Why does " smooth term" have "parametric" effect? I read a blog about Generalized Additive Model (GAM). In this blog, the author used summary(gam1), then some information is printed:
## Call: gam(formula = wage ~ s(age, df = 6) + s(year, df = 6) + education, 
##     data = Wage)
## ...
## Anova for Parametric Effects
##                   Df  Sum Sq Mean Sq F value    Pr(>F)    
## s(age, df = 6)     1  200717  200717 162.456 < 2.2e-16 ***
## s(year, df = 6)    1   22090   22090  17.879 2.425e-05 ***
## education          4 1069323  267331 216.372 < 2.2e-16 ***
## Residuals       2983 3685543    1236                      
## ... 
## Anova for Nonparametric Effects
##                 Npar Df  Npar F  Pr(F)    
## (Intercept)                               
## s(age, df = 6)        5 26.2089 <2e-16 ***
## s(year, df = 6)       5  1.0144 0.4074    
## education                                 

I am confused about the Anova for Parametric/Nonparametric Effects. Why are s(age, df = 6) and s(year, df = 6) in the parametric effect content, since they are smooth terms? Similarly, why are (Intercept) and education in the nonparametric effect content?
 A: The parametric part refers to the linear effect of the covariate involved in the smooth. The non-parametric part refers to nonlinearity beyond the linear/parametric part of the smooth.
If the nonlinear / nonparametric part is significant it suggests that a linear effect of that covariate is not supported by the data.
Presenting the information this way allows you to see what might be linear or effectively linear effects of covariates that you represented via smooth functions in setting up the model.
This is a little harder to do in mgcv as it depends on the basis type being used. For the default thin plate regression spline basis, one would need to request a basis with no null space (so no perfectly smooth terms, like a linear or constant functions):
m <- gam(y ~ x + s(x, m = c(2, 0)), data = foo, method = 'ML')

The m = c(2, 0) tells gam that you want a second order wiggliness penalty (so a penalty on the second derivative or curvature of the smooth) but zero null space. This omdel also includes a linear effect of x and an intercept/constant term.
