GEE — population-averaged regression with robust SE

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Advanced & specialized

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Fits a marginal (POPULATION-AVERAGE) regression for clustered or longitudinal outcomes.

Reports coefficients with Liang-Zeger ROBUST SANDWICH standard errors, QIC-based working-correlation selection across {independence, exchangeable, AR(1), unstructured} candidates, naïve-vs-robust SE comparison (robust SEs are valid even under wrong working correlation), and a population-average interpretation that contrasts with LMM's subject-specific one. Standard tool for clinical trials with repeated measures, multi-centre RCTs, and any clustered design where the population-average effect is the substantive estimand.

Worked example

What is the population-average effect of a programme on repeated binary outcomes?

Repeated yes/no adherence measures per patient were modelled with GEE (exchangeable correlation) for a marginal, population-averaged effect.

Result

The programme roughly doubled the population-averaged odds of adherence (OR = 2.01, 95% CI [1.35, 2.99], p < .001).

How you'd report it (APA)

A GEE (population-averaged) analysis showed the programme significantly increased adherence odds, OR = 2.01, 95% CI [1.35, 2.99], p < .001.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Repeated measures — population-average inference
    Blood pressure across 4 clinic visits per patient (n = 200 patients × 4 visits).
  • Clustered cross-sectional design
    Test score ~ ses + teacher-quality, clustered by school (n = 5000 students in 80 schools).

When NOT to — use instead

Hypotheses

H₀: β_j = 0 for each marginal (population-average) coefficient.
Hₐ: at least one β_j ≠ 0.

Parameter tested: vector of marginal coefficients β

Assumptions (and what to do if they fail)

Working correlation structure reflects the DESIGN: independence (smallest, assumes no within-cluster correlation), exchangeable (compound symmetry — all pairs equally correlated), AR(1) (first-order autoregressive — decays with time distance), unstructured (each pair has its own correlation; needs balanced panel and many clusters).medium

Check: Lowest-QIC structure.

If violated: Good news: robust sandwich SE is VALID even when the working correlation is wrong — it just loses efficiency.

Robust sandwich SE ≈ naïve model-based SE indicates the working correlation is well-specified. Large divergence is not a problem per se — robust SE is the primary — but signals the structure could be improved.low

Check: Per-coefficient robust/naïve SE ratio.

If violated: Robust SE remains valid; large divergence is informational only.

Every cluster contributes ≥ 2 observations. Singletons contribute nothing to the working correlation estimation.medium

Check: Min observations per cluster.

If violated: Singleton clusters contribute only to coefficient estimates, not to within-cluster correlation.

Ready to run a GEE — population-averaged regression with robust SE on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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