02-08-2017 01:23 AM
Recently, I fitted a fitted a relatively straightforward group by time model to some trial data:
proc MIXED DATA=…; class ID cond occas; model CESD= cond occas cond*occas/ DDFM=SATTERTH SOLUTION; repeated occas / type=un Rcorr subject=ID;
I decided to reverse the time variable (cond) to improve parameter interpretability. As expected, this produced appropriately changed model parameters but fit was identical in every other way except that some of degrees of freedom for tests of fixed effects and parameter estimates, calculated according to the Satterthwaite approximation were quite different. While the differences didn't change the outcome of significance tests in this case, there could be cases where this is not the case.
I can understand that with some R matrix structures and some recodings of the time factor, the model fit would differ and df would change, but I used an unstructured matrix: essentially the same model was being fit. I've looked at the math behind the Satterthwaite approximation can't see why reversing the categories would matter.
I'd be very interested if anyone can shed some light on this.
02-08-2017 11:03 AM
You may be running into near singularities with the UN parameterization. Try running both with an unstructured matrix using type=CHOL, which should be more stable.
I would guess that the diagnonals on the two UN runs are not identical, so that the df comes out different. Is that the case?
02-09-2017 03:49 AM
Thanks for your ideas Steve.
I don't think this is a numerical problem. The R matrix is robustly positive-definitive and the four occasions of measurement are only moderately correlated. I can't see how to specify a cholesky R matrix-it isn't one of the obvious options.
The UN R matrix is different with the time factor reversed but is simply reflected about the off diagonal, i.e., UN(1,1) becomes UN(4,4) and vice versa etc, but other than this transformation, it's the same structure yielding the same parameter estimates and I'd expect the df to be the same.
While it's not very informative, I've replicated the effect fitting the same model using the SPSS mixed procedure which also offers Satterthwaite dfs - same results and same differences with reversed time. I plan to try a few other datasets to see how repeatable the phenomenon is.