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Hox's Multilevel Analysis: Techniques and Applications states,

"Generalized Least Squares(GLS) estimates can be obtained from a Maximum Likelihood procedure by restricting the number of iterations to one."

I cant figure how it is so.

First of all, he doesn't state whether it's about ML or REML.

Second, as far as I know GLS is for error-variance-covariance structure. I know random intercept model has a equivalent model with fixed coefficients and error variance-covariance structure but I don't think it's possible for all Mixed model to have equivalent model with fixed coefficients and error variance-covariance structure. Is it right? or wrong?

So anyone can elaborate on them?

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  • $\begingroup$ It's very difficult to determine what it is you are asking here. I'd recommend rephrasing this and providing more detail. $\endgroup$ – StatsStudent Feb 17 '16 at 4:25
  • $\begingroup$ Well, it's just that i cant understand how "Generalized Least Squares(GLS) estimates can be obtained from a Maximum Likelihood procedure by restricting the number of iterations to one." is true. As far as I know, GLS is for the model without random effect... so how is it the ML with just one iteration is GLS??? $\endgroup$ – KH Kim Feb 17 '16 at 17:13
  • $\begingroup$ Of course we are talking about multilevel(mixed effect) model... $\endgroup$ – KH Kim Feb 17 '16 at 17:14
  • $\begingroup$ Got it. See my response below. $\endgroup$ – StatsStudent Feb 17 '16 at 18:27
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Maximum Likelihood procedures (like those in SAS) typically use as starting values, the OLS parameter estimates, so that is why setting iteration to 1 would work here.

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