# Weird AIC weights in model averaging

I conducted AIC selection on a set of models, and isolated my top 3 models. I then calculated the AIC weights of each model, and got the values 0.99, 1.92e-14,and 6.9e-18. I never saw weight values that low, and am worried I might have screwed up somewhere.

Has anyone else seen AIC weights like this?

• What are the AIC values of these three models? What do you mean by AIC weights? Are you trying to obtain a linear combination of models where each model is weighted by its AIC value? (If not, consider updating the title to reflect what you are actually doing.) Nov 20, 2022 at 11:54

If your models differ in AICs by something on the order of 60, then yes, AIC weights (per Burnham & Anderson, Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach, 2002, which I'll assume you are referring to) on the order you note can occur. In R:

> AICs <- c(0,60,60)
> (delta_AICs <- AICs-min(AICs))
[1]  0 60 60
> exp(-0.5*delta_AICs)/sum(exp(-0.5*delta_AICs))
[1] 1.000000e+00 9.357623e-14 9.357623e-14


However, AIC differences of 60 would indicate that the model fits are enormously different. One would typically not consider a model with an AIC 60 larger than the best model. Which is precisely what your weights imply.

• Thank you for your answer, that makes a lot of sense! My AIC values do have differences of over 60, so that checks out.
– Cam
Nov 21, 2022 at 0:49