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% $Id: glh.test.Rd 1523 2012-04-19 17:50:20Z warnes $
%
\name{glh.test}
\alias{glh.test}
\alias{print.glh.test}
\alias{summary.glh.test}
\title{ Test a General Linear Hypothesis for a Regression Model }
\description{
Test, print, or summarize a general linear hypothesis for a regression model
}
\usage{
glh.test(reg, cm, d=rep(0, nrow(cm)) )
\method{print}{glh.test}(x, digits=4,...)
\method{summary}{glh.test}(object, digits=4,...)
}
\arguments{
\item{reg}{ Regression model }
\item{cm}{ matrix . Each row specifies a linear combination of the
coefficients }
\item{d}{ vector specifying the null hypothis values for each linear
combination}
\item{x, object}{glh.test object}
\item{digits}{number of digits}
\item{...}{ optional parameters (ignored)}
}
\details{
Test the general linear hypothesis
\eqn{ C \hat{beta} = d }{C \%*\% \hat{beta} == d }
for the regression model \code{reg}.
The test statistic is obtained from the formula:
\deqn{f = \frac{(C \hat{\beta} - d)' ( C (X'X)^{-1} C' ) (C \hat{\beta}
- d) / r }{ SSE / (n-p) } }{
F = (C Beta-hat - d)' ( C (X'X)^-1 C' ) (C Beta-hat - d) / r /
( SSE / (n-p) )
}
Under the null hypothesis, f will follow a F-distribution with r and
n-p degrees of freedom.
}
\note{
When using treatment contrasts (the default) the first level of the
factors are subsumed into the intercept term. The estimated model
coefficients are then contrasts versus the first level. This
should be taken into account when forming contrast matrixes,
particularly when computing contrasts that include 'baseline'
level of factors.
See the comparison with \code{fit.contrast} in the examples below.
}
\value{
Object of class \code{c("glh.test","htest")} with elements:
\item{call }{Function call that created the object}
\item{statistic }{F statistic}
\item{parameter}{ vector containing the numerator (r) and denominator
(n-p) degrees of freedom }
\item{p.value}{ p-value}
\item{estimate}{ computed estimate for each row of \code{cm} }
\item{null.value}{ d }
\item{method}{ description of the method }
\item{data.name}{ name of the model given for \code{reg} }
\item{matrix}{ matrix specifying the general linear hypotheis
(\code{cm}) }
}
\references{ R.H. Myers, Classical and Modern Regression with
Applications, 2nd Ed, 1990, p. 105}
\author{Gregory R. Warnes \email{greg@warnes.net} }
\seealso{\code{\link{fit.contrast}}, \code{\link{estimable}},
\code{\link{contrasts}} }
\examples{
# fit a simple model
y <- rnorm(100)
x <- cut(rnorm(100, mean=y, sd=0.25),c(-4,-1.5,0,1.5,4))
reg <- lm(y ~ x)
summary(reg)
# test both group 1 = group 2 and group 3 = group 4
# *Note the 0 in the column for the intercept term*
C <- rbind( c(0,-1,0,0), c(0,0,-1,1) )
ret <- glh.test(reg, C)
ret # same as 'print(ret) '
summary(ret)
# To compute a contrast between the first and second level of the factor
# 'x' using 'fit.contrast' gives:
fit.contrast( reg, x,c(1,-1,0,0) )
# To test this same contrast using 'glh.test', use a contrast matrix
# with a zero coefficient for the intercept term. See the Note section,
# above, for an explanation.
C <- rbind( c(0,-1,0,0) )
glh.test( reg, C )
}
\keyword{ models }
\keyword{ regression }
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