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Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

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Abstract

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second-- order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 16.

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Date of creation: Jun 1992
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Handle: RePEc:upf:upfgen:16

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Web page: http://www.econ.upf.edu/

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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. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  3. Sik-Yum Lee & Kwok-Leung Tsui, 1982. "Covariance structure analysis in several populations," Psychometrika, Springer, vol. 47(3), pages 297-308, September.
  4. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
  5. Dijkstra, Theo, 1983. "Some comments on maximum likelihood and partial least squares methods," Journal of Econometrics, Elsevier, vol. 22(1-2), pages 67-90.
  6. Robert Jennrich, 1987. "Tableau algorithms for factor analysis by instrumental variable methods," Psychometrika, Springer, vol. 52(3), pages 469-476, September.
  7. 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.
  8. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer, vol. 54(1), pages 131-151, March.
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