F Tests for Mean and Covariance Structure Analysis

Ke-Hai Yuan and Peter M. Bentler

Journal of Educational and Behavioral Statistics, 1999, vol. 24, issue 3, 225-243

Abstract: Covariance structure analysis is used for inference and for dimension reduction with multivariate data. When data are not normally distributed, the asymptotic distribution free (ADF) method is often used to fit a proposed model. The ADF test statistic is asymptotically distributed as a chi-square variate. Experience with real data indicates that the ADF statistic tends to reject theoretically meaningful models. Empirical simulation shows that the ADF statistic rejects correct models too often for all but impractically large sample sizes. By comparing mean and covariance structure analysis with its analogue in the multivariate linear model, we propose some modified ADF test statistics whose distributions are approximated by F distributions. Empirical studies show that the distributions of the new statistics are more closely approximated by F distributions than are the original ADF statistics when referred to chi-square distributions. Detailed analysis indicates why the ADF statistic fails on large models and why F tests and corrections give better results. Implications for power analysis and model tests in other areas are discussed.

Keywords: asymptotic distribution free; F-test; Hotelling's T2; mean and covariance structure ' (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://journals.sagepub.com/doi/10.3102/10769986024003225 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:24:y:1999:i:3:p:225-243

DOI: 10.3102/10769986024003225

Access Statistics for this article

More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().