Many thanks to Roberto G. Gutierrez, StataCorp for his response to fit
the model as:
y(i12) = u(i2) - u(i1) + e(i12) = u(i2) + v(i12)
y(i23) = -u(i2) + u(i3) + e(i23) = -u(i2) + v(i23)
where
v(i12) = -u(i1) + e(i12)
v(i23) = u(i3) + e(i23)
Unfortunately using this approach to fitting the model doesn't give the
same estimates as using proc mixed in SAS. I believe this is because
using the parametrization proposed by Roberto, var(v) is not constrained
to be at least as large as var(u), or equivalently, var(e) is allowed to
be negative.
In my small dataset unfortunately relaxing the constraint that
var(v)>=var(u) results in a model fit with var(v)<var(u), which implies
var(e)<0 and different variance estimates than I get in proc mixed. I
look forward to the new collinear option in xtmixed, or an alternative
workaround using xtmixed.
Many thanks
Jonathan
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