# getting same AIC (or any other comparison criterion values) even after using different var-cov structures when comparing GLMM models

We are comparing models that are GLMM , in which for each one of them the fixed effects are exactly the same, but in the random effects portion, we used different variance-covariance structures (i.e Heterogeneous unstructured, Heterogeneous diagonal,Heterogeneous Toeplitz.) When we are using different variance covariance structures we are seeing same AICc values for all the models using: ICtab(newModel1,newModel4,newModel5,diag1,type="AICc",base=TRUE, delta=TRUE, weights=TRUE)R command. Results For all 4 models:

• AICc= -374.6
• dAICc= 0.0
• df= 16
• weight= 0.25

At the same time, we are seeing the same log-likelihood for all models as well. We are using the function glmmTMB to write our models in R. Why are we seeing same values if we expect the number of paramteres to vary depending on the var-cov structure ? List of models used for comparison below

newModel5 <- glmmTMB(log10(Rrs_max) ~ log10(Baseline) + cdose*microbiota_reordered+ microbiota_reordered*TXT_reordered + diag(cdose+1 | Mouse),
data=d_e, family="gaussian",REML=TRUE)

diag1<- glmmTMB(log10(Rrs_max) ~ log10(Baseline) + cdose*microbiota_reordered+ microbiota_reordered*TXT_reordered +
diag(cdose+0 | Mouse) + (1|Mouse),
data=d_e, family="gaussian",REML=TRUE)

newModel4 <- glmmTMB(log10(Rrs_max) ~ log10(Baseline) + cdose*microbiota_reordered + microbiota_reordered*TXT_reordered +
toep(cdose+0 | Mouse) + (1|Mouse),
data=d_e, family="gaussian",REML=TRUE)

newModel1 <- glmmTMB(log10(Rrs_max) ~ log10(Baseline) + cdose*microbiota_reordered + microbiota_reordered*TXT_reordered +
us(cdose+0 | Mouse) + (1|Mouse),
data=d_e, family="gaussian",REML=TRUE)


Any feedback would be much appreciated. Thank you in advanced