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I am using the gbm package and I am using the gbm.step function. In the ?gbm.step I see tree.complexity sets the complexity of individual trees. Is this equivalent to the depth of the tree ?

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There is a vignette by Jane Elith and John Leathwick for GBM's in dismopackage . The package actually uses gbm.step implementation from gbm package.

Vignette referes to

Elith, J., Leathwick, J.R., and Hastie, T. (2008). Boosted regression trees - a new technique for modelling ecological data. Journal of Animal Ecology

This is freely avalaible in the net and says:

Tree complexity (tc) controls whether interactions are fitted: a tc of 1 (single decision stump; two terminal nodes) fits an additive model, a tc of two fits a model with up to two-way interactions, and so on.

So, it seems it is a depth as you supposed.

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