Modified Distribution-Free Goodness-of-Fit Test Statistic
So Yeon Chun (),
Michael W. Browne () and
Alexander Shapiro ()
Additional contact information
Michael W. Browne: Ohio State University
Alexander Shapiro: Georgia Institute of Technology
Psychometrika, 2018, vol. 83, issue 1, 48-66
Abstract Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62–83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.
Keywords: covariance structures; distribution-free test statistic; asymptotics; Chi-square distribution; ill-conditioned problem (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s11336-017-9574-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:83:y:2018:i:1:d:10.1007_s11336-017-9574-9
Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2
Access Statistics for this article
Psychometrika is currently edited by Irini Moustaki
More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla ().