How do AIC and BIC help with model selection, and why can't I just use R-squared?

R-squared measures goodness of fit — how much variance your model explains. The problem: R-squared ALWAYS increases when you add variables, even useless ones. This makes it a terrible tool for model selection because it rewards complexity without penalizing overfitting.

The Overfitting Problem:

Adding a random noise variable to your model will increase R-squared slightly (in-sample) but degrade out-of-sample prediction. You need a metric that balances fit against complexity.

AIC (Akaike Information Criterion):

AIC = 2k - 2ln(L)

Where k = number of parameters, L = maximum likelihood. Lower AIC is better. The 2k term penalizes model complexity.

BIC (Bayesian Information Criterion):

BIC = k*ln(n) - 2ln(L)

Where n = number of observations. Lower BIC is better. BIC penalizes complexity MORE heavily than AIC because ln(n) > 2 for n > 8 (which is always true in practice).

Key Differences:

When They Disagree:

AIC and BIC often recommend different models. AIC prefers slightly more complex models (better predictions), while BIC prefers simpler ones (more interpretable).

Practical Example:

You're modeling quarterly corporate earnings growth using potential predictors: GDP growth, interest rates, credit spreads, oil prices, and consumer confidence.

• R-squared picks Model D (always picks the fullest model)
• AIC picks Model C (best balance of fit and parsimony)
• BIC picks Model B (most parsimonious adequate model)

For forecasting, you'd likely go with Model C (AIC). For understanding the key drivers, Model B (BIC) provides a cleaner story.

Exam Tip: If a CFA exam question asks which model to select using a given criterion, simply pick the model with the LOWEST AIC or BIC value. No calculation needed — just comparison.

Practice model selection problems in our CFA Level II question bank.