Two-term Edgeworth expansions of the distributions of fit indexes under fixed alternatives in covariance structure models

Asymptotic expansions of the distributions of thirteen fit indexes used in covariance structure analysts in practice are obtained. The fit indexes include the usual log likelihood ratio statistic for a posited model and the functions of this statistic and the corresponding statistic of the so-called baseline model of uncorrelated observed variables. The results are derived by the two-term Edgeworth expansion under fixed alternatives for possibly nonnormally distributed data. A numerical example using a misspecified factor analys model is shown to see the behavior of the asymptotic results in finite samples.