 Identifiability of additive regression components

In an additive regression model, each component can transfer a constant to the regression intercept, so impose empirical mean-zero constraints, or population mean-zero constraints when appropriate. Even after centering, nonzero component perturbations $h_j$ with ${\sum }_j{h}_j(x_{ij})=0$ at every observed point make the additive decomposition nonidentifiable. Extra smoothing penalties may resolve the fitted decomposition, but centering alone does not remove concurvity.

// Target: probability-and-statistics.bigb