\name{brownieREML}
\alias{brownieREML}
\title{REML version of brownie.lite}
\usage{
brownieREML(tree, x, maxit=2000, ...)
}
\arguments{
	\item{tree}{an object of class \code{"phylo"} or \code{"simmap"}. (See \code{\link{read.simmap}} and \code{\link{make.simmap}} for more information about the latter object class.)}
	\item{x}{a vector of tip values for species. \code{names(x)} should be the species names.}
	\item{maxit}{an optional integer value indicating the maximum number of iterations for optimization - may need to be increased for large trees.}
	\item{...}{optional arguments.}
}

\description{
	Fits a multi-rate Brownian motion evolution model using REML. (See \code{\link{brownie.lite}} for more details.)
}
\details{
	This function takes an object of class \code{"phylo"} or an object of class \code{"simmap"} with a mapped binary or multi-state trait (see \code{\link{read.simmap}}) and data for a single continuously valued character.  It then uses restricted maximum likelihood (REML) to fit the Brownian rate variation ("noncensored") model of O'Meara et al. (2006; \emph{Evolution}).  This function is similar to \code{\link{brownie.lite}} but uses REML (which is faster and unbiased) instead of ML.  REML optimization takes advantage of Felsenstein's (1985) contrasts algorithm.
}
\value{
	An object of class \code{"brownieREML"} containing the following components:
	\item{sig2.single}{is the rate, \eqn{\sigma^2}, for a single rate model - this is usually the "null" model.}
	\item{logL1}{log-likelihood of the single-rate model.}
	\item{sig2.multiple}{is a length \emph{p} (for \emph{p} rates) vector of BM rates (\eqn{\sigma_1^2}, \eqn{\sigma_2^2}, and so on) from the multi-rate model.}
	\item{logL2}{log-likelihood of the multi-rate model.}
	\item{convergence}{numerical value from \code{\link{optim}}.}
}
\references{
	Felsenstein, J. (1985) Phylogenies and the comparative method. \emph{American Naturalist}, \bold{125}, 1-15. 

	O'Meara, B. C., C. Ane, M. J. Sanderson, and P. C. Wainwright (2006) Testing for different rates of continuous trait evolution using likelihood. \emph{Evolution}, \bold{60}, 922-933.

	Revell, L. J. (2024) phytools 2.0: an updated R ecosystem for phylogenetic comparative methods (and other things). \emph{PeerJ}, \bold{12}, e16505.
}
\author{Liam Revell \email{liam.revell@umb.edu}}
\seealso{
	\code{\link{brownie.lite}}, \code{\link{evol.vcv}}, \code{\link{evol.rate.mcmc}}, \code{\link{ratebytree}}
}
\examples{
## load data from Revell & Collar (2009)
data(sunfish.tree)
data(sunfish.data)
## extract character of interest
gape.width<-setNames(sunfish.data$gape.width,
    rownames(sunfish.data))
## fit model
multiBM.reml<-brownieREML(sunfish.tree,
	gape.width)
print(multiBM.reml)
}
\keyword{phylogenetics}
\keyword{comparative method}
\keyword{continuous character}
\keyword{maximum likelihood}
