ctree assesses the null hypothesis of no association between the response and all regressor variables using a quadratic correlation test statistic. Depending on whether the involved variables are numeric, categorical, or survival, different types of scores are used in these correlation tests. See also: What is the test statistics used for a conditional inference regression tree?
Alternatively, a maximally-selected statistic can be used which makes a difference if one of the score functions used are multivariate (e.g., for multi-level categorical variables).
And, by default, the resulting p-values are Bonferroni-corrected for multiple testing across the number of regressor variables. Alternatively, the Bonferroni correction can be omitted (
"Univariate") or the test statistics themselves rather than their p-values can be used (
In most situations there should be no need to modify the defaults. For more details about the
ctree algorithm see:
vignette("ctree", package = "partykit") as well as the original manuscript: Torsten Hothorn, Kurt Hornik, Achim Zeileis (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651–674. doi:10.1198/106186006X133933
For the underlying conditional inference techniques:
vignette("LegoCondInf", package = "coin") as well as the original manuscript: Torsten Hothorn, Kurt Hornik, Mark A. Van de Wiel, Achim Zeileis (2006). A Lego System for Conditional Inference. The American Statistician, 60(3), 257–263. doi:10.1198/000313006X118430