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 `vignette("ctree", package = "partykit")`

for some remarks about the 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).