What percentage decrease in AIC is significant?

Question

I have two models with AIC values 2500 and 2590.

So.... Is that significant? What percentage decrease is usually considered significant?

Answer 1

AICs are not measured on a multiplicative scale, but on an additive one. In addition, the constant offset is not overly important, so it is sometimes implemented differently.

You need to look at additive differences between AICs. In your case, one model has an AIC that is $90$ below the other's. That is very strong evidence that the model with the smaller AIC is a better description of the data. You'd come to exactly the same conclusion if the one model's AIC were $-120$ and the other's $-30$.

Typically, you'd say that an AIC difference $\Delta\text{AIC}<2$ is little evidence, $2\leq\Delta\text{AIC}<5$ is weak evidence, $5\leq\Delta\text{AIC}<10$ is medium evidence and $10\leq\Delta\text{AIC}$ is strong evidence in favor of the model with the lower AIC value.

For more information, see Burnham & Anderson, Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach, and Burnham & Anderson, "Multimodel Inference: Understanding AIC and BIC in Model Selection" (2004, Sociological Methods & Research).