partykit (version 0.1-2)

ctree: Conditional Inference Trees

Description

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

Usage

ctree(formula, data, weights, subset, na.action = na.pass,
    control = ctree_control(...), ...)

Arguments

formula

a symbolic description of the model to be fit.

data

a data frame containing the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. Only non-negative integer valued weights are allowed.

na.action

a function which indicates what should happen when the data contain missing value.

control

a list with control parameters, see ctree_control.

...

arguments passed to ctree_control.

Value

• An object of class party.

Details

Function partykit::ctree is a reimplementation of (most of) party::ctree employing the new party infrastructure of the partykit infrastructure. Although the new code was already extensively tested, it is not yet as mature as the old code. If you notice differences in the structure/predictions of the resulting trees, please contact the package maintainers. See also below for some remarks about the internals of the different implementations and how they should be merged in future releases. 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 and no form of pruning or cross-validation or whatsoever is needed. 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.

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.

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

Implementation details and roadmap: As pointed above, the function ctree is a reimplementation of ctree. Not only the R code changed but also the underlying C code which at the moment does not support the xtrafo and ytrafo arguments due to efficiency considerations. The roadmap for future releases is the following: (1) Make party depend on partykit. (2) Merge the R code into a single ctree function but keeping the two underlying C functions separate. (3) The new interface will always return an object of class party but call the new and more efficient C code only if xtrafo was not used (while ytrafo should be integrated into the new C code).

References

Helmut Strasser and Christian Weber (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics, 8, 220--250.

Torsten Hothorn, Kurt Hornik, Mark A. van de Wiel and Achim Zeileis (2006). A Lego System for Conditional Inference. The American Statistician, 60(3), 257--263.

Torsten Hothorn, Kurt Hornik and Achim Zeileis (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651--674. Preprint available from http://eeecon.uibk.ac.at/~zeileis/papers/Hothorn+Hornik+Zeileis-2006.pdf

Examples

### regression
    airq <- subset(airquality, !is.na(Ozone))
    airct <- ctree(Ozone ~ ., data = airq)
    airct
    plot(airct)
    mean((airq$Ozone - predict(airct))^2)

    ### classification
    irisct <- ctree(Species ~ .,data = iris)
    irisct
    plot(irisct)
    table(predict(irisct), iris$Species)

    ### estimated class probabilities, a list
    tr <- predict(irisct, newdata = iris[1:10,], type = "prob")

    ### survival analysis
    if (require("ipred")) {
        data("GBSG2", package = "ipred")
        GBSG2ct <- ctree(Surv(time, cens) ~ .,data = GBSG2)
        predict(GBSG2ct, newdata = GBSG2[1:2,], type = "response")        
    }

    ### multivariate responses
    airq2 <- ctree(Ozone + Temp ~ ., data = airq)
    airq2
    plot(airq2)