# ctree

##### Conditional Inference Trees

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

- Keywords
- tree

##### Usage

```
ctree(formula, data, subset, weights, na.action = na.pass, offset, cluster,
control = ctree_control(…), ytrafo = NULL,
converged = NULL, scores = NULL, doFit = TRUE, …)
```

##### 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.

- offset
an optional vector of offset values.

- cluster
an optional factor indicating independent clusters. Highly experimental, use at your own risk.

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

- control
a list with control parameters, see

`ctree_control`

.- ytrafo
an optional named list of functions to be applied to the response variable(s) before testing their association with the explanatory variables. Note that this transformation is only performed once for the root node and does not take weights into account. Alternatively,

`ytrafo`

can be a function of`data`

and`weights`

. In this case, the transformation is computed for every node with corresponding weights. This feature is experimental and the user interface likely to change.- converged
an optional function for checking user-defined criteria before splits are implemented. This is not to be used and very likely to change.

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

- doFit
a logical, if

`FALSE`

, the tree is not fitted.- …
arguments passed to

`ctree_control`

.

##### Details

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).

##### Value

An object of class `party`

.

##### References

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.

##### Examples

```
# NOT RUN {
### 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("TH.data") && require("survival") &&
require("coin") && require("Formula")) {
data("GBSG2", package = "TH.data")
(GBSG2ct <- ctree(Surv(time, cens) ~ ., data = GBSG2))
predict(GBSG2ct, newdata = GBSG2[1:2,], type = "response")
plot(GBSG2ct)
### with weight-dependent log-rank scores
### log-rank trafo for observations in this node only (= weights > 0)
h <- function(y, x, start = NULL, weights, offset, estfun = TRUE, object = FALSE, ...) {
if (is.null(weights)) weights <- rep(1, NROW(y))
s <- logrank_trafo(y[weights > 0,,drop = FALSE])
r <- rep(0, length(weights))
r[weights > 0] <- s
list(estfun = matrix(as.double(r), ncol = 1), converged = TRUE)
}
### very much the same tree
(ctree(Surv(time, cens) ~ ., data = GBSG2, ytrafo = h))
}
### multivariate responses
airct2 <- ctree(Ozone + Temp ~ ., data = airq)
airct2
plot(airct2)
# }
```

*Documentation reproduced from package partykit, version 1.2-5, License: GPL-2 | GPL-3*