Least absolute deviation estimation in structural equation modeling

Enno Siemsen, Kenneth A. Bollen

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Least absolute deviation (LAD) is a well-known criterion to fit statistical models, but little is known about LAD estimation in structural equation modeling (SEM). To address this gap, the authors use the LAD criterion in SEM by minimizing the sum of the absolute deviations between the observed and the model-implied covariance matrices. Using Monte Carlo simulations, the authors compare the performance of this LAD estimator along several dimensions (bias, efficiency, convergence, frequencies of improper solutions, and absolute percentage deviation) to the full information maximum likelihood (ML) and unweighted least squares (ULS) estimators in structural equation modeling. The results for LAD are mixed: There are special conditions under which the LAD estimator outperforms ML and ULS, but the simulation evidence does not support a general claim that LAD is superior to ML and ULS in small samples.

Original languageEnglish (US)
Pages (from-to)227-265
Number of pages39
JournalSociological Methods and Research
Issue number2
StatePublished - Nov 2007

Bibliographical note

Copyright 2011 Elsevier B.V., All rights reserved.


  • Least absolute deviation
  • Robust estimation
  • Small sample research
  • Structural equation modeling


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