When I have a two mixed models (lme function) with different df then ANOVA summary shows the p-value of likelihood ratio test as following :
Model df AIC BIC logLik Test L.Ratio p-value
fsModel3 1 14 -1429.098 -1367.059 728.5489
fsModel1 2 15 -1428.438 -1361.968 729.2192 1 vs 2 1.340498 0.2469
However, when I compared two or more models with the same df ( same random effect ) only different fixed effects ( same number of fixed effects ). My ANOVA table look like this :
Model df AIC BIC logLik
fsModel2 1 14 -1428.469 -1366.431 728.2346
fsModel3 2 14 -1429.098 -1367.059 728.5489
fsModel4 3 14 -1428.886 -1366.847 728.4429
My intuition tell me that then I am selecting the model with the lowest AIC/BIC. Am I right ? Is there a reason why the L.Ratio can't be calculated on models with same df ?