期刊
PSYCHOMETRIKA
卷 80, 期 2, 页码 379-405出版社
SPRINGER
DOI: 10.1007/s11336-013-9386-5
关键词
Bartlett correction; Bayesian information criterion; maximum likelihood; type I errors
类别
资金
- National Natural Science Foundation of China [31271116]
- Ministry of Education, Science, Sports, and Culture of Japan [22650058]
- Grants-in-Aid for Scientific Research [25540012, 22650058] Funding Source: KAKEN
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 Na parts per thousand yenmax(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.
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