Asymptotic Relative Efficiency Comparison for some Fit Indices in Structural Equation Modeling

There are many fit statistics used in the structural equation modeling, and new ones are consistently being developed. Because of the variety of fit statistics, it is very important to be able to decide which fit statistics are appropriate to use in studies. When comparing any two statistics, the asymptotic relative efficiency (ARE) between them is used. The ARE can use as a power of the fit indices is one of the familiar optimal criteria. It is frequently more convenient, and also more suggestive, to use a measure of relative merit called the relative efficiency. This study aimed to compare of fit indices using Fraser’s asymptotic relative efficiency. The data sets were derived from the multivariate normal distribution using the mean vector and covariance matrix. It was determined that the most efficient fit indices in terms of asymptotic relative efficiency were Z-Test of Wilson & Hilferty (W&H), Root Mean Square Error of Approximation (RMSEA), and Chi-Square indices, respectively.