Rating Scale Trees

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Description

Recursive partitioning (also known as trees) based on rating scale models.

Usage

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rstree(formula, data, na.action, reltol = 1e-10,
  deriv = c("sum", "diff"), maxit = 100L, ...)

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

## S3 method for class 'rstree'
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. Additionally each item (column) should have the same maximum value (see pctree for a way to handle variable maximum values).

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).

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 rsmodel to optim.

...

arguments passed to the underlying functions, i.e., to mob_control for rstree, 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

Rating scale trees are an application of model-based recursive partitioning (implemented in mob) to rating scale models (implemented in rsmodel).

Various methods are provided for "rstree" objects, most of them inherit their behavior from "mob" objects (e.g., print, summary, etc.). For the rating scale models in the nodes of a tree, coef extracts all item parameters. The plot method employs the node_regionplot panel-generating function by default.

Various methods are provided for "rstree" objects, most of them inherit their behavior from "modelparty" objects (e.g., print, summary, etc.). For the RSMs 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 "rstree" inheriting from class "modelparty".

References

Komboz B, Zeileis A, Strobl C (2016). Tree-Based Global Model Tests for Polytomous Rasch Models. Educational and Psychological Measurement, forthcoming.

See Also

mob, rsmodel, pctree, raschtree

Examples

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o <- options(digits = 4)

## verbal aggression data from package psychotools
data("VerbalAggression", package = "psychotools")

## responses to the first other-to-blame situation (bus)
VerbalAggression$s1 <- VerbalAggression$resp[, 1:6]

## exclude subjects who only scored in the highest or the lowest categories
VerbalAggression <- subset(VerbalAggression, rowSums(s1) > 0 & rowSums(s1) < 12)

## fit rating scale tree model for the first other-to-blame situation
rst <- rstree(s1 ~ anger + gender, data = VerbalAggression)

## print tree (with and without parameters)
print(rst)
print(rst, FUN = function(x) " *")

## show summary for terminal panel nodes
summary(rst)

## visualization
plot(rst, type = "regions")
plot(rst, type = "profile")

## extract item and threshold parameters
coef(rst)
itempar(rst)
threshpar(rst)

## inspect parameter stability tests in all splitting nodes
library("strucchange")
sctest(rst, node = 1)
sctest(rst, node = 2)

options(digits = o$digits)