C33. GAMs and effective degrees of freedom
What is a GAM, and what do the effective degrees of freedom of a fitted smooth measure?
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Definitions/notation. A GAM models the conditional mean through g(\mu_i)=\beta_0+\sum_j f_j(x_{ij}), possibly with additional parametric terms, so effects are additive on the link scale. A smooth’s effective degrees of freedom (edf) measure its fitted flexibility after penalisation, not its polynomial degree; for an ordinary centred univariate smooth, edf near one is approximately linear.