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## yule.R (2011-11-03)
## Fits Yule Model to a Phylogenetic Tree
## yule: standard Yule model (constant birth rate)
## yule.cov: Yule model with covariates
## Copyright 2003-2011 Emmanuel Paradis
## This file is part of the R-package `ape'.
## See the file ../COPYING for licensing issues.
yule <- function(phy, use.root.edge = FALSE)
{
if (!is.binary.phylo(phy))
stop("tree must be dichotomous to fit the Yule model.")
X <- sum(phy$edge.length)
nb.node <- phy$Nnode
if (!is.null(phy$root.edge) && use.root.edge) X <- X + phy$root.edge
else nb.node <- nb.node - 1
lambda <- nb.node/X
se <- lambda/sqrt(nb.node)
loglik <- -lambda * X + lfactorial(phy$Nnode) + nb.node * log(lambda)
obj <- list(lambda = lambda, se = se, loglik = loglik)
class(obj) <- "yule"
obj
}
yule.cov <- function(phy, formula, data = NULL)
{
if (is.null(data)) data <- parent.frame()
n <- length(phy$tip.label)
nb.node <- phy$Nnode
if (!is.null(phy$node.label)) phy$node.label <- NULL
bt <- sort(branching.times(phy)) # branching times (from present to past)
bt <- rev(bt) # branching times from past to present
ni <- cumsum(rev(table(bt))) + 1
X <- model.matrix(formula, data)
Xi <- X[phy$edge[, 1], , drop = FALSE]
Xj <- X[phy$edge[, 2], , drop = FALSE]
dev <- function(b) {
2 * sum(((1/(1 + exp(-(Xi %*% b)))) +
(1/(1 + exp(-(Xj %*% b)))))
* phy$edge.length/2) -
2 * (sum(log(ni[-length(ni)])) +
sum(log((1/(1 + exp(-(X[-(1:(n + 1)), , drop = FALSE] %*% b)))))))
}
out <- nlm(function(p) dev(p), p = c(rep(0, ncol(X) - 1), -1),
hessian = TRUE)
Dev <- out$minimum
para <- matrix(NA, ncol(X), 2)
para[, 1] <- out$estimate
if (any(out$gradient == 0))
warning("The likelihood gradient seems flat in at least one dimension (null gradient):\ncannot compute the standard-errors of the parameters.\n")
else para[, 2] <- sqrt(diag(solve(out$hessian)))
rownames(para) <- colnames(X)
colnames(para) <- c("Estimate", "StdErr")
## fit the intercept-only model:
X <- model.matrix(~ 1, data = data.frame(X))
Xi <- X[phy$edge[, 1], , drop = FALSE]
Xj <- X[phy$edge[, 2], , drop = FALSE]
Dev.null <- nlm(function(p) dev(p), p = -1)$minimum
cat("\n---- Yule Model with Covariates ----\n\n")
cat(" Phylogenetic tree:", deparse(substitute(phy)), "\n")
cat(" Number of tips:", n, "\n")
cat(" Number of nodes:", nb.node, "\n")
cat(" Deviance:", Dev, "\n")
cat(" Log-likelihood:", -Dev/2, "\n\n")
cat(" Parameter estimates:\n")
print(para)
cat("\n")
cat("Null Deviance:", Dev.null, "\n")
cat(" Test of the fitted model: ")
chi <- Dev.null - Dev
df <- nrow(para) - 1
cat("chi^2 =", round(chi, 3), " df =", df,
" P =", round(1 - pchisq(chi, df), 3), "\n")
}
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