I am working through chapter 14 of the book Applied predictive modeling (Kuhn, Max, and Kjell Johnson. Applied predictive modeling. Vol. 26. New York: Springer, 2013.). For tree models with categorial predictors the splitting procedure can treat the data as grouped categories (no binary dummy variables are created). One approach is to order categories according to their proportion of samples in the selected class.
The upper plot in Figure 14.2 shows the probability of success for each category of the grant data. How is the probability of success calculated for each category? Is it based only on the number of samples which fall into one category or is it based on the observations of successfull CI grants which belong to each category?
How would a contingency table at the split between categories K and Q look like (as on page 371 of the book)? How is the Gini index computed at split K/Q (between categories K and Q) in order to produce the bottom plot in Figure 14.2?