user1745691 - 15 days ago 6x
R Question

# What is the difference between rel error and x error in a rpart decision tree?

I have a purely categorical dataframe from the UCI machine learning database
https://archive.ics.uci.edu/ml/datasets/Diabetes+130-US+hospitals+for+years+1999-2008

I am using rpart to form a decision tree based on a new category on whether patients return before 30 days (a new failed category).

I am using the following parameters for my decision tree

``````    tree_model <- rpart(Failed ~ race + gender + age+ time_in_hospital+ medical_specialty + num_lab_procedures+ num_procedures+num_medications+number_outpatient+number_emergency+number_inpatient+number_diagnoses+max_glu_serum+ A1Cresult+metformin+glimepiride+glipizide+glyburide+pioglitazone+rosiglitazone+insulin+change,method="class", data=training_data, control=rpart.control(minsplit=2, cp=0.0001, maxdepth=20, xval = 10), parms = list(split = "gini"))
``````

Printing the results yields:

``````       CP     nsplit rel error  xerror     xstd
1 0.00065883      0   1.00000  1.0000   0.018518
2 0.00057648      8   0.99424  1.0038   0.018549
3 0.00025621     10   0.99308  1.0031   0.018543
4 0.00020000     13   0.99231  1.0031   0.018543
``````

I see that the relative error is going down as the decision tree branches off, but the xerror goes up - which I don't understand as I would have thought that the error would reduce the more branches there are and the more complex the tree is.

I take it that the xerror is most important, since most methods for tree pruning would cut the tree at the root.

Can someone explain to me why the xerror is what is focused on when pruning the tree?
And when we summarise what the error of the decision tree classifier is, is the error 0.99231 or 1.0031?

A rule of thumb is to choose the lowest level where the `rel_error + xstd < xerror`.
If you run `plotcp` on your output it will also show you the optimal place to prune the tree.