By default, Minitab Statistical Software produces output for the smallest
tree with a misclassification cost within 1 standard error of the smallest
misclassification cost. Minitab lets you explore other trees from the sequence
that led to the identification of the optimal tree. Typically, you select an
alternative tree for one of the following two reasons:
- The optimal tree is part of a
pattern where the misclassification costs decrease. One or more trees that have
a few more nodes are part of the same pattern. Typically, you want to make
predictions from a tree with as much prediction accuracy as possible. If the
tree is simple enough, you can also use it to understand how each predictor
variable affects the response values.
- The optimal tree is part of a
pattern where the misclassification costs are relatively flat. One or more
trees with similar model summary statistics have much fewer nodes than the
optimal tree. Typically, a tree with fewer terminal nodes gives a clearer
picture of how each predictor variable affects the response values. A smaller
tree also makes it easier to identify a few target groups for further studies.
If the difference in prediction accuracy for a smaller tree is negligible, you
can also use the smaller tree to evaluate the relationships between the
response and the predictor variables
For example, in the following plot, the tree with 4 nodes is the optimal
tree. The next two larger trees are part of a pattern where the
misclassification cost decreases.
The 7-node tree has a misclassification cost that is less than the cost for
the 4-node tree. Because the 7-node tree is similar in complexity, you can use
the larger tree with its additional prediction accuracy to study the important
variables and to make predictions.
In addition to the criterion values for alternative trees, you can also
compare the complexity of trees and the usefulness of different nodes. Consider
the following examples of reasons that an analyst chooses a particular tree
that does not sacrifice performance when compared to other trees:
- The analyst chooses a smaller
tree that provides a clearer view of the most important variables.
- The analysis chooses a tree
because the splits are on variables that are easier to measure than the
variables in another tree.
- The analyst chooses a tree
because a particular terminal node is of interest.