# Can we get the specific formulation form of thin plate regression spline in GAM?

In mgcv package, the default smoother is thin plate regression spline. After building a GAM model, can we "write" the formula form of the thin plate regression spline? For example, in the form of y = k*x + b.

• Welcome to CV T X. As I understand it, Simon Wood wrote the critical text on this topic (specific to mgcv anyway): Wood, S. N. (2003). Thin plate regression splines. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65(1), 95–114. – Alexis Oct 5 '19 at 16:40
• A GAM is called a "non-parametic model" for a reason. – Roland Oct 7 '19 at 8:27