# What is the purpose of working on a logit scale in partial dependence plots?

What is the purpose of working on a logit scale in partial dependence plots (in binary classification)?

One could simply go about as follows:

1. Grow a forest
2. 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.
3. For each of the v data sets thus obtained, predict the response using random forest.
4. For each of the v data sets, average these predictions
5. 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):

Step 4.Compute average(log(predictions)-0.5(log(predicions) + log(1-predictions)))=average(0.5 logit(predictions))

Step 5.Plot v and the corresponding computed 1/2 logit(predictions)

Why?

• Perhaps there is a theoretical objection to averaging probabilities? I faced this issue in my plotmo package, and made some comments on it in Section 9.3 of the package vignette (link). – Stephen Milborrow Feb 22 '18 at 23:28