Thanks to several online resources, including this Cross Validated question, I am clear that - within Random Forests -
mtry represents the number of variables randomly sampled without replacement at each split of a tree.
What I am not clear on is if sampled without replacement means that a variable that was sampled for the first split, but passed on because another another randomly sampled variable provided greater outcome homogeneity, could be sampled again for the second split of the tree.
Here is a simple example:
I have a binary classification problem.
My dataset has 8 predictor variables:
I've set up my model where
For the first split of the first tree, the three randomly selected variables to test are
V7and the algorithm has determined that
V4provides the maximum homogeneity of the three variables.
I understand that
V4 is not an option for the randomly sampled variables of the second splits (2) because it is already being used for the first split.
My question is: Are
V7 available to be randomly sampled again in both of the second splits along with the variables that were not sampled in the first split? i.e., are the variables available for sampling in both of the second splits