Extracts an optimal subtree from a tree object of the classes
treethresh or wtthresh. Contrary to
subtree the values of the complexity parameter \(C\) does
not need to be given, but is determined using cross-validation.
# S3 method for treethresh
prune(object, v=5, sd.mult=0.5, plot=TRUE)
# S3 method for wtthresh
prune(object, v=5, sd.mult=0.5, plot=TRUE)An object of the class treethresh or
wtthresh according to which thresholding is to be
carried out.
The number of folds in the cross-validation used to determine the optimal subtree in the pruning step (see below for details).
The smallest subtree that is not sd.mult times
the standard error worse than the best loglikelihood will be chosen as
the optimal tree in the pruning step. (see below for details).
If plot=TRUE a plot of the relative predicted
loglikelihood estimated in the cross-validation against the complexity
parameter \(C\) is produced.
additional arguments (see above for supported arguments).
prune returns an object of the class
treethresh or wtthresh that contains a
tree pruned at value \(C\) (see the function prune
for details on the pruning process).
The tree grown by treethresh or wtthresh
often yields too many partitions leading to an overfit. The resulting
tree has to be 'pruned', i.e. the branches corresponding to the least
important regions have to be 'snipped off'.
As the TreeThresh model is a special case of a classification and regression tree, there exists a sequence of nested subtrees (i.e. a sequence of nested partitions) that maximises the regularised loglikelihood $$\ell + \alpha \cdot \textrm{\# partitions}.$$
The parameter \(\alpha\) controls the complexity of the resulting partition. For \(\alpha=0\) no pruning is carried out. If a large enough \(\alpha\) is chosen, only the root node of the tree is retained, i.e. no partitioning is done. Denote this value of \(\alpha\) by \(\\alpha_0\). The complexity parameter can thus be rescaled to $$C=\frac{\alpha}{\alpha_0}$$ yielding a complexity parameter ranging from \(0\) (no pruning) to \(1\) (only retain the root node).
The optimal value of the complexity parameter \(C\) (or, equivalently, \(\alpha\))
depends on the problem at hand and thus has to be chosen
carefully. prune estimates the optimal complexity parameter
\(C\) by a \(v\)-fold cross-validation. If sd.mult=0 the
value of \(C\) that yields the highest predictive loglikelihood in the
cross-validation is used to prune the tree object. If
sd.mult is not \(0\) the largest \(C\) that is not
sd.mult standard errors worse than the best \(C\) is used.