TY - JOUR
T1 - Bartlett correction of test statistics in structural equation modeling
AU - Okada, Kensuke
AU - Hosino, Takahiro
AU - Shigemasu, Kazuo
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2007/9
Y1 - 2007/9
N2 - Model selection is one of the most important steps in the application of structural equation modeling (SEM). In this process, the likelihood ratio test statistic, T, is a commonly employed index. Hypothesis testing can be performed on the basis that T asymptotically follows the χ2 distribution. Various fit indices have been proposed, most of which are based on the assumption that T asymptotically follows the χ2 distribution. When the size of the sample is small, however, the distribution of T deviates considerably from the χ2 distribution. This problem, especially pronounced when there is a large number of indicators per factor, is serious because it violates the theoretical justification of utilizing for model selection not only T, but also many other fit indices. In the present article, we propose a Bartlett correction of T to improve its approximation to the χ2 distribution. When the efficacy of our method was evaluated by Monte Carlo simulation, the results showed that this method was superior to the current standard.
AB - Model selection is one of the most important steps in the application of structural equation modeling (SEM). In this process, the likelihood ratio test statistic, T, is a commonly employed index. Hypothesis testing can be performed on the basis that T asymptotically follows the χ2 distribution. Various fit indices have been proposed, most of which are based on the assumption that T asymptotically follows the χ2 distribution. When the size of the sample is small, however, the distribution of T deviates considerably from the χ2 distribution. This problem, especially pronounced when there is a large number of indicators per factor, is serious because it violates the theoretical justification of utilizing for model selection not only T, but also many other fit indices. In the present article, we propose a Bartlett correction of T to improve its approximation to the χ2 distribution. When the efficacy of our method was evaluated by Monte Carlo simulation, the results showed that this method was superior to the current standard.
KW - Bartlett correction
KW - Goodness of fit
KW - Likelihood ratio test
KW - Structural equation modeling
UR - http://www.scopus.com/inward/record.url?scp=38149056460&partnerID=8YFLogxK
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U2 - 10.5926/jjep1953.55.3_382
DO - 10.5926/jjep1953.55.3_382
M3 - Article
AN - SCOPUS:38149056460
VL - 55
SP - 382
EP - 392
JO - Japanese Journal of Educational Psychology
JF - Japanese Journal of Educational Psychology
SN - 0021-5015
IS - 3
ER -