Advanced Search
MyIDEAS: Login to save this paper or follow this series

Asymptotic robust inferences in the analysis of mean and covariance structures


Author Info


Structural equation models are widely used in economic, social and behavioral studies to analyze linear interrelationships among variables, some of which may be unobservable or subject to measurement error. Alternative estimation methods that exploit different distributional assumptions are now available. The present paper deals with issues of asymptotic statistical inferences, such as the evaluation of standard errors of estimates and chi--square goodness--of--fit statistics, in the general context of mean and covariance structures. The emphasis is on drawing correct statistical inferences regardless of the distribution of the data and the method of estimation employed. A (distribution--free) consistent estimate of $\Gamma$, the matrix of asymptotic variances of the vector of sample second--order moments, will be used to compute robust standard errors and a robust chi--square goodness--of--fit squares. Simple modifications of the usual estimate of $\Gamma$ will also permit correct inferences in the case of multi-- stage complex samples. We will also discuss the conditions under which, regardless of the distribution of the data, one can rely on the usual (non--robust) inferential statistics. Finally, a multivariate regression model with errors--in--variables will be used to illustrate, by means of simulated data, various theoretical aspects of the paper.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
File Function: Whole Paper
Download Restriction: no

Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 3.

as in new window
Date of creation: Jun 1991
Date of revision:
Handle: RePEc:upf:upfgen:3

Contact details of provider:
Web page:

Related research



References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Satorra, Albert & Bentler, Peter M., 1990. "Model conditions for asymptotic robustness in the analysis of linear relations," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 235-249, December.
  2. Albert Satorra, 1992. "The variance matrix of sample second-order moments in multivariate linear relations," Economics Working Papers 8, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Newey, Whitney K., 1988. "Asymptotic Equivalence of Closest Moments and GMM Estimators," Econometric Theory, Cambridge University Press, vol. 4(02), pages 336-340, August.
  4. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer, vol. 54(1), pages 131-151, March.
  5. Neudecker, Heinz & Satorra, Albert, 1991. "Linear structural relations: Gradient and Hessian of the fitting function," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 57-61, January.
  6. Albert Satorra, 1990. "Robustness issues in structural equation modeling: a review of recent developments," Quality & Quantity: International Journal of Methodology, Springer, vol. 24(4), pages 367-386, November.
  7. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer, vol. 54(3), pages 409-425, September.
  8. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  10. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
Full references (including those not matched with items on IDEAS)


Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Coenders, Germà & Espinet, Josep Maria & Saez, Marc, 2001. "Predicting random level and seasonality of hotel prices. A structural equation growth curve approach," Working Papers of the Department of Economics, University of Girona 1, Department of Economics, University of Girona.
  2. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer, vol. 66(4), pages 507-514, December.
  3. Satorra, Albert, 1992. "The variance matrix of sample second-order moments in multivariate linear relations," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 63-69, September.
  4. Willem Saris, 2001. "What Influences Subjective Well-Being in Russia?," Journal of Happiness Studies, Springer, vol. 2(2), pages 137-146, June.
  5. Ab Mooijaart & Albert Satorra, 2012. "Moment Testing for Interaction Terms in Structural Equation Modeling," Psychometrika, Springer, vol. 77(1), pages 65-84, January.
  6. Karl Klauer, 2006. "Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach," Psychometrika, Springer, vol. 71(1), pages 7-31, March.
  7. Terje Skjerpen, 2008. "Engel elasticities, pseudo-maximum likelihood estimation and bootstrapped standard errors. A case study," Discussion Papers 532, Research Department of Statistics Norway.
  8. Bengt Muthén & Albert Satorra, 1995. "Technical aspects of Muthén's liscomp approach to estimation of latent variable relations with a comprehensive measurement model," Psychometrika, Springer, vol. 60(4), pages 489-503, December.
  9. Eva Ventura & Albert Satorra, 1998. "Lyfe-cycle effects on household expenditures: A latent-variable approach," Economics Working Papers 354, Department of Economics and Business, Universitat Pompeu Fabra.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:3. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.