\name{compar.gee}
\alias{compar.gee}
\alias{print.compar.gee}
\title{Comparative Analysis with GEEs}
\usage{
compar.gee(formula, data = NULL, family = "gaussian", phy,
          scale.fix = FALSE, scale.value = 1)
}
\arguments{
  \item{formula}{a formula giving the model to be fitted.}
  \item{data}{the name of the data frame where the variables in
    \code{formula} are to be found; by default, the variables are looked
    for in the global environment.}
  \item{family}{a character string specifying the distribution assumed
    for the response; by default a Gaussian distribution (with link
    identity) is assumed (see \code{?family} for details on specifying
    the distribution, and on changing the link function).}
  \item{phy}{an object of class \code{"phylo"}.}
  \item{scale.fix}{logical, indicates whether the scale parameter should
    be fixed (TRUE) or estimated (FALSE, the default).}
  \item{scale.value}{if \code{scale.fix = TRUE}, gives the value for the
    scale (default: \code{scale.value = 1}).}
}
\description{
  This function performs the comparative analysis using generalized
  estimating equations as described by Paradis and Claude (2002).
}
\details{
  If a data frame is specified for the argument \code{data} and that
  data frame has rownames, then its values are matched to the tip labels
  of \code{phy}, otherwise its values are taken to be in the same order
  than the tip labels of \code{phy}.

  If \code{data = NULL}, then it is assumed that the variables are in
  the same order than the tip labels of \code{phy}.
}
\value{
  an object of class "compar.gee" with the following components:
  \item{call}{the function call, including the formula.}
  \item{nobs}{the number of observations.}
  \item{coefficients}{the estimated coefficients (or regression parameters).}
  \item{residuals}{the regression residuals.}
  \item{family}{a character string, the distribution assumed for the response.}
  \item{link}{a character string, the link function used for the mean function.}
  \item{scale}{the scale (or dispersion parameter).}
  \item{W}{the variance-covariance matrix of the estimated coefficients.}
  \item{dfP}{the phylogenetic degrees of freedom (see Paradis and Claude
    for details on this).}
}
\references{
  Paradis, E. and Claude J. (2002) Analysis of comparative data using
  generalized estimating equations. \emph{Journal of theoretical
    Biology}, \bold{216}, 000--000.
}

\author{Emmanuel Paradis \email{paradis@isem.univ-montp2.fr}}

\seealso{
  \code{\link{read.tree}}, \code{\link{pic}}, \code{\link{compar.lynch}}
}
\examples{
### The example in Phylip 3.5c (originally from Lynch 1991)
### (the same analysis than in help(pic)...)
cat("((((Homo:0.21,Pongo:0.21):0.28,",
   "Macaca:0.49):0.13,Ateles:0.62):0.38,Galago:1.00);",
   file = "ex.tre", sep = "\n")
tree.primates <- read.tree("ex.tre")
X <- c(4.09434, 3.61092, 2.37024, 2.02815, -1.46968)
Y <- c(4.74493, 3.33220, 3.36730, 2.89037, 2.30259)
### Both regressions... the results are quite close to those obtained
### with pic().
compar.gee(X ~ Y, phy = tree.primates)
compar.gee(Y ~ X, phy = tree.primates)
### Now do the GEE regressions through the origin: the results are quite
### different!
compar.gee(X ~ Y - 1, phy = tree.primates)
compar.gee(Y ~ X - 1, phy = tree.primates)
unlink("ex.tre") # delete the file "ex.tre"
}
\keyword{regression}