Effects of sample size, model specification and factor loadings on the GFI in confirmatory factor analysis

The goodness-of-fit index [Jöreskog, K. G. & Sörbom, D. (1984). LISREL VI users guide (3rd ed.). Moorsville, IN: Scientific Software]is commonly used in confirmatory factor analysis to assess the discrepancy between the sample covariance matrix and the covariance matrix implied by the fitted model. It is common for values greater than 0.9 to be considered an indication of acceptable model fit. This Monte Carlo study examined the performance of the GFI under conditions of varying sample size, model specification and magnitude of factor loadings. It was found that these three factors influenced GFI independently, and jointly in terms of interactions. It was concluded that a cut-off value of 0.9 would result in an unacceptable number of misspecified models being accepted.