This free generalized additive mixed models calculator is designed for any analysis where the relationship between a predictor and an outcome is nonlinear or wiggly, and where observations may be clustered by group, site, subject, or species. Use a GAM/GAMM when:

• You suspect a curved (not straight-line) relationship — e.g., dose–response, growth curves, day-of-year effects.
• You have one or more continuous predictors and want to let the data choose the shape rather than imposing a polynomial.
• Your data are nested or clustered (sites, subjects, plots) and a random intercept is appropriate.
• You want a flexible alternative to polynomial regression that is less prone to wild end-tail behaviour.
• You want effect plots showing the partial smooth function s(X) with 95% confidence bands.

Worked example (built into this tool)

The default Air Temperature vs CO₂ dataset shows a clearly nonlinear relationship: temperature rises with CO₂ but with curvature that a linear regression would miss. A GAM captures this curve with one smooth term s(CO₂), producing an EDF > 1 (signalling nonlinearity), an F-test of the smooth's significance, and an R² that quantifies the proportion of variance explained.

Decision tree — should you use GAM/GAMM or another model?

1. Is the relationship roughly linear? → use OLS regression.
2. Is it nonlinear but a known parametric form (e.g., logistic)? → use that nonlinear model.
3. Is it nonlinear with unknown shape? → use a GAM.
4. Is the response a count or binary? → use a GAM with Poisson or binomial family.
5. Do you have repeated measures or clustering? → use a GAMM with random intercept.

The GAM model equation

Smooth term as a basis expansion

Penalised likelihood (cubic regression spline)

Effective Degrees of Freedom (EDF)

Where:

• g(·) — link function (identity for Gaussian, logit for binomial, log for Poisson)
• β₀ — overall intercept
• sⱼ(Xⱼ) — smooth function of the j-th predictor, built as a sum of basis functions bⱼ(x)
• k — number of basis functions; sets the upper limit on smooth complexity
• λ — smoothing penalty; larger λ shrinks the smooth toward a straight line
• S — penalty matrix (second-derivative roughness penalty)
• Zb — random-effects design matrix × random-effect coefficients (for GAMMs)
• EDF — effective degrees of freedom; ≈1 means linear, larger means more wiggle
• F-statistic — Wald-type test of whether the smooth differs from a flat line
• Deviance explained — analog of R² for GAMs: 1 − (residual deviance / null deviance)

1. Enter Your Data — paste comma-separated X and Y values, upload a CSV/Excel file, or use the manual table. Each cluster (group) is a separate row.
2. Choose a Sample Dataset — five built-in scenarios: Air Temp vs CO₂, Tree Diameter vs Height, Drug Dose Response, Hours Studied vs Exam Score, Day-of-Year vs Bird Counts.
3. Configure Settings — set α (0.01/0.05/0.10), basis dimension k (default 10), smoothing penalty λ (default 0.01), and whether to add a random intercept.
4. Run the Analysis — click ▶ Run GAM / GAMM Analysis. Results, four plots, and interpretation appear instantly.
5. Read the Summary Cards — EDF, F-statistic, p-value, R², deviance explained, AIC, sample size.
6. Read the Full Results Table — every coefficient and smooth-term statistic.
7. Examine the Plots — smooth fit with 95% CI, observed vs fitted, residuals vs fitted, Q–Q plot.
8. Check Assumptions — residual plots reveal heteroscedasticity, non-normality, and outliers.
9. Read the Interpretation — copy any of the five reporting templates for your write-up.
10. Export — download a plain-text report or PDF for your records.