Sigma in tree importance
sigma (how spread out a stay's GPS points are) has a modest weight in the simple model (+0.78 in the Final model). But the tree models rank it as one of their most important inputs:
| Run | σ rank |
|---|---|
| Stay-level, RF impurity / XGBoost gain | 2nd / 2nd |
| Stay-level, out-of-fold permutation | RF 1st, XGBoost 2nd |
| Row-level, RF impurity | 1st (0.31) |
| Row-level, XGBoost gain | 2nd, after the building indicator |
(Impurity, gain and permutation are three common ways to measure how much a tree model uses an input.)
There are two possible explanations:
- σ may work like a threshold: below some spread one answer is likely, above it another. One straight-line weight cannot show that.
- The trees may use σ as a stand-in for something related to it, such as how long the stay lasted or the surroundings.
σ² did not survive in the simple model (Stepwise VIF elimination). Other forms, such as log(σ) or a threshold, have not been tried yet.
In the row-level test, the trees learn the differences between types directly from the place-type input. f_distance ranks last in both tree models.
Sources: ML baseline, stay level (superseded), ML ceiling check, row level. Part of Complexity and transfer.