Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

Click here to sign up for SAGE Journal Email Alerts today!

Sign In to gain access to subscriptions and/or personal tools.
Sociological Methods & Research
This Article
Right arrow Abstract Freely available
Right arrow Free Full Text (Free PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Siemsen, E.
Right arrow Articles by Bollen, K. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Least Absolute Deviation Estimation in Structural Equation Modeling

Enno Siemsen

University of Illinois, Urbana-Champaign, siemsen{at}uiuc.edu.

Kenneth A. Bollen

University of North Carolina, Chapel Hill

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.

Key Words: least absolute deviation • structural equation modeling • robust estimation • small sample research

References

  • Anderson, James C. and David W. Gerbing. 1984. ``The Effect of Sampling Error on Convergence, Improper Solutions, and Goodness-of-Fit Indices for Maximum Likelihood Confirmatory Factor Analysis.'' Psychometrika 39:155-73.
  • Bassett, Gilbert and Roger Koenker. 1978. ``Asymptotic Theory of Least Absolute Error Regression.'' Journal of the American Statistical Association 73:618-22.[CrossRef][Web of Science]
  • Bentler, Peter M. and Chih-Ping Chou. 1987. ``Practical Issues in Structural Modeling.'' Sociological Methods & Research 16:78-117.[Abstract]
  • Bertsekas, Dimitri P. 1999. Nonlinear Programming. Belmont, MA: Athena Scientific.
  • Bollen, Kenneth A. 1989. Structural Equations With Latent Variables. New York: John Wiley.
  • Bollen, Kenneth A. 1996. ``An Alternative 2SLS Estimator for Latent Variable Models.'' Psychometrika 61:109-21.[CrossRef][Web of Science]
  • Boomsma, Anne and Jeffrey J. Hoogland. 2001. ``The Robustness of LISREL Modeling Revisited.'' Pp. 139-68 in Structural Equation Modeling: Present and Future, edited by R. Cudeck, S. H. C. du Toit, and D. Sörbom. Chicago: Scientific Software International.
  • Browne, Michael W. 1984. ``Asymptotically Distribution-Free Methods for the Analysis of Covariance Structures.'' British Journal of Mathematical and Statistical Psychology 37:62-83.
  • Chen, Feinian, Kenneth A. Bollen, Pamela Paxton, Patrick Curran, and James B. Kirby. 2001. ``Improper Solutions in Structural Equation Models.'' Sociological Methods & Research 29:468-508.[Abstract/Free Full Text]
  • Cheung, Gordon. 2004. ``How Many Subjects? Revisiting the Sample Size Issue in Structural Equation Modeling.'' Presented at the Academy of Management Meeting, New Orleans, LA.
  • Cudeck, Robert and Lisa L. O'Dell. 1994. ``Applications of Standard Error Estimates in Unrestricted Factor Analysis: Significance Tests for Factor Loadings and Correlations.'' Psychological Bulletin 115:475-87.[CrossRef][Web of Science][Medline] [Order article via Infotrieve]
  • Gerbing, David W. and James C. Anderson. 1985. ``The Effects of Sampling Error and Model Characteristics on Parameter Estimation for Maximum Likelihood Confirmatory Factor Analysis.'' Multivariate Behavioral Research 20:255-71.[CrossRef][Web of Science]
  • Gorsuch, Richard L. 1983. Factor Analysis. 2d ed. Hillsdale, NJ: Lawrence Erlbaum.
  • Greene, William H. 2002. Econometric Analysis. Englewood Cliffs, NJ: Prentice Hall.
  • Hancock, Gregory R. and Ralph O. Mueller. 2001. ``Rethinking Construct Reliability Within Latent Variable Systems.'' Pp. 195-216 in Structural Equation Modeling: Present and Future, edited by R. Cudeck, S. H. C. du Toit, and D. Sörbom. Chicago: Scientific Software International.
  • Harwood, Shane and Richard Scheines. 2002. ``Genetic Algorithm Search Over Causal Models.'' Technical Report CMU-Phil-131. Pittsburgh, PA: Carnegie Mellon University.
  • Hershberger, Scott L. 2003. ``The Growth of Structural Equation Modeling: 1994-2001.'' Structural Equation Modeling 10:35-46.[CrossRef][Web of Science]
  • Hill, Richard W. and Paul Holland. 1977. ``Two Robust Alternatives to Least-Squares Regression.'' Journal of the American Statistical Association 72:828-33.[CrossRef][Web of Science]
  • Jackson, Dennis L. 2001. ``Sample Size and the Number of Parameter Estimates in Maximum Likelihood Confirmatory Factor Analysis: A Monte-Carlo Investigation.'' Structural Equation Modeling 8:205-23.[CrossRef]
  • Jackson, Dennis L. 2003. ``Revisiting Sample Size and Number of Parameter Estimates: Some Support for the N:q Hypothesis.'' Structural Equation Modeling 10:128-41.[CrossRef][Web of Science]
  • Jöreskog, Karl G. 1969. ``A General Approach to Confirmatory Maximum Likelihood Factor Analysis.'' Psychometrika 34:183-202.[CrossRef][Web of Science]
  • Jöreskog, Karl G. and Dag Sörbom. 1996. LISREL 8: User's Reference Guide. Chicago: Scientific Software International.
  • Koenker, Roger and Gilbert Bassett. 1982. ``Robust Tests for Heteroskedasticity Based on Regression Quantiles.'' Econometrica 50:43-61.[CrossRef][Web of Science]
  • Lawley, D.N. 1940. ``The Estimation of Factor Loadings by the Method of Maximum Likelihood.'' Proceedings of the Royal Society of Edinburgh 60:64-82.
  • MacCallum, Robert C., Michael W. Browne, and Hazuki M. Sugawara. 1996. ``Power Analysis and Determination of Sample Size for Covariance Structure Modeling.'' Psychological Methods 1:130-49.[CrossRef][Web of Science]
  • MacCallum, Robert C., Keith F. Widaman, Shaobo Zhang, and Sehee Hong. 1999. ``Sample Size in Factor Analysis.'' Psychological Methods 4:84-99.[CrossRef][Web of Science]
  • Marcoulides, George A. and Zvi Drezner. 2001. ``Specification Searches in Structural Equation Models With a Genetic Algorithm.'' Pp. 154-64 in New Developments and Techniques in Structural Equation Modeling, edited by G. A. Marcoulides and R. E. Schumacker. Mahwah, NJ: Lawrence Erlbaum.
  • Marsh, Herbert W., John R. Balla, and Roderick P. McDonald. 1988. ``Goodness of Fit Indexes in Confirmatory Factor Analysis: The Effect of Sample Size.'' Psychological Bulletin 103:391-410.[CrossRef][Web of Science]
  • Marsh, Herbert W., Kit-Tai Hau, John R. Balla, and David Grayson. 1998. ``Is More Ever Too Much? The Number of Indicators Per Factor in Confirmatory Factor Analysis.'' Multivariate Behavioral Research 33:181-220.[CrossRef][Web of Science]
  • Matsueda, Ross L. and William T. Bielby. 1986. ``Statistical Power in Covariance Structure Models.'' Sociological Methodology 16:120-58.[CrossRef]
  • Mueller, Ralph O. 1997. ``Structural Equation Modeling: Back to the Basics.'' Structural Equation Modeling 4:353-69.
  • Muthén, Linda K. and Bengt O. Muthén. 2002. ``How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power.'' Structural Equation Modeling 9:599-620.[CrossRef][Web of Science]
  • Paxton, Pamela, Patrick Curran, Kenneth A. Bollen, Jim Kirby, and Feinian Chen. 2001. ``Monte Carlo Experiments: Design and Implementation.'' Structural Equation Modeling 8:287-312.[CrossRef]
  • Portnoy, Stephen and Roger Koenker. 1997. ``The Gaussian Hare and the Laplacian Tortoise: Computability of Squared-Error Versus Absolute-Error Estimators.'' Statistical Science 12:279-300.[CrossRef][Web of Science]
  • Rogers, William H. 1993. ``sg11.2: Calculation of Quantile Regression Standard Errors.'' Stata Technical Bulletin 13:8-9.
  • Shapiro, Alexander. 1983. ``Asymptotic Distribution Theory in the Analysis of Covariance Structures (A Unified Approach).'' South African Statistical Journal 37:62-83.
  • Storn, Rainer and Ken Price. 1997. ``Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces.'' Journal of Global Optimization 11: 341-59.[CrossRef][Web of Science]
  • Tanaka, J.S. 1987. ``How Big Is Big Enough: Sample Size and Goodness of Fit in Structural Equation Models With Latent Variables.'' Child Development 58:134-46.[CrossRef][Web of Science]
  • Velicer, Wayne F. and Joseph L. Fava. 1998. ``Effects of Variable and Subject Sampling on Factor Pattern Recovery.'' Psychological Methods 3:231-51.[CrossRef][Web of Science]

Sociological Methods & Research, Vol. 36, No. 2, 227-265 (2007)
DOI: 10.1177/0049124107301946
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Free Full Text (Free PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Siemsen, E.
Right arrow Articles by Bollen, K. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?