What does it mean "they differ in parameter space" regarding the compound symmetry and random intercept model? 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

 A: Let's assume that we have two measurements per subject $i$. The random intercepts model postulates that for any $j$ and $j'$, the correlation between the outcome measurements $Y_{ij}$ and $Y_{ij'}$ is 
$$\mbox{cor}(Y_{ij}, Y_{ij'}) = \frac{\sigma_b^2}{\sigma_b^2 + \sigma^2},$$
where $\sigma_b^2$ is the variance of the random intercepts and $\sigma^2$ is the variance of the error terms. The important note is that this correlation cannot be negative. This is because both the numerator and denominator are non-negative because they involve variance terms that are restricted to be non-negative.
However, the general compound symmetry matrix postulates that the same correlation is
$$\mbox{cor}(Y_{ij}, Y_{ij'}) = \rho,$$
where $\rho$ can freely vary in the interval $(-1, 1)$.
Hence, if this correlation in your data is, say $-0.2$, then you can never get that with a random-intercepts model. The random-intercepts model would tell you that the correlation is zero (because this is the closest permissible value to the true value of $-0.2$).
