If this helps anyone answering my question about an equivalent model
statement to SAS proc mixed,
u + Alpha_1(i) + Alpha_2(i) + M_{i}+ e_m(i) where
u = grand mean
Alpha = polygenic effects random (13 of them)
M = QTL effect fixed
e_m = random error
proc mixed data=a;
model trait = m1;
random alpha1-alpha13/type=TOEP(1);
I found this explanation of toeplitz:
TYPE=TOEP<(q)>
specifies a banded Toeplitz structure. This can be viewed as a
moving-average structure with order equal to q-1. The TYPE=TOEP
option is a full Toeplitz matrix, which can be viewed as an
autoregressive structure with order equal to the dimension of
the matrix. The specification TYPE=TOEP(1) is the same as , s^2 I,
where I is an identity matrix, and it can be useful for specifying
the same variance component for several effects.
