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Kline (2015) writes:

Two methods for continuous endogenous variables with multivariate normal distributions include generalized least squares (GLS) and unweighted least squares (ULS). The ULS method is actually a type of OLS estimation that minimizes the sum of squared differences between sample and predicted covariances. It can generate unbiased estimates across random samples, but it is not as efficient as the ML method (Kaplan, 2009). A drawback of the ULS method is the requirement that all observed variables have the same scale (i.e., the method is neither scale free nor scale invariant).

Why does ULS have this requirement while GLS doesn't? I understand from this answer that ULS and GLS are basically very similar, but the latter weights highly communal variables as more important in fitting.

Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford publications. Chicago

chl
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    Isn't ULS really just the good old OLS (ordinary least squares)? If so, it would be simpler to use the common name for it (OLS) instead of making up a new one (ULS). – Richard Hardy Apr 05 '17 at 15:15
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    @Richard the quoted description clearly indicates that ULS is not OLS. Indeed, because the units of a covariance are the product of the units of its two components, if the observed variables have different units then so will their various covariances, whence the squared differences will be in different units, making the meaning of their summation at best problematic and at worst deceptive. – whuber Apr 05 '17 at 15:48
  • @whuber, mea culpa, I was sloppy and did not read carefully. Thanks for noting. – Richard Hardy Apr 05 '17 at 15:55
  • Did you take a look at the formulas, e.g. here: http://users.ugent.be/~yrosseel/lavaan/evermann_slides.pdf – Jeremy Miles Apr 05 '17 at 18:45

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