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Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
Ye-Mao Xia
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
Ye-Mao Xia
Affiliation:
The Chinese University of Hong Kong
*
Requests for reprints should be sent to S. Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong. E-mail: sylee@sparc20c.sta.cuhk.edu.hk
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Abstract

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the development of robust methods to reduce the influence of outliers and the distributional deviation in the analysis. In this paper we develop a maximum likelihood (ML) approach that is robust to outliers and symmetrically heavy-tailed distributions for analyzing nonlinear SEMs with ignorable missing data. The analytic strategy is to incorporate a general class of distributions into the latent variables and the error measurements in the measurement and structural equations. A Monte Carlo EM (MCEM) algorithm is constructed to obtain the ML estimates, and a path sampling procedure is implemented to compute the observed-data log-likelihood and then the Bayesian information criterion for model comparison. The proposed methodologies are illustrated with simulation studies and an example.

Keywords

outliersheavy-tailed distributionsMCEM algorithmGibbs samplerpath samplingBayesian information criterion
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 565 - 585
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

The research described herein was fully supported by a grant (CUHK 4243/03H) from the Rearch Grants Council of the Hong Kong Special Administration Region. The authors are thankful to the Editor, the Associate Editor, and anonymous reviewers for valuable comments which improve the paper significantly, and are grateful to ICPSR and the relevant funding agency for allowing the use of their data.

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