M5P Interpretations and Questions I need some advice when interpreting the output of the M5P model as shown below; I have some questions:


*

*How is the 0.5 that determines the construction of each LM derived?

*What do the numbers in the parentheses refer to?

*What does 115% in LM8 mean? How can it be over 100%?



region=1,3,4 <= 0.5 : LM1 (20000/19.779%)
region=1,3,4 >  0.5 : 
|   in-store=0 <= 0.5 : 
|   |   region=4 <= 0.5 : 
|   |   |   region=3,4 <= 0.5 : 
|   |   |   |   age <= 55.5 : 
|   |   |   |   |   age <= 31.5 : 
|   |   |   |   |   |   age <= 24.5 : LM2 (1107/77.967%)
|   |   |   |   |   |   age >  24.5 : LM3 (2649/71.098%)
|   |   |   |   |   age >  31.5 : LM4 (8937/70.946%)
|   |   |   |   age >  55.5 : LM5 (3307/37.787%)
|   |   |   region=3,4 >  0.5 : LM6 (10999/37.952%)
|   |   region=4 >  0.5 : LM7 (13001/77.69%)
|   in-store=0 >  0.5 : LM8 (20000/115.636%)


I read in Wang & Whitten that the splits are supposed to be created by taking the SD(node.examples) <0.05*SD, but that doesnt match the output above.
Wang, Y., & Witten, I. H. (1996). Induction of model trees for predicting continuous classes.
 A: *

*M5P sets the split point mid-way between the two neighboring numeric values. So age <= 55.5 means that observations with age up to 55 assigned to one node and starting from 56 to the other node. For categorical variables, dummy variables like region=1,3,4 are constructed that can either be 0 or 1. Hence, M5P sets the split point at 0.5. One could argue that region != 1,3,4 might have been more intelligible than region=1,3,4 <= 0.5. See also this discussion on the Weka mailing list: http://weka.8497.n7.nabble.com/Categorical-Variables-in-M5Rules-or-M5P-td17589.html.

*The first number is simply the number of observations (aka instances) in that node. The second number gives the percentage of the RMSE in that node in relation to the RMSE of an intercept-only model on the entire learning data. (The latter RMSE is simply the standard deviation of the response/target variable on the full data.) See also this discussion on the Weka mailing list: http://weka.8497.n7.nabble.com/in-Regression-Tree-leafs-td36442.html#a36449.

*The models are not nested because they pertain to different subsamples of the data set. Hence, the ratio of RMSEs can be larger than 100%.
