party (version 0.2-3)

Conditional Trees: Conditional Trees

Description

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

Usage

ctree(formula, data, subset = NULL, weights = NULL, 
      controls = ctree_control(), xtrafo = NULL, ytrafo = NULL, 
      scores = NULL)

Arguments

formula

a symbolic description of the model to be fit.

data

an 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.

controls

an object of class TreeControl, which can be obtained using ctree_control.

xtrafo

an optional function to be applied to all input variables.

ytrafo

an optional function to be applied to all response variables.

scores

an optional named list of scores to be attached to ordered factors.

Value

• An object of class BinaryTree.

Details

Conditional 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 resonse. 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 a p-value (teststattype = "Bonferroni" or teststattype = "MonteCarlo" in ctree_control) or on the raw (standardized) test statistic (teststattype = "Raw"). 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.

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

For a general description of the methodology see Hothorn, Hornik and Zeileis (2004).

References

Torsten Hothorn, Kurt Hornik and Achim Zeileis (2004). Unbiased Recursive Partitioning: A Conditional Inference Framework. Technical Report Nr. 8, Research Report Series / Department of Statistics and Mathematics, WU Wien. http://epub.wu-wien.ac.at/dyn/openURL?id=oai:epub.wu-wien.ac.at:epub-wu-01_756

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

Examples

### regression
    data(airquality)
    airq <- subset(airquality, !is.na(Ozone))
    airct <- ctree(Ozone ~ ., data = airq, 
                   controls = ctree_control(maxsurrogate = 3))
    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 <- treeresponse(irisct, newdata = iris[1:10,])

    ### ordinal regression
    data(mammoexp) 
    mammoct <- ctree(ME ~ ., data = mammoexp) 
    plot(mammoct)

    ### estimated class probabilities
    treeresponse(mammoct, newdata = mammoexp[1:10,])

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

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