largest.
}
\usage{
-ace(x, phy, type = "continuous", method = "ML", CI = TRUE,
+ace(x, phy, type = "continuous", method = if (type == "continuous")
+ "REML" else "ML", CI = TRUE,
model = if (type == "continuous") "BM" else "ER",
- scaled = TRUE, kappa = 1, corStruct = NULL, ip = 0.1)
+ scaled = TRUE, kappa = 1, corStruct = NULL, ip = 0.1,
+ use.expm = FALSE)
\method{print}{ace}(x, digits = 4, ...)
\method{logLik}{ace}(object, ...)
\method{deviance}{ace}(object, ...)
structure to be used (this also gives the assumed model).}
\item{ip}{the initial value(s) used for the ML estimation procedure
when \code{type == "discrete"} (possibly recycled).}
+ \item{use.expm}{a logical specifying whether to use the package
+ \pkg{expm} to compute the matrix exponential (relevant only if
+ \code{type = "d"}). The default is to use the function
+ \code{matexpo} from \pkg{ape} (see details).}
\item{digits}{the number of digits to be printed.}
\item{object}{an object of class \code{"ace"}.}
\item{k}{a numeric value giving the penalty per estimated parameter;
\details{
If \code{type = "continuous"}, the default model is Brownian motion
where characters evolve randomly following a random walk. This model
- can be fitted by maximum likelihood (the default, Schluter et
- al. 1997), least squares (\code{method = "pic"}, Felsenstein 1985), or
- generalized least squares (\code{method = "GLS"}, Martins and Hansen
- 1997, Cunningham et al. 1998). In the latter case, the specification
- of \code{phy} and \code{model} are actually ignored: it is instead
- given through a correlation structure with the option
- \code{corStruct}.
+ can be fitted by residual maximum likelihood (the default), maximum
+ likelihood (Felsenstein 1973, Schluter et al. 1997), least squares
+ (\code{method = "pic"}, Felsenstein 1985), or generalized least
+ squares (\code{method = "GLS"}, Martins and Hansen 1997, Cunningham et
+ al. 1998). In the last case, the specification of \code{phy} and
+ \code{model} are actually ignored: it is instead given through a
+ correlation structure with the option \code{corStruct}.
- In the default setting (\code{method = "ML"} and \code{model = "BM"})
- the maximum likelihood estimation is done simultaneously on the
- ancestral values and the variance of the Brownian motion process;
- these estimates are then used to compute the confidence intervals in
- the standard way. The REML method first estimates the ancestral value
- at the root (aka, the phylogenetic mean), then the variance of the
- Brownian motion process is estimated by optimizing the residual
- log-likelihood. The ancestral values are finally inferred from the
- likelihood function giving these two parameters. If \code{method =
- "pic"} or \code{"GLS"}, the confidence intervals are computed using
- the expected variances under the model, so they depend only on the
- tree.
+ In the setting \code{method = "ML"} and \code{model = "BM"} (this used
+ to be the default until \pkg{ape} 3.0-7) the maximum likelihood
+ estimation is done simultaneously on the ancestral values and the
+ variance of the Brownian motion process; these estimates are then used
+ to compute the confidence intervals in the standard way. The REML
+ method first estimates the ancestral value at the root (aka, the
+ phylogenetic mean), then the variance of the Brownian motion process
+ is estimated by optimizing the residual log-likelihood. The ancestral
+ values are finally inferred from the likelihood function giving these
+ two parameters. If \code{method = "pic"} or \code{"GLS"}, the
+ confidence intervals are computed using the expected variances under
+ the model, so they depend only on the tree.
It could be shown that, with a continous character, REML results in
unbiased estimates of the variance of the Brownian motion process
- while ML gives a downward bias. Therefore the former is recommanded,
- even though it is not the default.
+ while ML gives a downward bias. Therefore the former is recommanded.
For discrete characters (\code{type = "discrete"}), only maximum
likelihood estimation is available (Pagel 1994). The model is
an equal-rates model (e.g., the first and third examples above),
\code{"ARD"} is an all-rates-different model (the second example), and
\code{"SYM"} is a symmetrical model (e.g., \code{matrix(c(0, 1, 2, 1,
- 0, 3, 2, 3, 0), 3)}). If a short-cut is used, the number of states
- is determined from the data.
+ 0, 3, 2, 3, 0), 3)}). If a short-cut is used, the number of states is
+ determined from the data.
+
+ With discrete characters it is necessary to compute the exponential of
+ the rate matrix. By default (and the only possible choice until
+ \pkg{ape} 3.0-7) the function \code{\link{matexpo}} in \pkg{ape} is
+ used. If \code{use.expm = TRUE}, the function
+ \code{\link[expm]{expm}}, in the package of the same name, is
+ used. \code{matexpo} is faster but quite inaccurate for large and/or
+ asymmetric matrices. In case of doubt, use the latter.
}
\value{
an object of class \code{"ace"} with the following elements:
reappraisal. \emph{Trends in Ecology & Evolution}, \bold{13},
361--366.
+ Felsenstein, J. (1973) Maximum likelihood estimation
+ of evolutionary trees from continuous characters. \emph{American Journal of Human Genetics}, \bold{25}, 471--492.
+
Felsenstein, J. (1985) Phylogenies and the comparative
method. \emph{American Naturalist}, \bold{125}, 1--15.