Example output:

Model |     N    ll(null)   ll(model)   df     AIC      BIC
--------------------------------------------------------------
.     |   3135   -1906.079   -1807.527   2   3619.054  3631.155

1. What Are AIC and BIC?

Both are information criteria used to compare models.

They answer:

Which model balances goodness-of-fit AND parsimony best?

They penalize complexity. AIC stands for:

Akaike Information Criterion

Named after: Hirotugu Akaike (1974)

BIC stands for:

Bayesian Information Criterion

Also called: Schwarz Criterion (Schwarz, 1978)

Quick Clinical Modeling Meaning

In one sentence:

• AIC = goodness-of-fit + mild penalty
• BIC = goodness-of-fit + strong penalty

Lower value = better model (when comparing models on same data).

---

1. Mathematical Definition

Let:

• LL = log-likelihood
• k = number of parameters
• N = sample size

AIC

AIC=−2LL+2k

BIC

BIC=−2LL+kln(N)

Notice:

• AIC penalty = 2k
• BIC penalty = k ln(N)

With N = 3135:

ln(3135)≈8.05

So BIC penalizes ~4× stronger than AIC here.

---

1. What Do They Mean Clinically?

They are not hypothesis tests.

They are:

Relative model quality measures.

Lower value = better model.

You NEVER interpret AIC alone.You compare between models.

---

1. What Does Your Output Mean?

From your model:

ll(model) = -1807.527
df = 2
AIC = 3619.054
BIC = 3631.155

This is:

• Logistic model
• 2 parameters (intercept + Age)

Now imagine you compare:

Best model = lowest AIC

---

1. When Should You Use AIC vs BIC?

🔹 AIC

Use when:

• Goal = prediction
• Want best approximating model
• Clinical prediction model development

🔹 BIC

Use when:

• Goal = explanatory modeling
• Prefer simpler model
• Large sample size
• Theory-driven

---

1. Important Warning From Stata Manual

Your help file warns:

AIC/BIC not comparable if likelihoods are based on different events.

Example:

• stcox vs streg → not comparable
• Different datasets → not comparable
• Different outcome types → not comparable

But:

✅ Logistic vs logistic ✅ Linear vs quadratic logistic ✅ Logistic vs MFP logistic

→ perfectly valid comparison.

---

1. How You Should Use It in Your Age Modeling

Here is the proper workflow:

* Linear
logistic ED_LOS_ge4h c.Age
est store lin

* Quadratic
logistic ED_LOS_ge4h c.Age##c.Age
est store quad

* MFP
mfp: logistic ED_LOS_ge4h Age
est store mfp

* Compare all
estat ic

Or better:

estimates stats lin quad mfp

Then compare:

• AIC
• BIC
• Log-likelihood

---

1. Clinical Interpretation Example

Suppose:

Interpretation:

• AIC prefers MFP
• BIC prefers Quadratic
• Quadratic more parsimonious
• MFP slightly better predictive fit

Decision depends on:

• Is this predictive model? → choose MFP
• Is this explanatory modeling? → choose quadratic

---

1. Key Concept: Why Not Use p-values Alone?

Because:

• Quadratic term may be non-significant
• But model still improves global fit
• p-value tests coefficient
• AIC evaluates whole model

This is why modeling uses AIC/BIC

---

1. Deep Insight (Very Important)

AIC does NOT tell you if model is correct.

It tells you:

Which model loses the least information relative to truth.

That is very different.

---

Summary

In Example ED LOS ≥ 4h model:

• Use LR test for nested comparison
• Use AIC/BIC for overall comparison
• Prefer AIC in prediction modeling
• Prefer BIC in explanatory modeling
• Always compare models fit on SAME dataset