Bartlett correction of test statistics in structural equation modeling

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.