Choosing the Right Model for Correlated Data: A Step-by-Step Guide [Repeated Measures, Multilevel Modeling, Mixed Effects, GEE Model, Random Effects, Robust SE, Longitudinal Data, Clustered Data]

STEP 1: 🔍 Describe Your Data Structure

Ask:

1. Are measurements repeated over time on the same subject?
2. Are observations nested in groups (e.g., patients in clinics, students in classes)?
3. Are there multiple levels of clustering (e.g., patients → doctors → hospitals)?
4. Is time spacing regular (every 3 months) or irregular?

---

STEP 2: 🧩 Identify the Correlation Source

---

STEP 3: 🎯 Choose the Analytical Goal

---

STEP 4: 📊 Map Your Scenario to the Model

---

STEP 5: 🧪 Select the Variance & Correlation Strategy

---

🔑 SECRET INSIGHT BOX

• GEE = population average, no prediction per patient
• Mixed-effects = subject-level prediction
• Random slope ≠ time interaction: it reflects natural heterogeneity in trends
• Always visualize trajectories before choosing slope models

---

🧭 Decision Map Summary

IF repeated measures → Is it over time?
     ├─ Yes: AR(1) or Random Slopes
     └─ No: Exchangeable or Random Intercepts

IF nested in groups:
     ├─ Just one level? → Random Intercepts
     └─ Multiple levels? → Multilevel model with nested random effects

IF unsure of pattern → Try Unstructured (if sample size supports it)

---

1  Describe Your Data Structure  🔍

Deep‑dive

Ask four questions before touching software:

1. Repeated over time? Same person measured >1 time ⇒ temporal correlation.
2. Nested groups? Patients in wards, eyes within patients, etc. ⇒ clustering.
3. Multiple levels? Patient → Doctor → Hospital ⇒ hierarchical nesting.
4. Timing pattern? Equally spaced visits favour AR(1); irregular timing often requires mixed‑effects with random slopes.

Why it matters – each “Yes” forces extra parameters in the covariance matrix. Incorrect specification inflates Type I error or wipes power.

Plain‑speak cheat

Write down “TIME?” and “NESTING?” first; the answers drive everything that follows.

---

2  Identify the Correlation Source  🧩

Deep‑dive

Plain‑speak cheat

If two rows share a patient‑ID, clinic‑ID, or visit‑date, they’re probably correlated.

---

3  Clarify Your Analytical Goal  🎯

Deep‑dive

Plain‑speak cheat

Pick GEE for public‑health answers; mixed‑effects for patient‑level answers.

---

4  Map Scenario → Model  📊

Deep‑dive

Plain‑speak cheat

One level = random intercept; time + one level = add random slope; many levels = stack random intercepts.

---

5  Pick Variance & Correlation Strategy  🧪

Deep‑dive

Plain‑speak cheat

Short panels → AR(1). Big uncertain panels → UN. Parallel lines? random‑intercept; diverging lines? random‑slope.

---

6  Reality Checks & Visuals  🔑

1. Spaghetti plot before modelling – are patient lines parallel?
2. Intraclass correlation (ICC) – if ≈0, maybe clustering is harmless.
3. Residual AC‑plot – confirms AR(1) choice.

Plain‑speak cheat

Plot first; if lines aren’t parallel your model shouldn’t be either.

---

Decision Flow (ASCII)  🧭

Start
 ├─ Repeated over time?
 │     ├─ Yes → Equal spacing?
 │     │      ├─ Yes → AR(1) or Random Slopes
 │     │      └─ No  → Random Slopes + Time-as-variable
 │     └─ No → Clustered?
 │            ├─ One level → Random Intercepts
 │            └─ ≥Two levels → Hierarchical Mixed
 └─ Unsure pattern → Try Unstructured (data permitting)

Worked Micro‑Example

Design: 150 COPD patients across 7 clinics, FEV1 at baseline, 3 m, 6 m.Goal: Predict individual recovery curves.

1. Structure → repeated + nested (patients in clinics).
2. Goal → subject‑specific.
3. Model → Mixed‑effects with random intercept (clinic) & intercept + slope (patient).
4. Spec (R):

lmer(FEV1 ~ time + (time|patient_id) + (1|clinic_id), data = copd)

1. Working correlation → implied by random effects; no extra AR(1) needed because random slopes capture within‑patient trajectory.

---

Quick Reference Card  📋 (TL;DR)