Variance matrix with equal diagonal entries in PROC MIXED Is it possible to specify a variance matrix for the random effects in PROC MIXED with the only restriction that the diagonal entries are equal ? I took a look in the help and I have not found, but this seems strange because such a variance structure is rather natural in some applications. 
(EDIT) Consider for instance such a dataset:
> dat
   Subject Dose   y
1        1    A  10
2        1    A  11
3        1    A  12
4        1    B  30
5        1    B  31
6        1    B  32
7        1    C 100
8        1    C 101
9        1    C 102
10       2    A  11
11       2    A  14
12       2    A  13
13       2    B  33
14       2    B  37
15       2    B  36
16       2    C 105
17       2    C 110
18       2    C 109
19       3    A   9
20       3    A  11
21       3    A  12
22       3    B  30
23       3    B  35
24       3    B  32
25       3    C 115
26       3    C 101
27       3    C 102


and the following model:
PROC MIXED DATA=dat ;
    CLASS SUBJECT DOSE ;
    MODEL y = DOSE ;
    RANDOM DOSE / subject=SUBJECT type=MYMATRIX ;
RUN; QUIT;

I want a matrix "MYMATRIX" with the same variance for each level of the DOSE factor, but not a compound symmetry matrix because the correlation between the means of the levels are different.
(EDIT2) The mathematical meaning of this model is the following one. Denoting by $i$ the index for the dose level and by $j$ the index for the subject, one has $$(y_{ijk} | \mu_{ij}) \sim_{\text{iid}} {\cal N}(\mu_{ij}, \sigma^2_w), \quad k=1, \ldots, 3 \quad \text{ for all } i,j$$ and $$ \begin{pmatrix} 
\mu_{1j} \\
\mu_{2j} \\
\mu_{3j}  
 \end{pmatrix}
 \sim_{\text{iid}} 
 {\cal N}_3
 \left( 
 \begin{pmatrix} 
\mu_1 \\
\mu_2 \\ 
\mu_3 
 \end{pmatrix}, 
 G
 \right), \quad j=1, \ldots, 3$$
The diagonal entries of the $G$ matrix are the between variances for each level of the dose. I want $G$ to be of the form $$G=\begin{pmatrix} \sigma^2_b & \sigma_{12} & \sigma_{13} \\  \sigma_{12} & \sigma^2_b & \sigma_{23} \\ \sigma_{13} &   \sigma_{23} & \sigma^2_b \end{pmatrix}$$
 A: If I do understand your model, you have a random dose effect for each subject:
$$ \gamma = \left(
\begin{array}{c}
\gamma_{1A} \\
\gamma_{1B} \\
\gamma_{1C} \\
\gamma_{2A} \\
\gamma_{2B} \\
\gamma_{2C} \\
\gamma_{3A} \\
\gamma_{3B} \\
\gamma_{3C} \\
\end{array}
\right), $$
and $G = \textrm{Var}(\gamma)$ has a block-diagonal structure with identical blocks over subjects:
$$ G = \left(
\begin{array}{ccc}
\star & \star & \star & 0 & 0 & 0 & 0 & 0 & 0 \\
\star & \star & \star & 0 & 0 & 0 & 0 & 0 & 0 \\
\star & \star & \star & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & \star & \star & \star & 0 & 0 & 0 \\
0 & 0 & 0 & \star & \star & \star & 0 & 0 & 0 \\
0 & 0 & 0 & \star & \star & \star & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & \star & \star & \star \\
0 & 0 & 0 & 0 & 0 & 0 & \star & \star & \star \\
0 & 0 & 0 & 0 & 0 & 0 & \star & \star & \star 
\end{array}
\right). $$
Now, the type option specifies the covariance structure of each block. If you specify type=vc (default) then each block will have the form
$$ \left(
\begin{array}{ccc}
\star & \star & \star \\
\star & \star & \star \\
\star & \star & \star 
\end{array}
\right) = \left(
\begin{array}{ccc}
\sigma_{_{G}}^{2} & 0 & 0 \\
0 & \sigma_{_{G}}^{2} & 0 \\
0 & 0 & \sigma_{_{G}}^{2} 
\end{array}
\right), $$
where $\sigma_{_{G}}^{2}$ is the single parameter of $G$ to be estimated. If you specify type=toep then
$$ \left(
\begin{array}{ccc}
\star & \star & \star \\
\star & \star & \star \\
\star & \star & \star 
\end{array}
\right) = \sigma_{_{G}}^{2} \left(
\begin{array}{ccc}
1 & \rho_1 & \rho_2 \\
\rho_1 & 1 & \rho_1 \\
\rho_2 & \rho_1 & 1
\end{array}
\right), $$
and now there are three parameters in $G$ to be estimated.
$$$$
If this does not fit your requirement, then you might want to have a look at the group option: all observations having the same level of the group effect have the same covariance parameters.
