Fitting a particular Gaussian model

Question

Using R or SAS, I want to fit the following Gaussian model: $$ \begin{pmatrix} y_{1j1} \\ y_{1j2} \\ y_{1j3} \\ y_{2j1} \\ y_{2j2} \\ y_{2j3} \end{pmatrix} \sim_{\text{i.i.d.}} {\cal N} \left( \begin{pmatrix} \mu_1 \\ \mu_1 \\ \mu_1 \\ \mu_2 \\ \mu_2 \\ \mu_2 \end{pmatrix} , \Sigma \right), j=1, \ldots n $$ with covariance matrix having the following structure: $$ \Sigma = \begin{pmatrix} \Sigma_0 & M \\ M & \Sigma_0 \end{pmatrix} $$ with $\Sigma_0$ a "compound symmetry" (exchangeable) covariance matrix and $M=\delta \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$, $\delta \in \mathbb{R}$. Importantly, I need a general exchangeable matrix $\Sigma_0$, with possibly negative correlation.

EDIT: In view of some comments (and even an answer) given below I should add a precision: I am not a beginner with PROC MIXED in SAS and nlme in R, and I know how to consult the documentations. But in spite of my experience I am not able to fit this model.

Answer 1

You haven't told us how many data points you have. You need a certain number for the parameters to be estimable. I don't think that SAS has a proc that fits multivariate distributions per se but if you were using proc mixed and y is in the model these parameters would be calculated and could be printed out. You would have to specify the covariance structure.