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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.

Suggested Citation

  • Satorra, Albert, 2002. "Asymptotic Robustness In Multiple Group Linear-Latent Variable Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 297-312, April.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:02:p:297-312_18
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    Cited by:

    1. 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.
    2. 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, vol. 16(4), pages 1-26, November.
    3. Biørn, Erik, 2017. "Identification and Method of Moments Estimation in Polynomial Measurement Error Models," Memorandum 01/2017, Oslo University, Department of Economics.
    4. D. Gunzler & W. Tang & N. Lu & P. Wu & X. Tu, 2014. "A Class of Distribution-Free Models for Longitudinal Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 543-568, October.
    5. 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.
    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. 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;The Psychometric Society, vol. 69(3), pages 437-457, September.
    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. 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.
    10. Vicente Prado-Gascó & Virginia Romero-Reignier & Patricia Mesa-Gresa & Ana Belén Górriz, 2020. "Subjective Well-Being in Spanish Adolescents: Psychometric Properties of the Scale of Positive and Negative Experiences," Sustainability, MDPI, vol. 12(10), pages 1-16, May.
    11. Miguel Ángel Albalá Genol & Edgardo Etchezahar & Juan Ignacio Guido & Joaquín Ungaretti, 2022. "Construct Validity of the Attitudes towards Maghrebis in Education Scale (AMES)," IJERPH, MDPI, vol. 19(12), pages 1-10, June.
    12. 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.
    13. 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.
    14. Betlem Sabrià Bernadó & Xavier Llinàs Audet & Sofia Isus Barado & Cristina Yáñez Aldecoa, 2014. "Estudio empírico de las contrariedades de los demandantes de formación continua en la Instituciones de Educación Superior españolas," Investigaciones de Economía de la Educación volume 9, in: Adela García Aracil & Isabel Neira Gómez (ed.), Investigaciones de Economía de la Educación 9, edition 1, volume 9, chapter 37, pages 715-729, Asociación de Economía de la Educación.
    15. Liébana-Cabanillas, Francisco & Sánchez-Fernández, Juan & Muñoz-Leiva, Francisco, 2014. "The moderating effect of experience in the adoption of mobile payment tools in Virtual Social Networks: The m-Payment Acceptance Model in Virtual Social Networks (MPAM-VSN)," International Journal of Information Management, Elsevier, vol. 34(2), pages 151-166.
    16. Francisco Liébana-Cabanillas & Francisco Muñoz-Leiva & J. Sánchez-Fernández, 2018. "A global approach to the analysis of user behavior in mobile payment systems in the new electronic environment," Service Business, Springer;Pan-Pacific Business Association, vol. 12(1), pages 25-64, March.

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