I'm looking at the depth of trees in a random forest model, using the
randomnForestExplainer package in R.
The model I'm using is a basic linear regression model where there are 3 important predictor variables (p) and the rest are noise (q).
The first test I ran I set p = 3 and q = 10 and found that the mean minimal depth of the variables was never over 7 trees.
However, for the second test I set p = 3 and q = 100 and found that the mean minimal depth of the variables was 17 trees.
this can be seen in the plots below for both tests, where the colour-coded bar on the right displays the minimal depth of each variable.
So, my question is: why does adding more noise variables to my model mean deeper trees?