\item{type}{the variable type; either \code{"continuous"} or
\code{"discrete"} (or an abbreviation of these).}
\item{method}{a character specifying the method used for
- estimation. Three choices are possible: \code{"ML"}, \code{"pic"},
- or \code{"GLS"}.}
+ estimation. Four choices are possible: \code{"ML"}, \code{"REML"},
+ \code{"pic"}, or \code{"GLS"}.}
\item{CI}{a logical specifying whether to return the 95\% confidence
intervals of the ancestral state estimates (for continuous
characters) or the likelihood of the different states (for discrete
\code{corStruct}.
In the default setting (i.e., \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;
+ "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 (see the package \pkg{geiger} for a different
- implementation). 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.
+ 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
+ over the latter, even though it is not the default.
For discrete characters (\code{type = "discrete"}), only maximum
likelihood estimation is available (Pagel 1994). The model is