Extract the effective degrees of freedom associated with each penalty in a gam fit

Description

Finds the coefficients penalized by each penalty and adds up their effective degrees of freedom. Very useful for t2 terms, but hard to interpret for terms where the penalties penalize overlapping sets of parameters (e.g. te terms).

Usage

pen.edf(x)

Arguments

Details

Useful for models containing t2 terms, since it splits the EDF for the term up into parts due to different components of the smooth. This is useful for figuring out which interaction terms are actually needed in a model.

Value

A vector of EDFs, named with labels identifying which penalty each EDF relates to.

Author(s)

Simon N. Wood simon.wood@r-project.org

See Also

t2

Examples

 
  require(mgcv)
  set.seed(20) 
  dat <- gamSim(1,n=400,scale=2) ## simulate data
  ## following `t2' smooth basically separates smooth 
  ## of x0,x1 into main effects + interaction.... 
  
  b <- gam(y~t2(x0,x1,bs="tp",m=1,k=7)+s(x2)+s(x3),
           data=dat,method="ML")
  pen.edf(b)
  
  ## label "rr" indicates interaction edf (range space times range space)
  ## label "nr" (null space for x0 times range space for x1) is main
  ##            effect for x1.
  ## label "rn" is main effect for x0
  ## clearly interaction is negligible
  
  ## second example with higher order marginals. 
  
  b <- gam(y~t2(x0,x1,bs="tp",m=2,k=7,full=TRUE)
             +s(x2)+s(x3),data=dat,method="ML")
  pen.edf(b)
  
  ## In this case the EDF is negligible for all terms in the t2 smooth
  ## apart from the `main effects' (r2 and 2r). To understand the labels
  ## consider the following 2 examples....
  ## "r1" relates to the interaction of the range space of the first 
  ##      marginal smooth and the first basis function of the null 
  ##      space of the second marginal smooth
  ## "2r" relates to the interaction of the second basis function of 
  ##      the null space of the first marginal smooth with the range 
  ##      space of the second marginal smooth.