Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses
AbstractThe normal distribution based likelihood ratio (LR) statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and covariance matrix as well as the model and sample size are always fixed. It is hard to justify the validity of the noncentral chi-square distribution for the resulting LR statistic even when data are normally distributed and sample size is large. By extending results in the literature, this paper develops normal distributions to describe the behavior of the LR statistic for mean and covariance structure analysis. A sequence of local alternative hypotheses is not necessary for the proposed distributions to be asymptotically valid. When the effect size is medium and above or when the model is not trivially misspecified, empirical results indicate that a refined normal distribution describes the behavior of the LR statistic better than the commonly used noncentral chi-square distribution, as measured by the Kolmogorov-Smirnov distance. Quantile-quantile plots are also provided to better understand the different distributions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 98 (2007)
Issue (Month): 6 (July)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ke-Hai Yuan & Peter Bentler, 2006. "Mean Comparison: Manifest Variable Versus Latent Variable," Psychometrika, Springer, vol. 71(1), pages 139-159, March.
- Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2005. "The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 237-264, October.
- Wakaki, Hirofumi & Eguchi, Shinto & Fujikoshi, Yasunori, 1990. "A class of tests for a general covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 313-325, February.
- Albert Satorra & Willem Saris, 1985. "Power of the likelihood ratio test in covariance structure analysis," Psychometrika, Springer, vol. 50(1), pages 83-90, March.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- James Steiger & Alexander Shapiro & Michael Browne, 1985. "On the multivariate asymptotic distribution of sequential Chi-square statistics," Psychometrika, Springer, vol. 50(3), pages 253-263, September.
- Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
- Shapiro, Alexander, 2009. "Asymptotic normality of test statistics under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 936-945, May.
- Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If references are entirely missing, you can add them using this form.