I want to choose the best random structure for my mixed-effects model. I have compared four models: without a random part, random intercept, random intercept and slope, and random effects:
gls0<-gls(time.dep~exper*group*fat*FL, method="REML",data=test) lme1<-lme(time.dep~exper*group*fat*FL, random=~1|ring,data=test,method="REML") lme2<-lme(time.dep~exper*group*fat*FL, random=~exper|ring,data=test,method="REML") lme3<-lme(time.dep~1, random=~1|ring,data=test,method="REML") AIC(gls0, lme1, lme2, lme3) df AIC gls0 17 36.34948 lme1 18 38.34948 lme2 20 36.53359 lme3 3 -60.41729
I suppose it is obvious that random effects model has the smallest AIC, since it has no parameters in the fixed part. But this model has the highest log-likelihood as well. Does it mean that my response variable depends mostly on the random variable (and if yes, how should I interpret this result, and what should I do with other explanatory variables)? Or should I choose the model without random structure at all (but then how should I deal with pseudoreplication)?