I'm looking at the description of the data, and I wonder if just some minor changes might help. Since obviously each animal is not seen on each farm, the subject effect should be OK, unless for some unknown reason the ID for animal is not unique to the farm.
Second, I think leaving out one term may be affecting what is happening--something involving farm by HLI. The models I see here don't have this effect, and it may be what you are seeing in the plots. Of course, this may be a matter of complete confounding, and is covered by the farm effect Have you tried:
proc mixed data=x
class animal farm genotype;
model mean_rr = genotype HLI genotype*HLI /solution htype=1;
random intercept/subject=farm;
random int HLI gentoype*HLI / subject=animal(farm) solution; run;
I certainly see nothing wrong with the type 1 tests, since most of the work is regression based, but that is just my opinion.
Have you tried this in GLIMMIX, with method=quad? The documentation (at least for 9.2) looks like it has something like this in the example under TECH=.
Good luck.
Steve Denham
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