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Asymptotic robust inferences in the analysis of mean and covariance structures

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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.

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  • Albert Satorra, 1991. "Asymptotic robust inferences in the analysis of mean and covariance structures," Economics Working Papers 3, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:3
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    1. 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.
    2. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    3. 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.
    4. 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.
    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. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 409-425, September.
    7. Newey, Whitney K., 1988. "Asymptotic Equivalence of Closest Moments and GMM Estimators," Econometric Theory, Cambridge University Press, vol. 4(2), pages 336-340, August.
    8. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    9. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
    10. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    1. 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.
    2. Ab Mooijaart & Albert Satorra, 2012. "Moment Testing for Interaction Terms in Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 65-84, January.
    3. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 507-514, December.
    4. Willem Saris, 2001. "What Influences Subjective Well-Being in Russia?," Journal of Happiness Studies, Springer, vol. 2(2), pages 137-146, June.
    5. Karl Klauer, 2006. "Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 7-31, March.
    6. Terje Skjerpen, 2008. "Engel elasticities, pseudo-maximum likelihood estimation and bootstrapped standard errors. A case study," Discussion Papers 532, Statistics Norway, Research Department.
    7. 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.
    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;The Psychometric Society, vol. 60(4), pages 489-503, December.
    9. 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.

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