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% $Id: estimable.Rd 1026 2006-11-29 00:04:54Z warnes $
%
\name{estimable}
\alias{estimable}
\alias{estimable.default}
\alias{estimable.lmer}
%\alias{.wald}
%\alias{.to.est}
\title{Contrasts and estimable linear functions of model coefficients}
\description{
Compute and test contrasts and other estimable linear
functions of model coefficients for for lm, glm, lme, lmer, and geese
objects
}
\usage{
estimable(obj, cm, beta0, conf.int=NULL, show.beta0, ...)
\method{estimable}{default} (obj, cm, beta0, conf.int=NULL, show.beta0, joint.test=FALSE, ...)
\method{estimable}{lmer}(obj, cm, beta0, conf.int=NULL,
show.beta0, sim.lmer=TRUE, n.sim=1000, ...)
%.wald(obj, cm,beta0=rep(0, ifelse(is.null(nrow(cm)), 1, nrow(cm))))
%.to.est(obj, params)
}
\arguments{
\item{obj}{Regression (lm,glm,lme,lmer) object. }
\item{cm}{Vector, List, or Matrix specifying estimable linear functions or
contrasts. See below for details.}
\item{beta0}{Vector of null hypothesis values}
\item{conf.int}{Confidence level. If provided, confidence intervals
will be computed.}
\item{joint.test}{Logical value. If TRUE a 'joint' Wald test for the
hypothesis \eqn{L \beta=\beta_0}{L \%*\% beta=beta0} is performed.
Otherwise 'row-wise' tests are performed, i.e. \eqn{(L
\beta)_i=\beta_{0i}}{(L \%*\% beta)[i]=beta0[i]}
}
\item{show.beta0}{Logical value. If TRUE a column for beta0 will be
included in the output table. Defaults to TRUE when beta0 is
specified, FALSE otherwise.}
\item{sim.lmer}{Logical value. If TRUE p-values and confidence
intervals will be estimated using \code{\Link[Matrix]{mcmcsamp}}.
}
\item{n.sim}{Number of MCMC samples to take in
\code{\Link[Matrix]{mcmcsamp}}.
}
\item{...}{ignored}
}
\details{
\code{estimable} computes an estimate, test statitic, significance
test, and (optional) confidence interval for each linear functions of
the model coefficients specified by \code{cm}.
The estimable function(s) may be specified via a vector, list, or
matrix. If \code{cm} is a vector, it should contained named elements
each of which gives the coefficient to be applied to the
corresponding parameter. These coefficients will be used to construct
the contrast matrix, with unspecified model parameters assigned zero
coefficients. If \code{cm} is a list, it should contain one or more
coefficient vectors, which will be used to construct rows of the
contrast matrix. If \code{cm} is a matrix, column names must match (a
subset of) the model parameters, and each row should contain the
corresponding coefficient to be applied. Model parameters which are
not present in the set of column names of \code{cm} will be set to zero.
The estimates and their variances are obtained by applying the
contrast matrix (generated from) \code{cm} to the model estimates
variance-covariance matrix. Degrees of freedom are obtained from the
appropriate model terms.
The user is responsible for ensuring that the specified
linear functions are meaningful.
For computing contrasts among levels of a single factor,
\code{\link{fit.contrast}} may be more convenient. For computing
contrasts between two specific combinations of model parameters, the
\code{contrast} function in Frank Harrell's Design library may be more
convenient.
%The \code{.wald} function is called internally by \code{estimable} and
%is not intended for direct use.
}
\note{
The estimated fixed effect parameter of \code{lme} objects may have
different degrees of freedom. If a specified contrast includes
nonzero coefficients for parameters with differing degrees of freedom,
the smallest number of degrees of freedom is used and a warning
message is issued.
}
\value{
Returns a matrix with one row per linear function. Columns contain
the beta0 value (optional, see \code{show.beta0} above), estimated
coefficients, standard errors, t values, degrees of freedom, two-sided
p-values, and the lower and upper endpoints of the
1-alpha confidence intervals.
}
\author{
BXC (Bendix Carstensen) \email{bxc\@novonordisk.com},
Gregory R. Warnes \email{Gregory\_R\_Warnes\@groton.pfizer.com},
Sren Hjsgaard \email{sorenh@agrsci.dk}, and
Randall C Johnson \email{rjohnson@ncifcrf.gov}
}
\seealso{
\code{\link{fit.contrast}},
\code{\link[stats]{lm}}, \code{\link[nlme]{lme}},
\code{\link[stats]{contrasts}},
\code{\link[Design]{contrast}},
}
\examples{
# setup example data
y <- rnorm(100)
x <- cut(rnorm(100, mean=y, sd=0.25),c(-4,-1.5,0,1.5,4))
levels(x) <- c("A","B","C","D")
x2 <- rnorm(100, mean=y, sd=0.5)
# simple contrast and confidence interval
reg <- lm(y ~ x)
estimable(reg, c( 0, 1, 0, -1) ) # full coefficient vector
estimable(reg, c("xB"=1,"xD"=-1) ) # just the nonzero terms
# Fit a spline with a single knot at 0.5 and plot the *pointwise*
# confidence intervals
library(gplots)
pm <- pmax(x2-0.5, 0) # knot at 0.5
reg2 <- lm(y ~ x + x2 + pm )
range <- seq(-2, 2, , 50)
tmp <- estimable(reg2,
cm=cbind(
'(Intercept)'=1,
'xC'=1,
'x2'=range,
'pm'=pmax(range-0.5, 0)
),
conf.int=0.95)
plotCI(x=range, y=tmp[, 1], li=tmp[, 6], ui=tmp[, 7])
# Fit both linear and quasi-Poisson models to iris data, then compute
# joint confidence intervals on contrasts for the Species and
# Sepal.Width by Species interaction terms.
data(iris)
lm1 <- lm (Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris)
glm1 <- glm(Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris,
family=quasipoisson("identity"))
cm <- rbind(
'Setosa vs. Versicolor' = c(0, 0, 1, 0, 1, 0),
'Setosa vs. Virginica' = c(0, 0, 0, 1, 0, 1),
'Versicolor vs. Virginica'= c(0, 0, 1,-1, 1,-1)
)
estimable(lm1, cm)
estimable(glm1, cm)
}
\keyword{ models }
\keyword{ regression }
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