I am dealing with GAM models. I don't understand the intercept term there. Consider the following simple model.
library(mgcv) n=1000 X1=rnorm(n,1,2) X2=rnorm(n,0,1) y= -1 + sin(X1) + exp(X2) + rnorm(n) fit=gam(y~s(X1)+s(X2)) summary(fit) #Family: gaussian #Link function: identity #Formula: y ~ s(X1) + s(X2) #Parametric coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.80632 0.03286 24.54 <2e-16 *** #Approximate significance of smooth terms: # edf Ref.df F p-value #s(X1) 7.938 8.718 59.88 <2e-16 *** #s(X2) 8.309 8.873 405.74 <2e-16 *** #R-sq.(adj) = 0.807 Deviance explained = 81% #GCV = 1.0987 Scale est. = 1.0798 n = 1000
The estimation of an intercept term 0.8 is far away from -1. I feel that this intercept there means something else. Then, how can I get an estimation of that -1 term?
Edit: just for better context. What I have is that the response $Y=f_1(X_1) + f_2(X_2) + \varepsilon$, where $\varepsilon$ is not nessesarily centered (nor normal actually). I want to estimate the distribution of this non-centered noise.