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Asymptotic Robustness In Multiple Group Linear-Latent Variable Models

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  • Satorra, Albert

Abstract

Standard methods for analyzing linear-latent variable models rely on the assumption that the observed variables are normally distributed. Normality allows statistical inferences to be carried out based solely on the first-and second-order moments. In general, inferences for nonnormally distributed data require the estimates of matrices of third-and fourth-order moments. In the present paper, we show that inferences based on normal theory retain validity and asymptotic efficiency under general assumptions that allow for considerable departure from normality. In particular, we obtain conditions under which correct asymptotic inferences are attained when replacing a matrix of higher order moments by a matrix that depends only on cross-product moments of the data.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 02 (April)
Pages: 297-312

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Handle: RePEc:cup:etheor:v:18:y:2002:i:02:p:297-312_18

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Cited by:
  1. Calabuig, F. & Núñez-Pomar, Juan & Prado-Gascó, Vicente & Añó, V., 2014. "Effect of price increases on future intentions of sport consumers," Journal of Business Research, Elsevier, vol. 67(5), pages 729-733.
  2. Juan Carlos Bou & Albert Satorra, 2003. "The persistence of abnormal returns at industry and firm levels," Economics Working Papers 729, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Juan Carlos Bou & Albert Satorra, 2014. "Univariate versus multivariate modeling of panel data," Economics Working Papers 1417, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Vega-Zamora, Manuela & Parras-Rosa, Manuel & Murgado-Armenteros, Eva María & Torres-Ruiz, Francisco José, 2013. "A Powerful Word: The Influence of the Term 'Organic' on Perceptions and Beliefs Concerning Food," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association (IAMA), vol. 16(4).
  5. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer, vol. 69(3), pages 437-457, September.
  6. Yuan, Ke-Hai & Bentler, Peter M., 2005. "Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 328-343, June.
  7. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
  8. Yuan, Ke-Hai & Bentler, Peter M., 2003. "Eight test statistics for multilevel structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 89-107, October.
  9. Ogasawara, Haruhiko, 2005. "Asymptotic robustness of the asymptotic biases in structural equation modeling," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 771-783, June.

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