Classification trees with unbiased multiway splits

Two univariate split methods and one linear combination split method are proposed for the construction of classification trees with multiway splits. Examples are given where the trees are more compact and hence easier to interpret than binary trees. A major strength of the univariate split methods is that they have negligible bias in variable selection, both when the variables differ in the number of splits they offer and when they differ in the number of missing values. This is an advantage because inferences from the tree structures can be adversely affected by selection bias. The new methods are shown to be highly competitive in terms of computational speed and classification accuracy of future observations.