How to Choose the Right Correlation-Corrected Statistic: Model Hierarchy for Repeated Measures (Best โ Fallback)
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๐ Model Hierarchy for Repeated Measures (Best โ Fallback)
| Rank | Model | Description |
| ๐ฅ 1 | Conditional Model โ Multi-level โ Random Effect | Subject-specific; captures both random intercepts and slopes |
| ๐ฅ 2 | Conditional Model โ Multi-level โ Fixed Effect | Subject/group-specific using dummy variables; no generalization |
| ๐ฅ 3 | Marginal Model โ Single-level โ Model-Based Variance | Population-averaged; requires correlation structure assumption |
| ๐ช 4 | Marginal Model โ Single-level โ Empirical (Robust SE) | Uses sandwich SE; structure-free fallback |
๐ Downgrade Pathway (When Data is Limited)
| Limitation | Downgrade to... | Reason |
| No group ID (e.g. id, cluster) | โ Can't use Conditional โ Use Marginal | Can't define within-subject correlation |
| Few groups (<5) | โ Random โ โ Fixed Effect | Random effects may overfit |
| Insufficient data for random slopes | โ Random slopes โ โ Random intercept or Fixed | Model may not converge |
| Unknown correlation structure | โ Model-based โ โ Empirical (robust SE) | Robust to mis-specification |
โ๏ธ 1. Random Effect vs Fixed Effect (Conditional Multilevel)
| Criterion | Fixed Effect | Random Effect |
| Uses dummy variables? | โ Yes | โ No (learns from distribution) |
| Can predict new/unseen groups? | โ No | โ Yes |
| Requires all groups in model? | โ Yes | โ No |
| Learns group-level variance? | โ No | โ Yes (estimates variance components) |
| Allows random slopes? | โ No | โ Yes (e.g., ` |
| Suitable for few groups? | โ Yes | โ Not stable with few clusters |
| Stata commands | xtreg, fe, reg outcome i.group | `mixed outcome ... |
โ๏ธ 2. Fixed Effect vs Marginal Model-Based
| Criterion | Fixed Effect | Marginal (Model-Based) |
| Focus on individual/group effect? | โ Yes | โ No (population-averaged) |
| Can predict individual response? | โ Limited to included groups | โ Not designed for this |
| Command in Stata | xtreg, fe, areg, reg i.group | xtgee ... corr(exchangeable) |
| Population-level interpretation? | โ Not primary aim | โ Yes |
| Needs large sample for stability? | โ Less dependent | โ More sensitive to cluster size |
| Suitable for few clusters? | โ Yes | โ Risky, may produce unstable estimates |
โ๏ธ 3. Marginal Model-Based vs Empirical (Robust SE)
| Criterion | Model-Based Variance | Empirical (Robust SE) |
| Requires correlation structure? | โ Yes (e.g., AR1, exchangeable) | โ No |
| Sensitive to mis-specification? | โ Yes | โ No (SE remains valid) |
| Uses sandwich estimator? | โ No | โ Yes |
| Higher power when correct? | โ Yes | โ 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) |
๐ Final Decision Strategy
Start with:
- Mixed Model (Random Intercept/Slope)โ if not feasible due to convergence/small N
- Fixed Effects Modelโ if still not feasible
- GEE with correlation structureโ if structure is unclear or unreliable
- GEE with robust (Empirical) SEย โ safest fallback
Let me know if you want side-by-side Stata syntax, visual simulations, or a clinical use case example.
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