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Robust Structural Equation Modeling with Missing Data and Auxiliary Variables

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan  and
Zhiyong Zhang
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Zhiyong Zhang
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Ke-Hai Yuan, Department of Psychology, University of Notre Dame, Notre Dame, IN 46556, USA. E-mail: [email protected]
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Abstract

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are provided in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from the National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood.

Keywords

auxiliary variablesestimating equationmissing at randomR package rsemsandwich-type covariance matrix
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 803 - 826
Copyright
Copyright © The Psychometric Society 2012

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Footnotes

The research was supported by Grants DA00017 and DA01070 from the National Institute on Drug Abuse.

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