swh:1:snp:813359ba77493c9d5dd1abad9a1f53490a8abf57
Tip revision: b1d73278a87bcb94c00cedbbaff294f96e71bbf0 authored by Torsten Hothorn on 13 April 2010, 00:00:00 UTC
version 1.0-11
version 1.0-11
Tip revision: b1d7327
MaxstatTest.Rd
\name{MaxstatTest}
\alias{maxstat_test}
\alias{maxstat_test.formula}
\alias{maxstat_test.IndependenceProblem}
\title{ Maximally Selected Statistics }
\description{
Testing the independence of a set of ordered or numeric covariates and a
response of arbitrary measurement scale against cutpoint alternatives.
}
\usage{
\method{maxstat_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots)
\method{maxstat_test}{IndependenceProblem}(object,
distribution = c("asymptotic", "approximate"),
teststat = c("max", "quad"),
minprob = 0.1, maxprob = 1 - minprob, ...)
}
\arguments{
\item{formula}{a formula of the form \code{y ~ x1 + ... + xp | block} where \code{y}
and covariates \code{x1} to \code{xp} can be variables measured at arbitrary scales;
\code{block} is an optional factor for stratification.}
\item{data}{an optional data frame containing the variables in the
model formula.}
\item{subset}{an optional vector specifying a subset of observations
to be used.}
\item{weights}{an optional formula of the form \code{~ w} defining
integer valued weights for the observations.}
\item{object}{an object inheriting from class \code{IndependenceProblem}.}
\item{distribution}{a character, the null distribution of the test statistic
can be approximated by its asymptotic distribution (\code{asymptotic})
or via Monte-Carlo resampling (\code{approximate}).
Alternatively, the functions
\code{\link{approximate}} or \code{\link{asymptotic}} can be
used to specify how the exact conditional distribution of the test statistic
should be calculated or approximated.}
\item{teststat}{a character, the type of test statistic to be applied: a
maximum type statistic (\code{max}) or a quadratic form
(\code{quad}).}
\item{minprob}{a fraction between 0 and 0.5;
consider only cutpoints greater than
the \code{minprob} * 100 \% quantile of \code{x}.}
\item{maxprob}{a fraction between 0.5 and 1;
consider only cutpoints smaller than
the \code{maxprob} * 100 \% quantile of \code{x}.}
\item{\dots}{further arguments to be passed to or from methods.}
}
\details{
The null hypothesis of independence of all covariates to the response
\code{y} against simple cutpoint alternatives is tested.
For an unordered covariate \code{x}, all possible partitions into two
groups are evaluated. The cutpoint is then a set of levels defining
one of the two groups.
}
\value{
An object inheriting from class \code{\link{IndependenceTest-class}} with
methods \code{\link{show}}, \code{\link{statistic}}, \code{\link{expectation}},
\code{\link{covariance}} and \code{\link{pvalue}}. The null distribution
can be inspected by \code{\link{pperm}}, \code{\link{dperm}},
\code{\link{qperm}} and \code{\link{support}} methods.
}
\references{
Rupert Miller \& David Siegmund (1982).
Maximally Selected Chi Square Statistics.
\emph{Biometrics} \bold{38}, 1011--1016.
Berthold Lausen \& Martin Schumacher (1992).
Maximally Selected Rank Statistics.
\emph{Biometrics} \bold{48}, 73--85.
Torsten Hothorn \& Berthold Lausen (2003).
On the Exact Distribution of Maximally Selected Rank
Statistics. \emph{Computational Statistics \& Data Analysis}
\bold{43}, 121--137.
Berthold Lausen, Torsten Hothorn, Frank Bretz \&
Martin Schumacher (2004). Optimally Selected Prognostic Factors.
\emph{Biometrical Journal} \bold{46}, 364--374.
J\"org M\"uller \& Torsten Hothorn (2004).
Maximally Selected Two-Sample Statistics as a new Tool for
the Identification and Assessment of Habitat Factors with
an Application to Breeding Bird Communities in Oak Forests.
\emph{European Journal of Forest Research}, \bold{123},
218--228.
Torsten Hothorn \& Achim Zeileis (2008).
Generalized maximally selected statistics, \emph{Biometrics},
\bold{64}(4), 1263--1269.
}
\examples{
### analysis of the tree pipit data in Mueller and Hothorn (2004)
maxstat_test(counts ~ coverstorey, data = treepipit)
### and for all possible covariates (simultaneously)
mt <- maxstat_test(counts ~ ., data = treepipit)
show(mt)$estimate
### reproduce applications in Sections 7.2 and 7.3
### of Hothorn & Lausen (2003) with limiting distribution
maxstat_test(Surv(time, event) ~ EF, data = hohnloser,
ytrafo = function(data) trafo(data, surv_trafo = function(x)
logrank_trafo(x, ties = "HL")))
maxstat_test(Surv(RFS, event) ~ SPF, data = sphase,
ytrafo = function(data) trafo(data, surv_trafo = function(x)
logrank_trafo(x, ties = "HL")))
}
\keyword{htest}