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Least Absolute Deviation Estimation in Structural Equation Modeling

Author

Listed:
  • Enno Siemsen

    (University of Illinois, Urbana-Champaign, siemsen@uiuc.edu.)

  • Kenneth A. Bollen

    (University of North Carolina, Chapel Hill)

Abstract

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.

Suggested Citation

  • Enno Siemsen & Kenneth A. Bollen, 2007. "Least Absolute Deviation Estimation in Structural Equation Modeling," Sociological Methods & Research, , vol. 36(2), pages 227-265, November.
    • Handle: RePEc:sae:somere:v:36:y:2007:i:2:p:227-265
    DOI: 10.1177/0049124107301946
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    References listed on IDEAS

    as
    1. Kenneth Bollen, 1996. "An alternative two stage least squares (2SLS) estimator for latent variable equations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 109-121, March.
    2. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    3. William Rogers, 1993. "Quantile regression standard errors," Stata Technical Bulletin, StataCorp LP, vol. 2(9).
    4. James Anderson & David Gerbing, 1984. "The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 155-173, June.
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