Well, now this is embarassing. I just worked out a series of forgettings on my part that led to my wasting of folks’ time here. First, in the recent entries here I forgot that in the post that kicked off the thread I’d worked out that my code and that of SUG 1.13 were identical (as @jsocolar poipnts out), and it’s the data declaration that I thought implied a difference/identifiability issue. Furthermore, this latter was itself forgetting that SUG 1.13 uses data/terminology that’s different-but-deceptively-similar to my typical data/terminology.
Specifically, it speaks of individuals associated with individual-level predictors, and individuals are lumped together in groups that are in turn associated with group-level predictors. Importantly, there’s only one observation of each individual.
I Ip1 Ip2 ... G Gp1 Gp2 ...
i1 + - ... g1 + - ...
i2 + - ... g1 + - ... // i1 & i2 share the same Ip's
i3 - + ... g1 + - ...
i4 - + ... g1 + - ... // i1:i4 share the same Gp's; i3 & i4 share the same Ip's
i5 + - ... g2 - + ...
i6 + - ... g2 - + ... // i5 & i6 share the same Ip's
i7 - + ... g2 - + ...
i8 - + ... g2 - + ... // i5:i8 share the same Gp's; i7 & i8 share the same Ip's
Whereas the way I typically have data structured, I still speak of individuals and groups, but of within-individual predictors and between-group predictors. This works out to meaning what SUG 1.13 calls a group, I call an individual, and what SUG 1.13 calls an individual, I call a trial:
t Ip1 Ip2 ... I Gp1 Gp2 ...
t1 + - ... i1 + - ...
t2 + - ... i1 + - ... // t1 & t2 share the same Ip's
t3 - + ... i1 + - ...
t4 - + ... i1 + - ... // t1:t4 share the same Gp's; t3 & t4 share the same Ip's
t5 + - ... i2 - + ...
t6 + - ... i2 - + ... // t5 & t6 share the same Ip's
t7 - + ... i2 - + ...
t8 - + ... i2 - + ... // t5:t8 share the same Gp's; t7 & t8 share the same Ip's
Using my terminology, if there were only one observation per combination of individual and within-individual predictors, then there would be identifiability issues as I was concerned about at the outset of this thread and the alternative multivariate I posted would be more appropriate. But I see now that this isn’t an issue for the data as discussed in SUG 1.13 and I was just forgetting the terminology-mapping 🤦