Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables

Ke-Hai Yuan (), Yubin Tian and Hirokazu Yanagihara

Psychometrika, 2015, vol. 80, issue 2, 379-405

Abstract: Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is T ML , a slight modification to the likelihood ratio statistic. Under normality assumption, T ML approximately follows a chi-square distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T ML rejects the correct model too often when p is not too small. Various corrections to T ML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T ML so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to T ML , and they control type I errors reasonably well whenever N≥max(50,2p). The formulations of the empirically corrected statistics are further used to predict type I errors of T ML as reported in the literature, and they perform well. Copyright The Psychometric Society 2015

Keywords: Bartlett correction; Bayesian information criterion; maximum likelihood; type I errors (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11336-013-9386-5 (text/html)
Access to full text is restricted to subscribers.

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:spr:psycho:v:80:y:2015:i:2:p:379-405

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-013-9386-5

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 () and Springer Nature Abstracting and Indexing ().