Splitting Criterion

Node splitting is based on the LogWorth statistic, which is reported in Candidate reports for nodes. LogWorth is calculated as follows:

-log10(p-value)

where the adjusted p-value is calculated in a complex manner that takes into account the number of different ways splits can occur. This calculation is very fair compared to the unadjusted p-value, which favors Xs with many levels, and the Bonferroni p-value, which favors Xs with small numbers of levels. Details about the method are discussed in Sall (2002).

For continuous responses, the Sum of Squares (SS) is reported in node reports. This is the change in the error sum-of-squares due to the split.

A candidate SS that has been chosen is:

SStest = SSparent - (SSright + SSleft) where SS in a node is just s2(n - 1).

Also reported for continuous responses is the Difference statistic. This is the difference between the predicted values for the two child nodes of a parent node.

For categorical responses, the G2 (likelihood-ratio chi-square) appears in the report. This is actually twice the [natural log] entropy or twice the change in the entropy. Entropy is Σ -log(p) for each observation, where p is the probability attributed to the response that occurred.

A candidate G2 that has been chosen is:

G2 test = G2 parent - (G2 left + G2 right).

Partition actually has two rates; one used for training that is the usual ratio of count to total, and another that is slightly biased away from zero. By never having attributed probabilities of zero, this allows logs of probabilities to be calculated on validation or excluded sets of data, used in Entropy R-Square.