Summary
In the context of structural equation models, we investigate the asymptotic and finite sample size distribution of competing X 2 goodness-offit test statistics. We allow for a) the data to be non-normal, b) the estimation method to be non-optimal, and c) the model to be misspecified. Power of the test is computed distinguishing whether asymptotic robustness (AR) holds or not. The power of the various test statistics is compared, asymptotically and using Monte Carlo simulation. A scaled version of a normal-theory (NT) goodness-of-fit test statistic for ULS analysis is included among the test statistics investigated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Browne, M.W. (1984): Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83
Curran, P. J., West, S. G., and Finch, J. F. Curran, P. J., West, S. G., and Finch, J. F. (1996): The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis, Psychological Methods, 1, 16–29.
Hu, L., Bentler, P. M., and Kano, Y. (1992): Can test statistics in covariance structure analysis be trusted?, Psychological Bulletin, 112, 351–362.
MacCallum, R., Browne, M.W. and Sugawara, H.M. (1996). Power analysis and determination of sample size for covariance structure modeling, Psychological Methods, 1, 130–149.
Satorra, A. (2001): Goodness-of-fittesting of structural equation models with multiple-group data and nonnormality. In: Cudeck, R., du Toit, S. and Sörbom D. (eds) Structural Equation Modeling: Present and Future, A Festschrift in honor of Karl G. Jöreskog, SSI Scientific Software: Lincolnwood, IL.
Satorra, A. (2002): Asymptotic robustness in multiple-group linear-latent variable models, Econometric Theory 18, 297–232.
Satorra, A. & P.M. Bentler (1991): Goodness-of-fit test under IV estimation: asymptotic robustness of a NT test statistic. In Proceedings of the Fifth International Symposium on Applied Stochastic Models and Data Analysis. R. Gutierrez y M.J. Valderrama (Edts.) (pp. 555–567 ). World Scientific: London.
Satorra, A. Sc Bentler, P.M. (1994): Corrections to test statistics and standard errors in covariance structure analysis, In: Latent variable analysis in developmental research, A. van Eye and C.C. Clogg, (edts), pp. 285–305, SAGE Publications: Thousand Oaks, CA
Satorra, A. Sc Neudecker, H. (1997): On the asymptotic distribution of x2 based test statistics in the analysis of moment structural models, Bulletin of the International Statistical Institute (Proceedings, Actes, Book 2 ), pp. 251–254.
Satorra, A. Sc W.E. Saris (1985): Power of the likelihood ratio test in covariance structure analysis, Psychometrika 50, 83–89.
Stroud, T.W.F. (1972): Fixed alternatives and Wald’s formulation of the non-central asymptotic behavior of the likelihood ratio statistic, The Annals of Statistics, 43, 447–454.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2003 Springer Japan
About this paper
Cite this paper
Satorra, A. (2003). Power of χ2 Goodness-of-fit Tests in Structural Equation Models: the Case of Non-Normal Data. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_5
Download citation
DOI: https://doi.org/10.1007/978-4-431-66996-8_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66998-2
Online ISBN: 978-4-431-66996-8
eBook Packages: Springer Book Archive