I'm interested in the differences in interpretation and functionality regarding weights and offsets in logistic regression trees. In my case, I am using XGBoost trees for logistic regression where the probability of event is < 1%. Each observation has a varying amount of exposure. Unfortunately I cannot share any data.

Similar questions have been asked here before. I understand how weights affect the model building solution for XGBoost. However, I do not understand the effect of offsets in tree-building. For example, this answer demonstrates for a GLM that

In a logistic regression, you would interpret a $\log Z$ offset in terms of the > odds ratios: a proportional change in $Z$ results in a given proportional change in $p/(1-p)$.

$$\begin{equation}\begin{split} \log (p/(1-p)) &= \beta' \mathrm{X} + \log Z \\ p/(1-p) &= Z \exp(\beta' \mathrm{X}) \end{split}\end{equation}$$

This question describes offsets for logistic and Poisson GLMs.

To sum up:

  1. Does an offset in a logistic tree have a similar effect and interpretation as a logistic GLM offset? I.e. does $p/(1-p) = Z \exp(\beta' \mathrm{X})$ hold for a logistic tree?

  2. In general, what's the proper way to handle varying exposure times in logistic trees?

  3. Does it make sense to use weights and offsets together?


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