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In Randall E. Schumacher's and Richard E. Lomax's book "Beginer guide to SEM", the writers keep saying that if non-normality is sensed, where you can't use ML, you can go for GLS/ADF/WLS.

But isnt GLS main assumption is normality? I initially thought it's editing mistake in the book, but such concept is repeated many times in the book.

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You would normally choose GLS over ML for computational efficiency, or, with a very small sample, the biased-ness of ML.

For severe departures from normality, you would not usually choose ML or GLS. The following table is taken from the seminal book by one of the godfathers of SEM, Kenneth Bollen, "Structural Equations with Latent Variables" , Wiley, 1989

Table 9.1 Properties of ML and GLS estimators with and without multinormal
observed variables:
               Consistency    Asymptotic      Asymptotic Cov-    Chi-square
                              Efficiency      ariance Matrix     Statistic
-------------------------------------------------------------------------------
Multinormal        Yes           Yes             Correct          Correct
No Kurtosis        Yes           Yes             Correct          Correct               
Elliptical         Yes           Yes            Incorrect        Incorrect
Arbitrary          Yes           No             Incorrect        Incorrect

https://onlinelibrary.wiley.com/doi/book/10.1002/9781118619179

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  • $\begingroup$ @Hussain does this answer your question ? If so, please consider marking it as the accepted answer. If not then please let us know why $\endgroup$ – Robert Long Sep 26 '20 at 18:21

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