Read the Model Summary

Understand EDF, significance tests, and fit statistics at a glance.

model.summary() is the primary diagnostic after fitting. It reports one row per smooth term and a block of overall fit statistics. Learning to read it fluently takes about five minutes and pays off every time you fit a model.

Fit a two-smooth model

The wages dataset records hourly wages alongside age and experience. Wages are positive and right-skewed, so wk.Gamma() is a natural choice.

import whittaker as wk

data = wk.load_dataset("wages")
# Fit two-smooth Gamma GAM
model = wk.GAM("wage ~ s(age) + s(experience)", family=wk.Gamma()).fit(data)
model.summary()
GAM fit summary
============================================================
Formula:    wage ~ s(age) + s(experience)
Family:     Gamma(link='log')
Inference:  GCV
Observations: 800
Coefficients: 19

Parametric coefficients:
  Term                       Estimate    Std.Err    t value    p-value
  ------------------------ ---------- ---------- ---------- ----------
  (Intercept)                  3.7109     0.0084    440.686    < 1e-16

Approximate significance of smooth terms:
  Term                        EDF Ref.df     Chi.sq    p-value
  ------------------------ ------ ------ ---------- ----------
  s(age)                     3.23      4   2473.551    < 1e-16
  s(experience)              2.82      3    177.907    < 1e-16

Total EDF:  7.05
Scale est:  0.056726
Deviance:   44.9806
Null dev:   205.9584
Dev. expl:  78.2%
GCV score:  0.057230
AIC:        5881.68
BIC:        5914.71

Smooth terms table

Each row in the upper block describes one smooth term.

Column Meaning
Name The smooth term as written in the formula, e.g. s(age)
EDF Effective degrees of freedom (how wiggly the fitted smooth actually is)
Ref.df Reference degrees of freedom used in the F-test denominator
F F-statistic testing whether the smooth differs significantly from zero
p-value Two-sided p-value for the F-test where small values indicate a real effect

EDF = 1 means the smooth collapsed to a straight line. EDF = 5 means it used five degrees of freedom to bend through the data.

Model statistics

The lower block summarises overall fit.

  • n: number of observations used in the fit.
  • Family: the distribution and link function (e.g. Gamma [log]).
  • Deviance explained: the proportion of null deviance accounted for by the model, analogous to R² in OLS.
  • GCV score: generalized cross-validation score used to select smoothing parameters (lower is better when comparing models on the same data).
  • Scale estimate: estimated dispersion parameter for the family.

EDF as a diagnostic

If the EDF of a smooth is close to the maximum allowed by the basis dimension k, the basis may be too small to capture the true curve shape. Whittaker will not automatically warn you, but the summary makes it visible: an EDF near k − 1 is a prompt to refit with a larger k. Recipe 23 covers the formal k-index test for basis dimension adequacy.

The edf attribute holds one value per smooth term as a list of floats.

model.edf
[3.227258222729782, 2.8235746255378054]

Compare these values against the default basis dimension (usually k = 10, giving a maximum EDF near 9). A value close to the ceiling is a signal to increase k.