# pctree

##### Partial Credit Trees

Recursive partitioning (also known as trees) based on partial credit models.

- Keywords
- tree

##### Usage

```
pctree(formula, data, na.action, nullcats = c("keep", "downcode", "ignore"),
reltol = 1e-10, deriv = c("sum", "diff"), maxit = 100L, …)
```# S3 method for pctree
predict(object, newdata = NULL,
type = c("probability", "cumprobability", "mode", "median", "mean",
"category-information", "item-information", "test-information", "node"),
personpar = 0, …)

# S3 method for pctree
plot(x, type = c("regions", "profile"), terminal_panel = NULL,
tp_args = list(...), tnex = 2L, drop_terminal = TRUE, ...)

##### Arguments

- formula
A symbolic description of the model to be fit. This should be of type

`y ~ x1 + x2`

where`y`

should be a matrix with items in the columns and observations in the rows and`x1`

and`x2`

are used as partitioning variables.- data
a data frame containing the variables in the model.

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

`NA`

s).- nullcats
character. How null categories should be treated. See

`pcmodel`

for details.- deriv
character. If "sum" (the default), the first derivatives of the elementary symmetric functions are calculated with the sum algorithm. Otherwise ("diff") the difference algorithm (faster but numerically unstable) is used.

- reltol, maxit
- …
arguments passed to the underlying functions, i.e., to

`mob_control`

for`pctree`

, and to the underlying`predict`

and`plot`

methods, respectively.- object, x
an object of class

`"raschtree"`

.- newdata
optional data frame with partitioning variables for which predictions should be computed. By default the learning data set is used.

- type
character specifying the type of predictions or plot. For the

`predict`

method, either just the ID of the terminal`"node"`

can be predicted or some property of the model at a given person parameter (specified by`personpar`

).- personpar
numeric person parameter (of length 1) at which the predictions are evaluated.

- terminal_panel, tp_args, tnex, drop_terminal
arguments passed to

`plot.modelparty`

/`plot.party`

.

##### Details

Partial credit trees are an application of model-based recursive partitioning
(implemented in `mob`

) to partial credit models
(implemented in `pcmodel`

).

Various methods are provided for `"pctree"`

objects, most of them
inherit their behavior from `"modelparty"`

objects (e.g., `print`

, `summary`

,
etc.). For the PCMs in the nodes of a tree, `coef`

extracts all item and threshold
parameters except those restricted to be zero. `itempar`

and `threshpar`

extract all item and threshold parameters (including the restricted ones).
The `plot`

method by default employs the `node_regionplot`

panel-generating function and the `node_profileplot`

panel-generating
function is provided as an alternative.

##### Value

An object of S3 class `"pctree"`

inheriting from class `"modelparty"`

.

##### References

Komboz B, Zeileis A, Strobl C (2018).
Tree-Based Global Model Tests for Polytomous Rasch Models.
*Educational and Psychological Measurement*, **78**(1), 128--166.
10.1177/0013164416664394

##### See Also

##### Examples

```
# NOT RUN {
o <- options(digits = 4)
## verbal aggression data from package psychotools
data("VerbalAggression", package = "psychotools")
## use response to the second other-to-blame situation (train)
VerbalAggression$s2 <- VerbalAggression$resp[, 7:12]
## exclude subjects who only scored in the highest or the lowest categories
VerbalAggression <- subset(VerbalAggression, rowSums(s2) > 0 & rowSums(s2) < 12)
## fit partial credit tree model
pct <- pctree(s2 ~ anger + gender, data = VerbalAggression)
## print tree (with and without parameters)
print(pct)
print(pct, FUN = function(x) " *")
## show summary for terminal panel nodes
summary(pct)
## visualization
plot(pct, type = "regions")
plot(pct, type = "profile")
## extract item and threshold parameters
coef(pct)
itempar(pct)
threshpar(pct)
## inspect parameter stability tests in the splitting node
if(require("strucchange")) sctest(pct, node = 1)
options(digits = o$digits)
# }
# NOT RUN {
## partial credit tree on artificial data from Komboz et al. (2018)
data("DIFSimPC", package = "psychotree")
pct2 <- pctree(resp ~ gender + age + motivation, data = DIFSimPC)
plot(pct2, ylim = c(-4.5, 4.5), names = paste("I", 1:8))
# }
```

*Documentation reproduced from package psychotree, version 0.15-3, License: GPL-2 | GPL-3*