= Solution
The original PDF's age smooth is nearly flat, its uncertainty band includes zero across the age range, and its approximate <p-value> is $0.859$. The exposure smooth is increasing and convex: it is fairly flat at low exposure and rises more steeply at high exposure. Its <effective degrees of freedom> $1.895$ suggest a modest departure from a straight line, rather than a highly oscillatory relationship.
A suitable simpler model is therefore the grouped <quasibinomial regression>
$$
\boxed{\log\frac{p_i}{1-p_i}=\beta_0+\beta_1 e_i+\beta_2e_i^2,\qquad
\operatorname{Var}(Y_i)=\phi m_ip_i(1-p_i),}
$$
with age omitted and dispersion estimated. A positive quadratic coefficient captures the convex exposure relationship; retaining the linear term respects the usual polynomial hierarchy. This model should be refitted, rather than assigning coefficients from the smooth plot. Compare its residual pattern and dispersion-adjusted fit with the additive model to check that the quadratic approximation is adequate. \b[An exposure-only quadratic logit model is a justified parsimonious candidate], while the graph does not justify a sharp threshold or a zero-dispersion model.
Back to article page
