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+\name{mob}
+\encoding{latin1}
+
+\alias{mob}
+\alias{mob-class}
+\alias{coef.mob}
+\alias{deviance.mob}
+\alias{fitted.mob}
+\alias{logLik.mob}
+\alias{predict.mob}
+\alias{print.mob}
+\alias{residuals.mob}
+\alias{sctest.mob}
+\alias{summary.mob}
+\alias{weights.mob}
+
+\title{Model-based Recursive Partitioning}
+
+\description{
+  MOB is an algorithm for model-based recursive partitioning yielding
+  a tree with fitted models associated with each terminal node.
+}
+
+\usage{
+mob(formula, weights, data = list(), na.action = na.omit, model = glinearModel,
+  control = mob_control(), \dots)
+
+\method{predict}{mob}(object, newdata = NULL, type = c("response", "node"), \dots)
+\method{summary}{mob}(object, node = NULL, \dots)
+\method{coef}{mob}(object, node = NULL, \dots)
+\method{sctest}{mob}(x, node = NULL, \dots)
+}
+
+\arguments{
+  \item{formula}{A symbolic description of the model to be fit. This
+    should be of type \code{y ~ x1 + \dots + xk | z1 + \dots + zl} where
+    the variables before the \code{|} are passed to the \code{model} and
+    the variables after the \code{|} are used for partitioning.}
+  \item{weights}{An optional vector of weights to be used in the fitting
+    process. Only non-negative integer valued weights are allowed (default = 1).}
+  \item{data}{A data frame containing the variables in the model.}
+  \item{na.action}{A function which indicates what should happen when the data
+    contain \code{NA}s, defaulting to \code{\link{na.omit}}.}
+  \item{model}{A model of class \code{"\linkS4class{StatModel}"}. See details
+    for requirements.}
+  \item{control}{A list with control parameters as returned by
+    \code{\link{mob_control}}.}
+  \item{\dots}{Additional arguments passed to the \code{fit} call for
+    the \code{model}.}
+  \item{object, x}{A fitted \code{mob} object.}
+  \item{newdata}{A data frame with new inputs, by default the learning data
+    is used.}
+  \item{type}{A character string specifying whether the response should be
+    predicted (inherited from the \code{predict} method for the \code{model})
+    or the ID of the associated terminal node.}
+  \item{node}{A vector of node IDs for which the corresponding method should
+    be applied.}
+}
+
+\details{
+Model-based partitioning fits a model tree using the following algorithm:
+  \enumerate{
+    \item \code{fit} a \code{model} (default: a generalized linear model
+          \code{"\linkS4class{StatModel}"} with formula \code{y ~ x1 + \dots + xk}
+	  for the observations in the current node.
+    \item Assess the stability of the model parameters with respect to each
+          of the partitioning variables \code{z1}, \dots, \code{zl}. If
+	  there is some overall instability, choose the variable \code{z}
+	  associated with the smallest \eqn{p} value for partitioning, otherwise
+	  stop. For performing the parameter instability fluctuation test,
+	  a \code{\link[sandwich]{estfun}} method and a \code{\link{weights}} method is
+	  needed.
+    \item Search for the locally optimal split in \code{z} by minimizing the
+          objective function of the \code{model}. Typically, this will be
+	  something like \code{\link{deviance}} or the negative \code{\link{logLik}}
+	  and can be specified in \code{\link{mob_control}}.
+    \item Re-fit the \code{model} in both children, using \code{\link{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
+\code{vignette("MOB")}.  
+  
+For the fitted MOB tree, several standard methods are inherited if they are
+available for fitted \code{model}s, such as \code{print}, \code{predict},
+\code{residuals}, \code{logLik}, \code{deviance}, \code{weights}, \code{coef} and
+\code{summary}. By default, the latter four return the result (deviance, weights,
+coefficients, summary) for all terminal nodes, but take a \code{node} argument
+that can be set to any node ID. The \code{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.
+}
+
+\value{
+  An object of class \code{mob} inheriting from \code{\link{BinaryTree-class}}.
+  Every node of the tree is additionally associated with a fitted model.
+}
+
+\references{ 
+
+   Achim Zeileis, Torsten Hothorn, and Kurt Hornik (2008). Model-Based
+   Recursive Partitioning. \emph{Journal of Computational and Graphical Statistics}, 
+   \bold{17}(2), 492--514.
+
+}
+
+\seealso{\code{\link{plot.mob}}, \code{\link{mob_control}}}
+
+\examples{
+
+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))
+}
+}
+\keyword{tree}