I'm trying to fit a mixed model with an exponential autocorrelation structure. The key part of the code is:
model lnwater = year
/ solution outp = fitspreds ;
random int year / sub=OBJECTID solution;
repeated / type=sp(exp)(julian) local sub=OBJECTID;
Where julian records the normalized julian date when measurements were taken, and year is the normalized year in which the data was recorded.
After I fit the model I get a message in the log that "NOTE: Estimated G matrix is not positive definite.", and SAS reports a fixed effect estimate of zero for the yearnew variable. For the G-matrix to be zero would mean that one of the random effects was irrelevant, but the only random effect in the model is year, so it looks like this result is telling me that year has no effect on the fixed or the random effects. Is this a correct way to interpret this? Can anyone suggest a better autocorrelation structure for this model-- I'm fairly sure that there should be some autocorrelation, as I'm modeling change in water level in some lakes between years. I could be wrong, of course...
PS I've also tried using AR(1) autocorrelation using the following command in the above model:
repeated / type=AR(1) sub=OBJECTID;
This gave me some reasonable-looking numbers, but I don't know how to tell SAS to use the julian variable to measure distance between points with AR(1). Can anyone help me on that?