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\name{glsD}
\alias{glsD}
\alias{print.glsD}
\title{Fit Linear Model Using Generalized Least Squares}
\usage{
glsD(model, data, correlation, weights, subset, method, na.action,
control, verbose, B=0, dupCluster=FALSE, pr=FALSE,
opmeth=c('optimize','optim'))
\method{print}{glsD}(x, digits=4, \dots)
}
\arguments{
\item{model}{a two-sided linear formula object describing the
model, with the response on the left of a \code{~} operator and the
terms, separated by \code{+} operators, on the right.}
\item{data}{an optional data frame containing the variables named in
\code{model}, \code{correlation}, \code{weights}, and
\code{subset}. By default the variables are taken from the
environment from which \code{gls} is called.}
\item{correlation}{an optional \code{corStruct} object describing the
within-group correlation structure. See the documentation of
\code{corClasses} for a description of the available \code{corStruct}
classes. If a grouping variable is to be used, it must be specified in
the \code{form} argument to the \code{corStruct}
constructor. Defaults to \code{NULL}, corresponding to uncorrelated
errors.}
\item{weights}{an optional \code{varFunc} object or one-sided formula
describing the within-group heteroscedasticity structure. If given as
a formula, it is used as the argument to \code{varFixed},
corresponding to fixed variance weights. See the documentation on
\code{varClasses} for a description of the available \code{varFunc}
classes. Defaults to \code{NULL}, corresponding to homoscesdatic
errors.}
\item{subset}{an optional expression indicating which subset of the rows of
\code{data} should be used in the fit. This can be a logical
vector, or a numeric vector indicating which observation numbers are
to be included, or a character vector of the row names to be
included. All observations are included by default.}
\item{method}{a character string. If \code{"REML"} the model is fit by
maximizing the restricted log-likelihood. If \code{"ML"} the
log-likelihood is maximized. Defaults to \code{"REML"}.}
\item{na.action}{a function that indicates what should happen when the
data contain \code{NA}s. The default action (\code{na.fail}) causes
\code{gls} to print an error message and terminate if there are any
incomplete observations.}
\item{control}{a list of control values for the estimation algorithm to
replace the default values returned by the function \code{glsControl}.
Defaults to an empty list.}
\item{verbose}{an optional logical value. If \code{TRUE} information on
the evolution of the iterative algorithm is printed. Default is
\code{FALSE}.}
\item{B}{number of bootstrap resamples to fit and store, default is
none}
\item{dupCluster}{set to \code{TRUE} to have \code{glsD} when
bootstrapping to consider multiply-sampled clusters as if they were
one large cluster when fitting using the \code{gls} algorithm}
\item{pr}{set to \code{TRUE} to show progress of bootstrap resampling}
\item{opmeth}{specifies whether the \code{optimize} or the \code{optim}
function is to be used for optimization}
\item{x}{the result of \code{glsD}}
\item{digits}{number of significant digits to print}
\item{\dots}{ignored}
}
\description{
This function fits a linear model using generalized least
squares. The errors are allowed to be correlated and/or have unequal
variances. \code{glsD} is a slightly enhanced version of the
Pinheiro and Bates \code{glsD} function in the \code{nlme} package to
make it easy to use with the Design library and to implement cluster
bootstrapping (primarily for nonparametric estimates of the
variance-covariance matrix of the parameter estimates and for
nonparametric confidence limits of correlation parameters).
}
\value{
an object of classes \code{glsD}, \code{Design}, and \code{gls}
representing the linear model
fit. Generic functions such as \code{print}, \code{plot}, and
\code{summary} have methods to show the results of the fit. See
\code{glsObject} for the components of the fit. The functions
\code{resid}, \code{coef}, and \code{fitted} can be used to extract
some of its components. \code{glsD} returns the following components
not returned by \code{gls}: \code{Design}, \code{assign},
\code{formula}, \code{opmeth} (see arguments), \code{B} (see
arguments), \code{bootCoef} (matrix of \code{B} bootstrapped
coefficients), \code{boot.Corr} (vector of bootstrapped correlation
parameters), \code{Nboot} (vector of total sample size used in each
bootstrap (may vary if have unbalanced clusters), and \code{var}
(sample variance-covariance matrix of bootstrapped coefficients).
}
\references{
Pinheiro J, Bates D (2000): Mixed effects models in S and S-Plus. New
York: Springer-Verlag.
}
\author{Jose Pinheiro \email{jcp@research.bell-labs.com},
Douglas Bates \email{bates@stat.wisc.edu},
Frank Harrell \email{f.harrell@vanderbilt.edu},
Patrick Aboyoun \email{aboyoun@insightful.com}
}
\seealso{
\code{\link{gls}}
\code{\link{glsControl}}, \code{\link{glsObject}},
\code{\link{varFunc}}, \code{\link{corClasses}}, \code{\link{varClasses}}
}
\examples{
\dontrun{
ns <- 20 # no. subjects
nt <- 10 # no. time points/subject
B <- 10 # no. bootstrap resamples
# usually do 100 for variances, 1000 for nonparametric CLs
rho <- .5 # AR(1) correlation parameter
V <- matrix(0, nrow=nt, ncol=nt)
V <- rho^abs(row(V)-col(V)) # per-subject correlation/covariance matrix
d <- expand.grid(tim=1:nt, id=1:ns)
d$trt <- factor(ifelse(d$id <= ns/2, 'a', 'b'))
true.beta <- c(Intercept=0,tim=.1,'tim^2'=0,'trt=b'=1)
d$ey <- true.beta['Intercept'] + true.beta['tim']*d$tim +
true.beta['tim^2']*(d$tim^2) + true.beta['trt=b']*(d$trt=='b')
set.seed(13)
library(MASS) # needed for mvrnorm
d$y <- d$ey + as.vector(t(mvrnorm(n=ns, mu=rep(0,nt), Sigma=V)))
dd <- datadist(d); options(datadist='dd')
# library(nlme) # S-Plus: library(nlme3) or later
f <- glsD(y ~ pol(tim,2) + trt, correlation=corCAR1(form= ~tim | id),
data=d, B=B)
f
f$var # bootstrap variances
f$varBeta # original variances
summary(f)
anova(f)
plot(f, tim=NA, trt=NA)
# v <- Variogram(f, form=~tim|id, data=d)
}
}
\keyword{models}
|
