Conditional Trees {party} | R Documentation

## 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 = ptrafo, ytrafo = ptrafo,
          scores = NULL)

### 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.
`controls` | an object of class `TreeControl`, which can be obtained using `ctree_control`.
`xtrafo` | a function to be applied to all input variables. By default, the `ptrafo` function is applied.
`ytrafo` | a function to be applied to all response variables. By default, the `ptrafo` function is applied.
`scores` | an optional named list of scores to be attached to ordered factors.

### 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 multiplicity adjusted p-values (`testtype = "Bonferroni"` or `testtype = "MonteCarlo"` 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.

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 (2006).

### Value

An object of class `BinaryTree-class`.

### References

Torsten Hothorn, Kurt Hornik and Achim Zeileis (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics (accepted). Preprint available from http://statmath.wu-wien.ac.at/~zeileis/papers/Hothorn+Hornik+Zeileis-2006.pdf

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

### Examples

        ### regression
        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
        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,])
        }

[Package party version 0.8-6 Index]