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Structural equation modeling with heavy tailed distributions

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Abstract

Data in social and behavioral sciences typically possess heavy tails. Structural equation modeling is commonly used in analyzing interrelations among variables of such data. Classical methods for structural equation modeling fit a proposed model to the sample covariance matrix, which can lead to very inefficient parameter estimates. By fitting a structural model to a robust covariance matrix for data with heavy tails, one generally gets more efficient parameter estimates. Because many robust procedures are available, we propose using the empirical efficiency of a set of invariant parameter estimates in identifying an optimal robust procedure. Within the class of elliptical distributions, analytical results show that the robust procedure leading to the most efficient parameter estimates also yields a most powerful test statistic. Examples illustrate the merit of the proposed procedure. The relevance of this procedure to data analysis in a broader context is noted.

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Authors and Affiliations

  1. Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA

    Ke-Hai Yuan

  2. University of California, Los Angeles, USA

    Peter M. Bentler

  3. The Chinese University of Hong Kong, China

    Wai Chan

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  1. Ke-Hai Yuan
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  2. Peter M. Bentler
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  3. Wai Chan
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Correspondence to Ke-Hai Yuan.

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The authors thank the editor, an associate editor and four referees for their constructive comments, which led to an improved version of the paper.

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Yuan, KH., Bentler, P.M. & Chan, W. Structural equation modeling with heavy tailed distributions. Psychometrika 69, 421–436 (2004). https://doi.org/10.1007/BF02295644

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