by Zhiyong Zhang and Ke-Hai Yuan

To be presented at the 121st Annual Convention of the American Psychological Association at Honolulu, HI, August 4, 2013.

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Being capable of modeling latent variables and measurement errors simultaneously, structural equation modeling (SEM) has become one of the most popular statistical methods in social and behavioral research, where missing data are common, especially when data are collected longitudinally. Many procedures have been developed for modeling missing data in SEM, most of which are normal-distribution-based maximum likelihood (NML). However, NML estimates (NMLE) can be very inefficient or even biased when data have heavy tails or are contaminated.

This workshop aims to introduce a newly developed two-stage robust method and related software for SEM analysis to handle practical data, possibly with both missingness and contamination (Yuan & Zhang, 2011, 2012). Technical details of the two-stage robust method will be first reviewed. Then, using real data from National Longitudinal Survey of Youth 1997 cohort, we will demonstrate how to use the free online software WebSEM to practically conduct robust SEM analysis

• Demonstration of differences between NML and robust methods
• Two-stage and direct robust methods
• Structural equation model diagnostics of outlying observations
• Bias and efficiency of parameter estimates
• Performance of test statistics
• Missing data and influence of auxiliary variables
• Slides

The online software WebSEM is available at https://websem.psychstat.org. By clicking the link, you will be directed to log in. If you have not registered as a user, please do so following the on-screen instruction.

• Robust alpha
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• Growth curve modeling
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• Mediation analysis
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• Multiple group analysis
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• Robust alpha
• Growth curve modeling
• Mediation analysis
• Multiple group analysis

• Zhang, Z., & Yuan, K.-H. (2013). Robust Coefficient Alpha for Non-normal and Missing data.
• Yuan, K.-H. (2013).Expectation-robust algorithm and estimating equation for means and covariances with missing data.
• Yuan, K.-H., Tong, X., & Zhang, Z. (2013). Bias and Efficiency for SEM with Missing Data and Auxiliary Variables: Two-Stage Robust Method versus Two-Stage ML
• Tong, X., Zhang, Z., & Yuan, K.-H. (in press). Evaluation of Test Statistics for Robust Structural Equation Modeling with Nonnormal Missing Data. Structural Equation Modeling: An Interdisciplinary Journal
• Zhang, Z., & Wang, L. (2013). Methods for mediation analysis with missing data. Psychometrika, 78(1), 154-184.
• Yuan, K.-H., & Zhang, Z. (2012). Structural equation modeling diagnostics using R package semdiag and EQS. Structural Equation Modeling: An Interdisciplinary Journal, 19(4), 683-702.
• Yuan, K.-H., & Zhang, Z. (2012). Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika, 77(4), 803-826.
• Yuan, K.-H., & Zhong, X. (2008). Outliers, leverage observations and influential cases in factor analysis: Minimizing their effect using robust procedures. Sociological Methodology, 38, 329-268.
• Zhang, Z., & Yuan, K.-H. (2012). WebSEM manual. [Software]. Available from https://websem.psychstat.org.