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\name{glht-methods}
\alias{summary.glht}
\alias{confint.glht}
\alias{coef.glht}
\alias{vcov.glht}
\alias{univariate}
\alias{adjusted}
\alias{Ftest}
\alias{Chisqtest}
\title{ Methods for General Linear Hypotheses }
\description{
Simultaneous tests and confidence intervals for general linear
hypotheses.
}
\usage{
\method{summary}{glht}(object, test = adjusted(), ...)
\method{confint}{glht}(object, parm, level = 0.95, ...)
\method{coef}{glht}(object, rhs = FALSE, ...)
\method{vcov}{glht}(object, ...)
univariate()
adjusted(type = c("free", "Shaffer", "Westfall", p.adjust.methods),
...)
Ftest()
Chisqtest()
}
\arguments{
\item{object}{ an object of class \code{\link{glht}}.}
\item{test}{ a function for computing p values.}
\item{parm}{ additional parameters, currently ignored.}
\item{level}{ the confidence level required.}
\item{rhs}{logical, indicating whether the linear function
\eqn{K \hat{\beta}} or the right hand side
\eqn{m} (\code{rhs = TRUE}) of the linear hypothesis
should be returned.}
\item{type}{ the multiplicity adjustment (\code{adjusted})
to be applied. See below and \code{\link{p.adjust}}.}
\item{...}{ additional arguments, such as \code{maxpts},
\code{abseps} or \code{releps} to
\code{\link[mvtnorm]{pmvnorm}} in \code{adjusted} or
\code{\link[mvtnorm]{qmvnorm}} and \code{adjusted = FALSE}
in \code{confint}.}
}
\details{
The methods for general linear hypotheses as described by objects returned
by \code{\link{glht}} can be used to actually test the global
null hypothesis, each of the partial hypotheses and for
simultaneous confidence intervals for the linear function $K \beta$.
The \code{\link{coef}} and \code{\link{vcov}} methods compute the linear
function $K \hat{\beta}$ and its covariance, respectively.
The \code{test} argument to \code{summary} takes a function specifying
the type of test to be applied. Classical Chisq (Wald test) or F statistics
for testing the global hypothesis $H_0$ are implemented in functions
\code{Chisqtest} and \code{Ftest}. Several approaches to multiplicity adjusted p
values for each of the linear hypotheses are implemented
in function \code{adjusted}. The \code{type}
argument to \code{adjusted} specifies the method to be applied:
\code{"free"} implements adjusted p values based on the joint
normal or $t$ distribution of the linear function, and
\code{"Shaffer"} and \code{"Westfall"} implement logically constraint
multiplicity adjustments (Shaffer, 1986; Westfall, 1997).
In addition, all adjustment methods
implemented in \code{\link{p.adjust}} are available as well.
Simultaneous confidence intervals for linear functions can be computed
using method \code{\link{confint}}. Univariate confidence intervals
can be computed by specifying the additional argument \code{adjusted = FALSE}
to \code{confint}.
All simultaneous inference procedures implemented here control
the family-wise error rate (FWER). Multivariate
normal and $t$ distributions, the latter one only for models of
class \code{\link{lm}}, are evaluated using the procedures
implemented in package \code{mvtnorm}.
}
\value{
\code{summary} computes (adjusted) p values for general linear hypotheses,
\code{\link{confint}} computes (adjusted) confidence intervals.
\code{\link{coef}} returns estimates of the linear function $K \beta$
and \code{\link{vcov}} its covariance.
}
\references{
Juliet P. Shaffer (1986),
Modified sequentially rejective multiple test procedures.
\emph{Journal of the American Statistical Association},
\bold{81}, 826--831.
Peter H. Westfall (1997),
Multiple testing of general contrasts using logical constraints
and correlations. \emph{Journal of the American Statistical Association},
\bold{92}, 299--306.
}
\examples{
### set up a two-way ANOVA with interactions
amod <- aov(breaks ~ wool * tension, data = warpbreaks)
### set up all-pair comparisons for factor `tension'
wht <- glht(amod, linfct = mcp(tension = "Tukey"))
### 95\% simultaneous confidence intervals
plot(print(confint(wht)))
### the same (for balanced designs only)
TukeyHSD(amod, "tension")
### corresponding adjusted p values
summary(wht)
### confidence bands for a simple linear model, `cars' data
plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)",
las = 1)
### fit linear model and add regression line to plot
lmod <- lm(dist ~ speed, data = cars)
abline(lmod)
### a grid of speeds
speeds <- seq(from = min(cars$speed), to = max(cars$speed),
length = 10)
### linear hypotheses: 10 selected points on the regression line != 0
K <- cbind(1, speeds)
### set up linear hypotheses
cht <- glht(lmod, linfct = K)
### confidence intervals, i.e., confidence bands, and add them plot
cci <- confint(cht)
lines(speeds, cci$confint[,"lwr"], col = "blue")
lines(speeds, cci$confint[,"upr"], col = "blue")
### simultaneous p values for parameters in a Cox model
if (require("survival") && require("MASS")) {
data("leuk", package = "MASS")
leuk.cox <- coxph(Surv(time) ~ ag + log(wbc), data = leuk)
### set up linear hypotheses
lht <- glht(leuk.cox, linfct = diag(length(coef(leuk.cox))))
### adjusted p values
print(summary(lht))
}
}
\keyword{htest}
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