What is the purpose of working on a logit scale in Partial Dependence Plots? (binary classification)
One could simply go about as follows:
- Grow a forest
- Suppose x has v distinct values in the training data set. Construct v data sets as follows. For each of the v values of x make up a new data se where x only takes on that value, leaving all the other values untouched.
- For each of the v data sets thus obtained, predict the response using random forest.
- For each of the v data sets, average these predictions
- Plot v and the corresponding averaged predictions
Instead of just doing that, in literature they go on and replace step 4 and 5 by (see also partialPlot in R package randomForest):
4.Compute average(log(predictions)-0.5(log(predicions) + log(1-predictions)))=average(0.5 logit(predictions))
5.Plot v and the corresponding computed 1/2 logit(predictions)
Why?
