How to Choose the Right Correlation-Corrected Statistic: Model Hierarchy for Repeated Measures (Best → Fallback)

📊 Model Hierarchy for Repeated Measures (Best → Fallback)

Rank	Model	Description
🥇 1	Conditional Model — Multi-level — Random Effect	Subject-specific; captures both random intercepts and slopes
🥈 2	Conditional Model — Multi-level — Fixed Effect	Subject/group-specific using dummy variables; no generalization
🥉 3	Marginal Model — Single-level — Model-Based Variance	Population-averaged; requires correlation structure assumption
🪙 4	Marginal Model — Single-level — Empirical (Robust SE)	Uses sandwich SE; structure-free fallback

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🔁 Downgrade Pathway (When Data is Limited)

Limitation	Downgrade to...	Reason
No group ID (e.g. id, cluster)	❌ Can't use Conditional → Use Marginal	Can't define within-subject correlation
Few groups (<5)	❌ Random → ✅ Fixed Effect	Random effects may overfit
Insufficient data for random slopes	❌ Random slopes → ✅ Random intercept or Fixed	Model may not converge
Unknown correlation structure	❌ Model-based → ✅ Empirical (robust SE)	Robust to mis-specification

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⚔️ 1. Random Effect vs Fixed Effect (Conditional Multilevel)

Criterion	Fixed Effect	Random Effect
Uses dummy variables?	✅ Yes	❌ No (learns from distribution)
Can predict new/unseen groups?	❌ No	✅ Yes
Requires all groups in model?	✅ Yes	❌ No
Learns group-level variance?	❌ No	✅ Yes (estimates variance components)
Allows random slopes?	❌ No	✅ Yes (e.g., `
Suitable for few groups?	✅ Yes	❌ Not stable with few clusters
Stata commands	xtreg, fe, reg outcome i.group	`mixed outcome ...

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⚔️ 2. Fixed Effect vs Marginal Model-Based

Criterion	Fixed Effect	Marginal (Model-Based)
Focus on individual/group effect?	✅ Yes	❌ No (population-averaged)
Can predict individual response?	✅ Limited to included groups	❌ Not designed for this
Command in Stata	xtreg, fe, areg, reg i.group	xtgee ... corr(exchangeable)
Population-level interpretation?	❌ Not primary aim	✅ Yes
Needs large sample for stability?	❌ Less dependent	✅ More sensitive to cluster size
Suitable for few clusters?	✅ Yes	❌ Risky, may produce unstable estimates

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⚔️ 3. Marginal Model-Based vs Empirical (Robust SE)

Criterion	Model-Based Variance	Empirical (Robust SE)
Requires correlation structure?	✅ Yes (e.g., AR1, exchangeable)	❌ No
Sensitive to mis-specification?	❌ Yes	✅ No (SE remains valid)
Uses sandwich estimator?	❌ No	✅ Yes
Higher power when correct?	✅ Yes	❌ Lower power if model structure unknown
Best for...	Known structure, more clusters	Small samples or uncertain correlation
Stata commands	xtgee ... corr(ar1)	xtgee ... vce(robust)

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🔚 Final Decision Strategy

Start with:

1. Mixed Model (Random Intercept/Slope)→ if not feasible due to convergence/small N

2. Fixed Effects Model→ if still not feasible

3. GEE with correlation structure→ if structure is unclear or unreliable

4. GEE with robust (Empirical) SE ← safest fallback

Let me know if you want side-by-side Stata syntax, visual simulations, or a clinical use case example.