TY - JOUR

T1 - Bartlett correction of test statistics in structural equation modeling

AU - Okada, Kensuke

AU - Hosino, Takahiro

AU - Shigemasu, Kazuo

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

UR - http://www.scopus.com/inward/citedby.url?scp=38149056460&partnerID=8YFLogxK

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 -