pctree function

Partial Credit Trees

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

pctree(formula, data, na.action, nullcats = c("keep", "downcode", "ignore"),
  reltol = 1e-10,  deriv = c("sum", "diff"), maxit = 100L, ...)

## S3 method for class 'pctree'
predict(object, newdata = NULL,
  type = c("probability", "cumprobability", "mode", "median", "mean",
    "category-information", "item-information", "test-information", "node"),
  personpar = 0, ...)

## S3 method for class '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 (NAs).

• 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 via pcmodel

  to optim.

• ...: 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.

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. tools:::Rd_expr_doi("10.1177/0013164416664394")

Returns

An object of S3 class "pctree" inheriting from class "modelparty".

See Also

mob, pcmodel, rstree, raschtree

Examples

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)

## 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))