I've condudted a first order factor model (CFA) using AMOS and a second order factor model. I noticed that the fit indix (GFI) was included in the AMOS output for the first order model but it was missing in the second order model, why is that?
The GFI doesn't appear outside of LISREL because it doesn't work - it's way too liberal. Karl Joreskog tells a funny story that the early versions of LISREL only had the chi-square statistic and it was very unpopular because models were always rejected. He developed and implemented the GFI and every model fitted well, and LISREL became very popular. It's a good story, not sure how true it is.
This study shows that it's junk.
Shevlin, M., & Miles, J. N. V. (1998). Effects of sample size, model specification and factor loadings on the GFI in confirmatory factor analysis. Personality and Individual Differences, 25(1), 85–90. https://doi.org/10.1016/S0191-8869(98)00055-5