The study design was for a dental in vitro implant study. There were 3 scanners, and there were 3 models they would like to compare. Basically they used each scanner to scan each of the model 10 times. They would like to compare the 3*3=9 means. The variance among groups were significantly different, so I included a random effect of _residual_. My question was whether I should include scanner*model effect in the random effects? If I included the two random effects as I list below, the estimated G matrix is not positive definite. Should I use the first random effect or second random effect? Thank you.
proc glimmix data=waleed1;
class scanner model;
model Total_Dist = scanner model scanner*model/ solution ddfm=kr ;
random _residual_ / group=scanner*model;
random scanner*model;
lsmeans scanner*model/slice=scanner diff adjust=tukey;
run;