I am comparing three relatively simple GLMs having a Gamma distribution with AIC and BIC. The aim is to identify the effects of fertilizers (fdung), year and site on biomass of a specific grass species. Hence, the aim is not to predict new values but merely to identify the effects of the three factors.
Here are the models used:
res1 <- glm((Biomass..g.m².) ~ fdung * fyear * fblock, family=Gamma(link="identity")) res2 <- glm((Biomass..g.m².) ~ fdung * fyear + fblock, family=Gamma(link="identity")) res3 <- glm((Biomass..g.m².) ~ fdung + fyear + fblock, family=Gamma(link="identity"))
I expect the third model to be the most simplistic one and want to confirm this by an information criterion. However, when looking at AIC and BIC I get this output.
AIC(res1,res2,res3) BIC(result1,res2,res3) df AIC df BIC res1 49 5271.617 res1 49 5465.198 res2 16 5334.234 res2 16 5397.44 res3 10 5331.253 res3 10 5370.760
For AIC, the most complex model is "best" and for BIC the one with fewest df is best. I am thinking that with regard to my aim (identify effects on biomass) I should trust BIC.
Am I wrong here with my conclusion?
I already tried mixed effect models with the fblock as random factor but then the model with the Gamma distribution did not work any more and also I could not use fblock as fixed effect any more (leading to NAs for fblock), but this is not part of my question.