I have a few questions regarding the variable importance in random forest. The
importance function outputs two types of importance measures (
1 = mean decrease in accuracy,
2 = mean decrease in node impurity). For the 2nd measure, the manual says:
The second measure is the total decrease in node impurities from splitting on the variable, averaged over all trees.
Does “over all trees” actually mean “over all trees where that predictor is used as a splitter”?
At each split, what’s the criteria to choose which predictor to use as a splitter? Could a predictor be used more than once as splitters in the same tree?
Is it guaranteed that each predictor got at least one chance to be used as splitter in the building of the forest? If not, what would be that predictor’s importance value?