AIC vs BIC
🎯 Purpose¶
Choose between AIC and BIC for model selection based on your project goals.
📚 What They Measure¶
-
AIC (Akaike Information Criterion)
➔ Tradeoff between model fit and model complexity.
➔ Better for predictive accuracy focus. -
BIC (Bayesian Information Criterion)
➔ Stricter penalty for model complexity.
➔ Better for finding the simplest true model.
📈 AIC (Akaike Information Criterion)¶
- Minimizes information loss.
- Lighter penalty for model complexity.
- Prefers models with better predictive performance, even if slightly more complex.
- Lower AIC = better model.
- Best when: - Goal is strong prediction. - OK with adding extra features. - Example: Machine learning pipelines, forecasting.
📉 BIC (Bayesian Information Criterion)¶
- Penalizes model complexity more heavily.
- Stronger punishment as dataset size (n) grows.
- Prefers simpler, smaller models that may explain the data almost as well.
- Lower BIC = better model.
- Best when: - Goal is parsimony (simpler, interpretable models). - High penalty for adding unnecessary features. - Example: Scientific research, model interpretability.
🧠 Quick Decision Table¶
| Question | Use AIC | Use BIC |
|---|---|---|
| Focus on predictive accuracy | ✅ | ❌ |
| Focus on finding simplest true model | ❌ | ✅ |
| Accept slightly bigger models? | ✅ | ❌ |
| Penalize extra variables harshly? | ❌ | ✅ |
| Dataset is large (n > 1000)? | Maybe | ✅ Strongly favors BIC |
| ___ | ||
| ## 📈 Quick Rules |
| Situation | Preferred |
|---|---|
| Focused on best prediction | ✅ AIC |
| Focused on true model identification (simplicity) | ✅ BIC |
| Small or moderate dataset (n < 1000) | ✅ AIC often fine |
| Large dataset (n > 1000) | ✅ BIC penalty becomes stronger |
| ___ |
📘 Analyst Tip¶
- In small datasets (n < 500), AIC and BIC often behave similarly.
- In large datasets, BIC becomes much harsher about adding variables.
- Always state clearly which metric you used for model selection in reports!
🧠 Intuitive Summary¶
| Metric | Behavior |
|---|---|
| AIC | "Find the best approximation for reality (allow some complexity)" |
| BIC | "Find the simplest explanation with strongest evidence" |
🎯 Practical Advice¶
- When in doubt:
➔ Use AIC first for flexible modeling.
➔ Double-check BIC if your goal is strict parsimony (smallest good model).
✅ Lowest AIC or BIC = Best model under that criterion!
💡 Tip¶
"In exploratory modeling, you can compare both AIC and BIC to see if they agree. If they point to the same model, your choice is more robust. If they disagree, revisit your project goals—predictive focus leans toward AIC, while interpretability and simplicity lean toward BIC."