Partially linear model
Topic of Additive smooths, part of Smoothing
Partially linear model
| Type | Topic |
| Taught in | Additive smooths |
| Part | Smoothing |
A regression with ordinary coefficients for the terms you want to interpret and smooth functions for the terms you only adjust for: g(\mu)=\mathbf{x}^\top\boldsymbol\beta+f(z).
In Additive smooths
From Additive smooths
A free function of all three covariates together would fit a surface we could not explain to a surgeon. Two-way interactions are already hard. Three-way interactions are where we stop. The compromise is a partially linear model: a coefficient for the term you want a unit-change sentence about, and a smooth for the terms you are only adjusting for. Ambient temperature in a lab, or the weight of a patient in a trial of two treatments, is the second kind. Dose and treatment are the first kind.