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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.

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