-## ace.R (2010-12-08)
+## ace.R (2011-07-18)
## Ancestral Character Estimation
-## Copyright 2005-2010 Emmanuel Paradis and Ben Bolker
+## Copyright 2005-2011 Emmanuel Paradis and Ben Bolker
## This file is part of the R-package `ape'.
## See the file ../COPYING for licensing issues.
nb.tip <- length(phy$tip.label)
nb.node <- phy$Nnode
if (nb.node != nb.tip - 1)
- stop('"phy" is not rooted AND fully dichotomous.')
+ stop('"phy" is not rooted AND fully dichotomous.')
if (length(x) != nb.tip)
- stop("length of phenotypic and of phylogenetic data do not match.")
+ stop("length of phenotypic and of phylogenetic data do not match.")
if (!is.null(names(x))) {
if(all(names(x) %in% phy$tip.label))
x <- x[phy$tip.label]
obj <- list()
if (kappa != 1) phy$edge.length <- phy$edge.length^kappa
if (type == "continuous") {
- if (method == "pic") {
+ switch(method, "REML" = {
+ minusLogLik <- function(sig2) {
+ if (sig2 < 0) return(1e100)
+ V <- sig2 * vcv(phy)
+ ## next three lines borrowed from dmvnorm() in 'mvtnorm'
+ distval <- mahalanobis(x, center = mu, cov = V)
+ logdet <- sum(log(eigen(V, symmetric = TRUE, only.values = TRUE)$values))
+ (nb.tip * log(2 * pi) + logdet + distval)/2
+ }
+ mu <- rep(ace(x, phy, method="pic")$ace[1], nb.tip)
+ out <- nlm(minusLogLik, 1, hessian = TRUE)
+ sigma2 <- out$estimate
+ se_sgi2 <- sqrt(1/out$hessian)
+ tip <- phy$edge[, 2] <= nb.tip
+ minus.REML.BM <- function(p) {
+ x1 <- p[phy$edge[, 1] - nb.tip]
+ x2 <- numeric(length(x1))
+ x2[tip] <- x[phy$edge[tip, 2]]
+ x2[!tip] <- p[phy$edge[!tip, 2] - nb.tip]
+ -(-sum((x1 - x2)^2/phy$edge.length)/(2 * sigma2) -
+ nb.node * log(sigma2))
+ }
+ out <- nlm(function(p) minus.REML.BM(p),
+ p = rep(mu[1], nb.node), hessian = TRUE)
+ obj$resloglik <- -out$minimum
+ obj$ace <- out$estimate
+ names(obj$ace) <- (nb.tip + 1):(nb.tip + nb.node)
+ obj$sigma2 <- c(sigma2, se_sgi2)
+ if (CI) {
+ se <- sqrt(diag(solve(out$hessian)))
+ tmp <- se * qt(0.025, nb.node)
+ obj$CI95 <- cbind(obj$ace + tmp, obj$ace - tmp)
+ }
+ }, "pic" = {
if (model != "BM")
- stop('the "pic" method can be used only with model = "BM".')
+ stop('the "pic" method can be used only with model = "BM".')
## See pic.R for some annotations.
phy <- reorder(phy, "pruningwise")
phenotype <- numeric(nb.tip + nb.node)
names(obj$ace) <- (nb.tip + 1):(nb.tip + nb.node)
if (CI) {
se <- sqrt(ans[[8]])
- CI95 <- matrix(NA, nb.node, 2)
- CI95[, 1] <- obj$ace + se * qnorm(0.025)
- CI95[, 2] <- obj$ace - se * qnorm(0.025)
- obj$CI95 <- CI95
+ tmp <- se * qnorm(0.025)
+ obj$CI95 <- cbind(obj$ace + tmp, obj$ace - tmp)
}
- }
- if (method == "ML") {
+ }, "ML" = {
if (model == "BM") {
tip <- phy$edge[, 2] <= nb.tip
dev.BM <- function(p) {
names(obj$ace) <- (nb.tip + 1):(nb.tip + nb.node)
se <- sqrt(diag(solve(out$hessian)))
obj$sigma2 <- c(out$estimate[1], se[1])
- se <- se[-1]
if (CI) {
- CI95 <- matrix(NA, nb.node, 2)
- CI95[, 1] <- obj$ace + se * qt(0.025, nb.node)
- CI95[, 2] <- obj$ace - se * qt(0.025, nb.node)
- obj$CI95 <- CI95
+ tmp <- se[-1] * qt(0.025, nb.node)
+ obj$CI95 <- cbind(obj$ace + tmp, obj$ace - tmp)
}
}
- }
- if (method == "GLS") {
+ }, "GLS" = {
if (is.null(corStruct))
- stop('you must give a correlation structure if method = "GLS".')
+ stop('you must give a correlation structure if method = "GLS".')
if (class(corStruct)[1] == "corMartins")
- M <- corStruct[1] * dist.nodes(phy)
+ M <- corStruct[1] * dist.nodes(phy)
if (class(corStruct)[1] == "corGrafen")
- phy <- compute.brlen(attr(corStruct, "tree"),
- method = "Grafen",
- power = exp(corStruct[1]))
+ phy <- compute.brlen(attr(corStruct, "tree"),
+ method = "Grafen",
+ power = exp(corStruct[1]))
if (class(corStruct)[1] %in% c("corBrownian", "corGrafen")) {
dis <- dist.nodes(attr(corStruct, "tree"))
MRCA <- mrca(attr(corStruct, "tree"), full = TRUE)
obj$ace <- drop(varAY %*% invV %*% (x - GM) + GM)
names(obj$ace) <- (nb.tip + 1):(nb.tip + nb.node)
if (CI) {
- CI95 <- matrix(NA, nb.node, 2)
se <- sqrt((varA - varAY %*% invV %*% t(varAY))[cbind(1:nb.node, 1:nb.node)])
- CI95[, 1] <- obj$ace + se * qnorm(0.025)
- CI95[, 2] <- obj$ace - se * qnorm(0.025)
- obj$CI95 <- CI95
+ tmp <- se * qnorm(0.025)
+ obj$CI95 <- cbind(obj$ace + tmp, obj$ace - tmp)
}
- }
+ })
} else { # type == "discrete"
if (method != "ML")
- stop("only ML estimation is possible for discrete characters.")
+ stop("only ML estimation is possible for discrete characters.")
if (!is.factor(x)) x <- factor(x)
nl <- nlevels(x)
lvls <- levels(x)
}
} else {
if (ncol(model) != nrow(model))
- stop("the matrix given as `model' is not square")
+ stop("the matrix given as 'model' is not square")
if (ncol(model) != nl)
- stop("the matrix `model' must have as many rows
-as the number of categories in `x'")
+ stop("the matrix 'model' must have as many rows as the number of categories in 'x'")
rate <- model
np <- max(rate)
}
cat("\n")
if (!is.null(x$loglik))
cat(" Log-likelihood:", x$loglik, "\n\n")
+ if (!is.null(x$resloglik))
+ cat(" Residual log-likelihood:", x$resloglik, "\n\n")
ratemat <- x$index.matrix
if (is.null(ratemat)) { # to be improved
class(x) <- NULL
- x$loglik <- x$call <- NULL
+ x$resloglik <- x$loglik <- x$call <- NULL
print(x)
} else {
dimnames(ratemat)[1:2] <- dimnames(x$lik.anc)[2]
\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
projects / ape.git / commitdiff