# How to interpret increase to AIC and adjusted r-squared?

I understand adjusted r-squared and AIC can be used to select an ideal model from a group. Higher AIC is worse but higher ar2 is better.

After adding a categorical variable to an OLS model, my adjusted r-squared went up and so did my AIC. Some of the categorical values are associated with a high p-value.

Three questions:

1. How can I interpret the discrepancy?
2. I tend to favor including the variable because of the ar2 effect. Is this a fair justification?
3. Is either metric generally preferred among AR2 and AIC?
• Why are you choosing between these models? Why don't you just have one model that you fit, and that's the model?
– Dave
Oct 13 '21 at 17:29
• See this thread regarding the lack of justification for $R^2_{adj.}$ as a model selection criterion. Oct 13 '21 at 17:32
• Thanks @RichardHardy! @Dave my use case is identifying the most important features (eg forward selection/backwards elimination) Oct 13 '21 at 17:53
• – Dave
Oct 13 '21 at 17:57
• @Dave I have theory-based supervision of the variable pool, I'm not maximizing r-squared, I am performing cross-validation...I think those objections are largely leveraged against some other form of selection. Do you have anything in the way of positive, preferred suggestion? Oct 13 '21 at 18:01