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?
   

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STEP 2: 🧩 Identify the Correlation Source

Data Type	What Makes It Correlated?	Example
Repeated measures	Same subject over time	BP at 1, 3, 6 months
Clustered data	Subjects in same unit	Patients in ward
Hierarchical data	Nested clusters	Patient → doctor → hospital
Paired/matched data	Shared factors	Left eye vs right eye

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STEP 3: 🎯 Choose the Analytical Goal

Goal	Use Model That Estimates...	Best For
Population-level average	Marginal model (GEE)	Guidelines, public health
Subject-specific trends	Conditional model (Mixed Effects)	Individual prediction, growth curves
Group-specific effects	Multilevel model	School/ward/hospital policy
Only need corrected SEs	Empirical variance correction	Regression w/ cluster SEs

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STEP 4: 📊 Map Your Scenario to the Model

Scenario	Best Model	Correlation Correction
Single-level repeated measures (time)	GEE or Mixed Effects	AR(1) or Exchangeable
Nested groups (patients in clinics)	Multilevel Mixed Model	Random Intercepts
Grouped + repeated (patients in hospitals over time)	Mixed Model with Random Intercepts + Slopes	Hierarchical + Time correlation
No strong structure but correlated outcomes	GEE with Robust SE	Empirical correction
Very small sample or irregular visits	Unstructured correlation	Data-defined estimation

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STEP 5: 🧪 Select the Variance & Correlation Strategy

Component	Option	When to Use
Variance Estimation	Empirical (Robust SE)	When model fit isn’t your focus, but SE correction is critical
	Model-based	When you trust your model structure & correlation
Correlation Structure	Exchangeable	Equal correlation (common in clusters)
	AR(1)	Time-spaced data where closer = more correlated
	Unstructured	Large sample, unknown pattern
Random Effect Specification	Random Intercepts	Different starting levels
	Random Slopes	Different trends over time or treatment

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🔑 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
  

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🧭 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)

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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.

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2  Identify the Correlation Source  🧩

Deep‑dive

Data type	Mechanism	Typical example	Quick diagnostic plot
Repeated measures	Within‑subject memory	BP at 1, 3, 6 months	Spaghetti plot of each patient
Clustered	Shared care environment	Patients in same ICU	Box‑and‑whisker by cluster
Hierarchical	Stacked clustering	Patient → Doctor	Variance‐components plot
Paired	Biological pairing	Left vs Right eye	Bland‑Altman / scatter of pair

Plain‑speak cheat

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

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3  Clarify Your Analytical Goal  🎯

Deep‑dive

Goal	Key question	Proper model family	Interpretation focus
Population average	“What is the mean effect across everyone?”	GEE / Marginal	Guidelines & policy
Subject‑specific	“How does this patient change?”	Mixed‑effects (conditional)	Precision medicine
Group effects	“Do hospitals differ?”	Multilevel mixed	Quality benchmarking
Just robust SEs	“I only fear clustered SE inflation.”	OLS/GLM + Sandwich	Simple regressions

Plain‑speak cheat

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

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4  Map Scenario → Model  📊

Deep‑dive

Scenario	Best model	Working correlation / random structure	R / Stata hint
6 time‑points per patient, no sites	GEE	AR(1) or exchangeable	geeglm(..., corstr="ar1")
Patients clustered in 12 clinics, one outcome	Mixed (random intercept)	Random intercept only	`lmer(Y ~ X + (1
Patients in 12 clinics, 5 visits each	Mixed (int + slope)	Random int + slope by patient; random int by clinic	`lmer(Y ~ time + (time
4000 patients, 2 exams each, need quick answer	GLM + cluster‑robust SE	Sandwich (empirical)	glm(...); sandwich()
30 patients, 10 uneven visits	Unstructured mixed (if convergence)	UN covariance	lme(..., correlation=corSymm())

Plain‑speak cheat

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

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5  Pick Variance & Correlation Strategy  🧪

Deep‑dive

Choice point	Options	Use when	Caveat
Variance estimator	Empirical (robust)	Large N, misspecified corr. OK	Still biased if clusters < 30
	Model‑based	Correlation well‑specified	Sensitive to wrong pattern
Correlation pattern	Exchangeable	All pairs equally related (wards)	Over‑simplifies time data
	AR(1)	Equal spacing & decay	Fails if visits irregular
	Unstructured	Plenty of rows/cluster	Parameter‑hungry
Random effect	Intercept	Baseline shifts only	Assumes parallel trajectories
	Intercept + Slope	Heterogeneous change rates	Needs ≥3 time points/subject

Plain‑speak cheat

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

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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.

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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)

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

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Quick Reference Card  📋 (TL;DR)

Ask	If “Yes” →	Model
Time repeated?	Equal gaps	GEE/Mixed + AR(1)
	Unequal gaps	Mixed + Random Slopes
Single clustering level?	—	Mixed + Random Intercept
Multiple levels?	—	Multilevel Mixed
Need only robust SE?	—	Sandwich