Repeating AIC values with proc Glimmix in SAS

Question

I am comparing several models using PROC GLIMMIX, and many of my models are coming out with the exact same AIC value, even when new variables are added. For example, the code below yields the exact same AIC values, even though the variables are changing. Is this a problem with the code or with my understanding of AIC? I'm new to both SAS and generalized linear mixed models.

proc glimmix data=data1;
class x1 x4;
model Response = x1 x2 x3;
random x1;

proc glimmix data=data1;
class x1 x4;
model Response = x1 x2;
random x1;

proc glimmix data=data1;
class x1 x4;
model Response = x1 x3;
random x1;

proc glimmix data=data1;
class x1 x4;
model Response = x1;
random x1;

Any help you could provide would be much appreciated!

Answer 1

Three things come to mind:

1) In GLIMMIX, the fixed effects factors are specified on the MODEL statement, and the random effects factors are specified on the RANDOM statement. If X1 is random, it should not be included in the MODEL statement.

2) For these models that assume a normal distribution, GLIMMIX is using REML by default. To compare models using AIC, estimation must use a true maximum likelihood method, which REML is not. Use METHOD=LAPLACE.

3) To compare models using AIC, all models must use exactly the same set of response data. In the first model, the response is RESPONSE; for the others, it is GULL.