  Two new approaches for checking the dimension of the basis functions when
using penalized regression smoothers are presented. The first approach is a
test for adequacy of the basis dimension based on an estimate of the residual
variance calculated by differencing residuals that are neighbours according to
the smooth covariates. The second approach is based on estimated degrees of
freedom for a smooth of the model residuals with respect to the model
covariates. In comparison with basis dimension selection algorithms based on
smoothness selection criterion (GCV, AIC, REML) the above procedures are
computationally efficient enough for routine use as part of model checking.
