2 NEW GOODNESS-OF-FIT INDEXES FOR COVARIANCE MATRICES WITH LINEAR STRUCTURES

Two new indices each based on two different methods of estimating the population covariance matrix SIGMA are derived. Certain algebraic results on these indices are also reported. A case study has been presented to show how the proposed indices in comparison to Joreskog-Sorbom's GFI are more efficient in detecting the 'best' structure out of 13 competing structures hypothesized for the Graduate Record Examination data. Algebraically it has also been shown that the limiting value of GFI fails to reach the desired value of zero under model misspecification. A Monte Carlo study also shows that with increasing sample size the proposed indices as compared to others show more and more sensitivity to model misspecification. Other advantages of the indices as measures of structural closeness of SIGMA to S are discussed.