect of outlying cases are really robust. The ML procedure is not recommended for use with non-normally distributed data in practice although it may possess asymptotic robustness.

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This research was supported by NSF grant DMS04-37167, the James McKeen Cattell Fund, and grants DA01070 and DA00017 from the National Institute on Drug Abuse.

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