GAM without coding

The honest part

What a GAM is, and when it beats a straight line

A generalized additive model is a GLM in which the effect of a predictor is allowed to curve. Instead of one coefficient per variable, the model fits a smooth s(x) — here a cubic regression spline with a penalty on curvature — and lets the data decide how wiggly that curve may be. The penalty is what keeps it from chasing noise: the smoothing parameter λ is selected by GCV when the scale is estimated (gaussian, Gamma) or UBRE when it is fixed (poisson, binomial), the same criterion mgcv uses with method="GCV.Cp".

The numbers to read are the effective degrees of freedom (edf) of the smooth — near 1 means the curve is essentially a line — and the smooth's own test. Magic Stat reports edf, edf1, ref.df, the Wood (2013) smooth test with the exact Davies p, the deviance explained and the adjusted R², then draws s(x) with ±2SE bands.

It is not always the right model. If the relationship is plausibly linear, a standard GLM is simpler, easier to report and its coefficient is directly interpretable. If your data are clustered or repeated, the dependence belongs in a mixed model or GEE, not in a smoother. And the reproduction caveat is worth stating: current mgcv defaults to REML, which selects a slightly different λ — to match Magic Stat in R you set method="GCV.Cp".

What it does

What Magic Stat gives you for GAM

A penalized cubic regression spline (mgcv's bs = "cr") with knots at the quantiles of the smooth variable, on a single s(var) term, at a basis size you set (k, default 10, reduced automatically when the variable has fewer unique values, with a note in the report).
Four families with their canonical links: gaussian → identity, poisson → log, binomial → logit, Gamma → inverse. Non-canonical links are deliberately not offered — a 1:1 replica of mgcv's non-canonical branch would need different fitting machinery.
Parametric terms, numeric and categorical, entered alongside the smooth. Categorical predictors use treatment contrasts with the first category (alphabetical) as reference, the model matrix R builds.
The gam summary, laid out as tables: parametric coefficients (coef, SE, t or z, p), total edf, smooth edf, edf1, ref.df, smoothing parameter λ, scale, deviance, null deviance, deviance explained %, adjusted R², GCV/UBRE score, residual df and convergence.
The smooth test itself: the Wood (2013) statistic with the exact Davies p, reported as F when the scale is estimated and Chi.sq when it is fixed.
The s(x) curve with ±2SE, exported at publication quality (PNG, SVG, PDF, JPEG, TIFF) and editable in a large window, with the fitted values and the whole model written into the report.

How it works

From outcome and smooth to the curve

Load the data. one row per observation; the outcome, the smooth variable and any parametric predictors are ordinary columns.
Choose the response and family. the family's canonical link is applied — counts suggest poisson, 0/1 suggests binomial.
Set the smooth term. pick the variable to smooth and the basis size k (leave it at 10 unless you have a reason).
Add parametric terms. optional numeric or categorical predictors that enter with a linear effect.
Read and export. edf and the smooth's p tell you whether the curve is real; the plot goes to the gallery and the model to the report.

Options

The settings, out in the open

Families: gaussian · poisson · binomial · Gamma — canonical link in each case.

Smooth: one s(var) term (cubic regression spline, bs = "cr") · basis size k (3–50, default 10).

Smoothing selection: GCV when the scale is estimated · UBRE when it is fixed — mgcv's method = "GCV.Cp".

Parametric predictors: any mix of numeric and categorical columns; categorical entry uses treatment contrasts with the first category as reference.

Frequently asked

GAM questions, answered honestly

GAM or a linear model?

If the effect is plausibly a straight line, use a linear model or GLM: the coefficient is simpler to report and easier to interpret. Reach for a GAM when the data show curvature you cannot justify with a polynomial, and read the smooth's edf — near 1 means the smoother collapsed towards a line.

Why GCV and not REML?

Magic Stat follows mgcv's method = "GCV.Cp". Modern mgcv defaults to REML, which selects a slightly different λ, so to reproduce a Magic Stat fit in R you set method = "GCV.Cp" explicitly. The results are close, not identical, and the difference is stated rather than hidden.

How do I know the smooth is real?

The smooth test (Wood 2013, exact Davies p) answers whether s(x) explains variation beyond a constant, and edf tells you how curved it is. A significant smooth with edf close to 1 is barely distinguishable from a line.

Can I include categorical predictors?

Yes, alongside the smooth and with treatment contrasts (first category alphabetically as reference), the coding R uses. Non-canonical links are not offered; each family uses its canonical link only.

Does the analysis run locally?

Yes. The fit runs on your computer; nothing but an anonymous installation counter leaves the machine.