Generalized Estimating Equations (GEE)
GEE handles regression for correlated/clustered data — longitudinal studies, repeated measures, or clustered designs where observations within a subject/cluster are not independent.
Step 1 — Provide your data
Each row is one observation:
- Subject ID — cluster identifier
- Time Point — when observed
- Outcome — dependent variable
- Covariates — independent variables
Supports Excel Import, Sample Data Generator, and Manual Entry.
Step 2 — Configure the model
Outcome family:
| Family | Use when |
|---|---|
| Gaussian | Continuous outcomes |
| Binomial | Binary outcomes (0/1) |
| Poisson | Count outcomes |
Link function:
| Link | Typical pairing |
|---|---|
| Identity | Gaussian |
| Logit | Binomial |
| Log | Poisson |
Working correlation structure:
| Structure | Assumption |
|---|---|
| Independence | No within-cluster correlation |
| Exchangeable | Uniform correlation (0.3) |
| AR(1) | Decay with time distance (0.5^k) |
| Unstructured | All pairwise estimated |
Step 3 — Results
- Coefficients table — Estimate, SE, Z-value, p-value, 95% CI per variable
- Working Correlation Matrix
- Model fit — Quasi-likelihood, AIC, BIC
- Convergence status — converged, iterations, final tolerance
- Model summary — subjects, observations, time points, family/link/correlation
- Interpretation — adaptive plain-language summary
A UniversalChatBot is available for discussion.
Statistical methods used
Model
g(E[Y_ij]) = beta0 + beta_time * t_ij + sum(beta_k * X_ijk)
Estimation — Iterative least squares, max 20 iterations.
Standard errors — Conservative estimates accounting for within-cluster correlation.
Confidence intervals and p-values (Wald)
95% CI: beta +/- 1.96 * SE, Z = beta / SE, p = 2*(1 - Phi(|Z|))
Quasi-likelihood
| Family | Formula |
|---|---|
| Gaussian | -0.5 * sum((y - mu)^2) |
| Binomial | sum(y*log(mu) + (1-y)*log(1-mu)) |
| Poisson | sum(y*log(mu) - mu) |
Key property: GEE produces consistent population-average estimates even when the working correlation structure is misspecified.