I read discussions on how the random intercept model is not equivalent to the compound symmetry. I understand, that the CS model allows for a case, where the responses are more similar across subjects than "within subjects", but there is one thing I don't understand - "parameter space". In addition to the simplified answer, it was said, that "both methods differ in parameter spaces". What does it mean? What kind of parameters is mentioned?
For example: Is it possible to fit mixed-models via gls?
Also beware of the difference in parameter spaces: the parameter space for the compound symmetry model is bigger than it is for the random intercept model. The random-effect variance is necessarily non-negative which leads to a non-negative corr but the corr in the compound symmetry model can also be negative (though not too much). So while two model fits can be equivalent (if ρ≥0) they need not be (if ρ<0) and strictly speaking the underlying models are not the same. – Rune H Christensen May 23 '18 at 6:35