ctree function - RDocumentation (2024)

Recursive partitioning for continuous, censored, ordered, nominal and multivariate response variables in a conditional inference framework.

An object of class party.

Function partykit::ctree is a reimplementation of (most of) party::ctree employing the new party infrastructure of the partykit infrastructure. The vignette vignette("ctree", package = "partykit") explains internals of the different implementations.

Conditional inference trees estimate a regression relationship by binary recursive partitioning in a conditional inference framework. Roughly, the algorithm works as follows: 1) Test the global null hypothesis of independence between any of the input variables and the response (which may be multivariate as well). Stop if this hypothesis cannot be rejected. Otherwise select the input variable with strongest association to the response. This association is measured by a p-value corresponding to a test for the partial null hypothesis of a single input variable and the response. 2) Implement a binary split in the selected input variable. 3) Recursively repeate steps 1) and 2).

The implementation utilizes a unified framework for conditional inference, or permutation tests, developed by Strasser and Weber (1999). The stop criterion in step 1) is either based on multiplicity adjusted p-values (testtype = "Bonferroni" in ctree_control) or on the univariate p-values (testtype = "Univariate"). In both cases, the criterion is maximized, i.e., 1 - p-value is used. A split is implemented when the criterion exceeds the value given by mincriterion as specified in ctree_control. For example, when mincriterion = 0.95, the p-value must be smaller than $0.05$ in order to split this node. This statistical approach ensures that the right-sized tree is grown without additional (post-)pruning or cross-validation. The level of mincriterion can either be specified to be appropriate for the size of the data set (and 0.95 is typically appropriate for small to moderately-sized data sets) or could potentially be treated like a hyperparameter (see Section~3.4 in Hothorn, Hornik and Zeileis, 2006). The selection of the input variable to split in is based on the univariate p-values avoiding a variable selection bias towards input variables with many possible cutpoints. The test statistics in each of the nodes can be extracted with the sctest method. (Note that the generic is in the strucchange package so this either needs to be loaded or sctest.constparty has to be called directly.) In cases where splitting stops due to the sample size (e.g., minsplit or minbucket etc.), the test results may be empty.

Predictions can be computed using predict, which returns predicted means, predicted classes or median predicted survival times and more information about the conditional distribution of the response, i.e., class probabilities or predicted Kaplan-Meier curves. For observations with zero weights, predictions are computed from the fitted tree when newdata = NULL.

By default, the scores for each ordinal factor x are 1:length(x), this may be changed for variables in the formula using scores = list(x = c(1, 5, 6)), for example.

For a general description of the methodology see Hothorn, Hornik and Zeileis (2006) and Hothorn, Hornik, van de Wiel and Zeileis (2006).

Hothorn T, Hornik K, Van de Wiel MA, Zeileis A (2006). A Lego System for Conditional Inference. The American Statistician, 60(3), 257--263.

Hothorn T, Hornik K, Zeileis A (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651--674.

Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. Journal of Machine Learning Research, 16, 3905--3909.

Strasser H, Weber C (1999). On the Asymptotic Theory of Permutation Statistics. Mathematical Methods of Statistics, 8, 220--250.