Beta Regression Trees

Description

Fit beta regression trees via model-based recursive partitioning.

Usage

betatree(formula, partition,
  data, subset = NULL, na.action = na.omit, 
  link = "logit", link.phi = "log", control = betareg.control(),
  ...)

betaReg(control = betareg.control())

Arguments

Details

Beta regression trees are an application of model-based recursive partitioning (implemented in mob, see Zeileis et al. 2008) to beta regression (implemented in betareg, see Cribari-Neto and Zeileis 2010). For plugging in betareg into mob some glue is required which is provided by betaReg. See also Grün at al. (2012) for more details.

Various methods are provided for "betatree" objects, most of them inherit their behavior from "mob" objects (e.g., print, summary, coef, etc.). The plot method employs the node_bivplot panel-generating function.

betaReg is a wrapper function that creates a "StatModel" object with certain fitting parameters passed on to betareg.fit for fitting beta regression models. It is the S4 interface required for plug-in to mob. The user does not have to call this directly but can simply use the betatree interface.

Value

betatree() returns an object of S3 class "betatree" which is a list containing only a single element of S4 class "mob" (because this is currently not exported from the party package).

betaReg returns an S4 object of class "StatModel" that fits beta regression models with the specified control arguments. When applied to data, it returns S3 objects of class "betaReg" inheriting from "betareg".

References

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. http://www.jstatsoft.org/v34/i02/.

Grün, B., Kosmidis, I., and Zeileis, A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1–25. http://www.jstatsoft.org/v48/i11/.

Zeileis, A., Hothorn, T., and Hornik K. (2008). Model-Based Recursive Partitioning. Journal of Computational and Graphical Statistics, 17(2), 492–514.

See Also

betareg, betareg.fit, mob

Examples

## data with two groups of dyslexic and non-dyslexic children
data("ReadingSkills", package = "betareg")
## additional random noise (not associated with reading scores)
set.seed(1071)
ReadingSkills$x1 <- rnorm(nrow(ReadingSkills))
ReadingSkills$x2 <- runif(nrow(ReadingSkills))
ReadingSkills$x3 <- factor(rnorm(nrow(ReadingSkills)) > 0)

## fit beta regression tree: in each node
##   - accurcay's mean and precision depends on iq
##   - partitioning is done by dyslexia and the noise variables x1, x2, x3
## only dyslexi is correctly selected for splitting
bt <- betatree(accuracy ~ iq | iq, ~ dyslexia + x1 + x2 + x3,
  data = ReadingSkills, minsplit = 10)
plot(bt)

## inspect result
coef(bt)
sctest(bt)
summary(bt, node = 2)
summary(bt, node = 3)

## add a numerical variable with relevant information for splitting
ReadingSkills$x4 <- rnorm(nrow(ReadingSkills), c(-1.5, 1.5)[ReadingSkills$dyslexia])

bt2 <- betatree(accuracy ~ iq | iq, ~ x1 + x2 + x3 + x4,
  data = ReadingSkills, minsplit = 10)
plot(bt2)

## inspect result
coef(bt2)
sctest(bt2)
summary(bt2, node = 2)
summary(bt2, node = 3)

Results