Model-based Recursive Partitioning
MOB is an algorithm for model-based recursive partitioning yielding a tree with fitted models associated with each terminal node.
mob(formula, weights, data = list(), na.action = na.omit, model = glinearModel,
control = mob_control(), ...)
## S3 method for class 'mob'
predict(object, newdata = NULL, type = c("response", "node"), ...)
## S3 method for class 'mob'
summary(object, node = NULL, ...)
## S3 method for class 'mob'
coef(object, node = NULL, ...)
## S3 method for class 'mob'
sctest(x, node = NULL, ...)formula |
A symbolic description of the model to be fit. This
should be of type |
weights |
An optional vector of weights to be used in the fitting process. Only non-negative integer valued weights are allowed (default = 1). |
data |
A data frame containing the variables in the model. |
na.action |
A function which indicates what should happen when the data
contain |
model |
A model of class |
control |
A list with control parameters as returned by
|
... |
Additional arguments passed to the |
object, x |
A fitted |
newdata |
A data frame with new inputs, by default the learning data is used. |
type |
A character string specifying whether the response should be
predicted (inherited from the |
node |
A vector of node IDs for which the corresponding method should be applied. |
Model-based partitioning fits a model tree using the following algorithm:
fit a model (default: a generalized linear model
"StatModel" with formula y ~ x1 + ... + xk
for the observations in the current node.
Assess the stability of the model parameters with respect to each
of the partitioning variables z1, ..., zl. If
there is some overall instability, choose the variable z
associated with the smallest p value for partitioning, otherwise
stop. For performing the parameter instability fluctuation test,
a estfun method and a weights method is
needed.
Search for the locally optimal split in z by minimizing the
objective function of the model. Typically, this will be
something like deviance or the negative logLik
and can be specified in mob_control.
Re-fit the model in both children, using reweight
and repeat from step 2.
More details on the conceptual design of the algorithm can be found in
Zeileis, Hothorn, Hornik (2008) and some illustrations are provided in
vignette("MOB").
For the fitted MOB tree, several standard methods are inherited if they are
available for fitted models, such as print, predict,
residuals, logLik, deviance, weights, coef and
summary. By default, the latter four return the result (deviance, weights,
coefficients, summary) for all terminal nodes, but take a node argument
that can be set to any node ID. The sctest method extracts the results
of the parameter stability tests (aka structural change tests) for any given
node, by default for all nodes. Some examples are given below.
An object of class mob inheriting from BinaryTree-class.
Every node of the tree is additionally associated with a fitted model.
Achim Zeileis, Torsten Hothorn, and Kurt Hornik (2008). Model-Based Recursive Partitioning. Journal of Computational and Graphical Statistics, 17(2), 492–514.
set.seed(290875)
if(require("mlbench")) {
## recursive partitioning of a linear regression model
## load data
data("BostonHousing", package = "mlbench")
## and transform variables appropriately (for a linear regression)
BostonHousing$lstat <- log(BostonHousing$lstat)
BostonHousing$rm <- BostonHousing$rm^2
## as well as partitioning variables (for fluctuation testing)
BostonHousing$chas <- factor(BostonHousing$chas, levels = 0:1,
labels = c("no", "yes"))
BostonHousing$rad <- factor(BostonHousing$rad, ordered = TRUE)
## partition the linear regression model medv ~ lstat + rm
## with respect to all remaining variables:
fmBH <- mob(medv ~ lstat + rm | zn + indus + chas + nox + age +
dis + rad + tax + crim + b + ptratio,
control = mob_control(minsplit = 40), data = BostonHousing,
model = linearModel)
## print the resulting tree
fmBH
## or better visualize it
plot(fmBH)
## extract coefficients in all terminal nodes
coef(fmBH)
## look at full summary, e.g., for node 7
summary(fmBH, node = 7)
## results of parameter stability tests for that node
sctest(fmBH, node = 7)
## -> no further significant instabilities (at 5% level)
## compute mean squared error (on training data)
mean((BostonHousing$medv - fitted(fmBH))^2)
mean(residuals(fmBH)^2)
deviance(fmBH)/sum(weights(fmBH))
## evaluate logLik and AIC
logLik(fmBH)
AIC(fmBH)
## (Note that this penalizes estimation of error variances, which
## were treated as nuisance parameters in the fitting process.)
## recursive partitioning of a logistic regression model
## load data
data("PimaIndiansDiabetes", package = "mlbench")
## partition logistic regression diabetes ~ glucose
## wth respect to all remaining variables
fmPID <- mob(diabetes ~ glucose | pregnant + pressure + triceps +
insulin + mass + pedigree + age,
data = PimaIndiansDiabetes, model = glinearModel,
family = binomial())
## fitted model
coef(fmPID)
plot(fmPID)
plot(fmPID, tp_args = list(cdplot = TRUE))
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