\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
Akaike information criterion of a tree. If no such values are
available, \code{NULL} is returned.
- \code{anova} is another generic function that is used to compare
+ \code{anova} is another generic function which is used to compare
nested models: the significance of the additional parameter(s) is
tested with likelihood ratio tests. You must ensure that the models
are effectively nested (if they are not, the results will be
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}.
+ given through a correlation structure with the option
+ \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;
+ 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
+ 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