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fitMk.R
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fitMk.R
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## function for conditional likelihoods at nodes
## written by Liam J. Revell 2015, 2016
## with input from (& structural similarity to) function ace by E. Paradis et al. 2013
fitMk<-function(tree,x,model="SYM",fixedQ=NULL,...){
if(hasArg(output.liks)) output.liks<-list(...)$output.liks
else output.liks<-FALSE
if(hasArg(q.init)) q.init<-list(...)$q.init
else q.init<-length(unique(x))/sum(tree$edge.length)
if(hasArg(opt.method)) opt.method<-list(...)$opt.method
else opt.method<-"nlminb"
if(hasArg(min.q)) min.q<-list(...)$min.q
else min.q<-1e-12
N<-Ntip(tree)
M<-tree$Nnode
if(is.matrix(x)){
x<-x[tree$tip.label,]
m<-ncol(x)
states<-colnames(x)
} else {
x<-to.matrix(x,sort(unique(x)))
x<-x[tree$tip.label,]
m<-ncol(x)
states<-colnames(x)
}
if(hasArg(pi)) pi<-list(...)$pi
else pi<-"equal"
if(pi[1]=="equal") pi<-setNames(rep(1/m,m),states)
else if(pi[1]=="estimated"){
pi<-if(!is.null(fixedQ)) statdist(fixedQ) else statdist(summary(fitMk(tree,x,model),quiet=TRUE)$Q)
cat("Using pi estimated from the stationary distribution of Q assuming a flat prior.\npi =\n")
print(round(pi,6))
cat("\n")
}
else pi<-pi/sum(pi)
if(is.null(fixedQ)){
if(is.character(model)){
rate<-matrix(NA,m,m)
if(model=="ER"){
k<-rate[]<-1
diag(rate)<-NA
} else if(model=="ARD"){
k<-m*(m-1)
rate[col(rate)!=row(rate)]<-1:k
} else if(model=="SYM"){
k<-m*(m-1)/2
ii<-col(rate)<row(rate)
rate[ii]<-1:k
rate<-t(rate)
rate[ii]<-1:k
}
} else {
if(ncol(model)!=nrow(model))
stop("model is not a square matrix")
if(ncol(model)!=ncol(x))
stop("model does not have the right number of columns")
rate<-model
k<-max(rate)
}
Q<-matrix(0,m,m)
} else {
rate<-matrix(NA,m,m)
k<-m*(m-1)
rate[col(rate)!=row(rate)]<-1:k
Q<-fixedQ
}
index.matrix<-rate
tmp<-cbind(1:m,1:m)
rate[tmp]<-0
rate[rate==0]<-k+1
liks<-rbind(x,matrix(0,M,m,dimnames=list(1:M+N,states)))
pw<-reorder(tree,"pruningwise")
lik<-function(pp,output.liks=FALSE,pi){
if(any(is.nan(pp))||any(is.infinite(pp))) return(1e50)
comp<-vector(length=N+M,mode="numeric")
Q[]<-c(pp,0)[rate]
diag(Q)<--rowSums(Q)
parents<-unique(pw$edge[,1])
root<-min(parents)
for(i in 1:length(parents)){
anc<-parents[i]
ii<-which(pw$edge[,1]==parents[i])
desc<-pw$edge[ii,2]
el<-pw$edge.length[ii]
v<-vector(length=length(desc),mode="list")
for(j in 1:length(v))
v[[j]]<-EXPM(Q*el[j])%*%liks[desc[j],]
vv<-if(anc==root) Reduce('*',v)[,1]*pi else Reduce('*',v)[,1]
comp[anc]<-sum(vv)
liks[anc,]<-vv/comp[anc]
}
if(output.liks)return(liks[1:M+N,,drop=FALSE])
logL<--sum(log(comp[1:M+N]))
return(if(is.na(logL)) Inf else logL)
}
if(is.null(fixedQ)){
if(length(q.init)!=k) q.init<-rep(q.init[1],k)
if(opt.method=="optim")
fit<-optim(q.init,function(p) lik(p,pi=pi),method="L-BFGS-B",lower=rep(min.q,k))
else
fit<-nlminb(q.init,function(p) lik(p,pi=pi),lower=rep(0,k),upper=rep(1e50,k))
obj<-list(logLik=
if(opt.method=="optim") -fit$value else -fit$objective,
rates=fit$par,
index.matrix=index.matrix,
states=states,
pi=pi,
method=opt.method)
if(output.liks) obj$lik.anc<-lik(obj$rates,TRUE,pi=pi)
} else {
fit<-lik(Q[sapply(1:k,function(x,y) which(x==y),index.matrix)],pi=pi)
obj<-list(logLik=-fit,
rates=Q[sapply(1:k,function(x,y) which(x==y),index.matrix)],
index.matrix=index.matrix,
states=states,
pi=pi)
if(output.liks) obj$lik.anc<-lik(obj$rates,TRUE,pi=pi)
}
class(obj)<-"fitMk"
return(obj)
}
## print method for objects of class "fitMk"
print.fitMk<-function(x,digits=6,...){
cat("Object of class \"fitMk\".\n\n")
cat("Fitted (or set) value of Q:\n")
Q<-matrix(NA,length(x$states),length(x$states))
Q[]<-c(0,x$rates)[x$index.matrix+1]
diag(Q)<-0
diag(Q)<--rowSums(Q)
colnames(Q)<-rownames(Q)<-x$states
print(round(Q,digits))
cat("\nFitted (or set) value of pi:\n")
print(x$pi)
cat(paste("\nLog-likelihood:",round(x$logLik,digits),"\n"))
cat(paste("\nOptimization method used was \"",x$method,"\"\n\n",sep=""))
}
## summary method for objects of class "fitMk"
summary.fitMk<-function(object,...){
if(hasArg(digits)) digits<-list(...)$digits
else digits<-6
if(hasArg(quiet)) quiet<-list(...)$quiet
else quiet<-FALSE
if(!quiet) cat("Fitted (or set) value of Q:\n")
Q<-matrix(NA,length(object$states),length(object$states))
Q[]<-c(0,object$rates)[object$index.matrix+1]
diag(Q)<-0
diag(Q)<--rowSums(Q)
colnames(Q)<-rownames(Q)<-object$states
if(!quiet) print(round(Q,digits))
if(!quiet) cat(paste("\nLog-likelihood:",round(object$logLik,digits),"\n\n"))
invisible(list(Q=Q,logLik=object$logLik))
}
## logLik method for objects of class "fitMk"
logLik.fitMk<-function(object,...){
lik<-object$logLik
attr(lik,"df")<-length(object$rates)
lik
}
## AIC method
AIC.fitMk<-function(object,...,k=2){
np<-length(object$rates)
-2*logLik(object)+np*k
}
## S3 plot method for objects of class "fitMk"
plot.fitMk<-function(x,...){
if(hasArg(signif)) signif<-list(...)$signif
else signif<-3
if(hasArg(main)) main<-list(...)$main
else main<-NULL
if(hasArg(cex.main)) cex.main<-list(...)$cex.main
else cex.main<-1.2
if(hasArg(cex.traits)) cex.traits<-list(...)$cex.traits
else cex.traits<-1
if(hasArg(cex.rates)) cex.rates<-list(...)$cex.rates
else cex.rates<-0.6
if(hasArg(show.zeros)) show.zeros<-list(...)$show.zeros
else show.zeros<-TRUE
if(hasArg(tol)) tol<-list(...)$tol
else tol<-1e-6
if(hasArg(mar)) mar<-list(...)$mar
else mar<-c(1.1,1.1,3.1,1.1)
if(hasArg(lwd)) lwd<-list(...)$lwd
else lwd<-1
Q<-matrix(NA,length(x$states),length(x$states))
Q[]<-c(0,x$rates)[x$index.matrix+1]
diag(Q)<-0
spacer<-0.1
plot.new()
par(mar=mar)
xylim<-c(-1.2,1.2)
plot.window(xlim=xylim,ylim=xylim,asp=1)
if(!is.null(main)) title(main=main,cex.main=cex.main)
nstates<-length(x$states)
step<-360/nstates
angles<-seq(0,360-step,by=step)/180*pi
if(nstates==2) angles<-angles+pi/2
v.x<-cos(angles)
v.y<-sin(angles)
for(i in 1:nstates) for(j in 1:nstates)
if(if(!isSymmetric(Q)) i!=j else i>j){
dx<-v.x[j]-v.x[i]
dy<-v.y[j]-v.y[i]
slope<-abs(dy/dx)
shift.x<-0.02*sin(atan(dy/dx))*sign(j-i)*if(dy/dx>0) 1 else -1
shift.y<-0.02*cos(atan(dy/dx))*sign(j-i)*if(dy/dx>0) -1 else 1
s<-c(v.x[i]+spacer*cos(atan(slope))*sign(dx)+
if(isSymmetric(Q)) 0 else shift.x,
v.y[i]+spacer*sin(atan(slope))*sign(dy)+
if(isSymmetric(Q)) 0 else shift.y)
e<-c(v.x[j]+spacer*cos(atan(slope))*sign(-dx)+
if(isSymmetric(Q)) 0 else shift.x,
v.y[j]+spacer*sin(atan(slope))*sign(-dy)+
if(isSymmetric(Q)) 0 else shift.y)
if(show.zeros||Q[i,j]>tol){
if(abs(diff(c(i,j)))==1||abs(diff(c(i,j)))==(nstates-1))
text(mean(c(s[1],e[1]))+1.5*shift.x,
mean(c(s[2],e[2]))+1.5*shift.y,
round(Q[i,j],signif),cex=cex.rates,
srt=atan(dy/dx)*180/pi)
else
text(mean(c(s[1],e[1]))+0.3*diff(c(s[1],e[1]))+
1.5*shift.x,
mean(c(s[2],e[2]))+0.3*diff(c(s[2],e[2]))+
1.5*shift.y,
round(Q[i,j],signif),cex=cex.rates,
srt=atan(dy/dx)*180/pi)
arrows(s[1],s[2],e[1],e[2],length=0.05,
code=if(isSymmetric(Q)) 3 else 2,lwd=lwd)
}
}
text(v.x,v.y,x$states,cex=cex.traits,
col=make.transparent("black",0.7))
}
## S3 plot method for objects resulting from fitDiscrete
plot.gfit<-function(x,...){
if("mkn"%in%class(x$lik)==FALSE){
stop("Sorry. No plot method presently available for objects of this type.")
} else {
obj<-list()
QQ<-.Qmatrix.from.gfit(x)
obj$states<-colnames(QQ)
m<-length(obj$states)
obj$index.matrix<-matrix(NA,m,m)
k<-m*(m-1)
obj$index.matrix[col(obj$index.matrix)!=row(obj$index.matrix)]<-1:k
obj$rates<-QQ[sapply(1:k,function(x,y) which(x==y),obj$index.matrix)]
class(obj)<-"fitMk"
plot(obj,...)
}
}
## wraps around expm
## written by Liam Revell 2011, 2017
EXPM<-function(x,...){
e_x<-if(isSymmetric(x)) matexpo(x) else expm(x,...)
dimnames(e_x)<-dimnames(x)
e_x
}
## function to simulate multiple-rate Mk multiMk
## written by Liam J. Revell 2018
sim.multiMk<-function(tree,Q,anc=NULL,nsim=1,...){
if(hasArg(as.list)) as.list<-list(...)$as.list
else as.list<-FALSE
ss<-rownames(Q[[1]])
tt<-map.to.singleton(reorder(tree))
P<-vector(mode="list",length=nrow(tt$edge))
for(i in 1:nrow(tt$edge))
P[[i]]<-expm(Q[[names(tt$edge.length)[i]]]*tt$edge.length[i])
if(nsim>1) X<- if(as.list) vector(mode="list",length=nsim) else
data.frame(row.names=tt$tip.label)
for(i in 1:nsim){
a<-if(is.null(anc)) sample(ss,1) else anc
STATES<-matrix(NA,nrow(tt$edge),2)
root<-Ntip(tt)+1
STATES[which(tt$edge[,1]==root),1]<-a
for(j in 1:nrow(tt$edge)){
new<-ss[which(rmultinom(1,1,P[[j]][STATES[j,1],])[,1]==1)]
STATES[j,2]<-new
ii<-which(tt$edge[,1]==tt$edge[j,2])
if(length(ii)>0) STATES[ii,1]<-new
}
x<-as.factor(
setNames(sapply(1:Ntip(tt),function(n,S,E) S[which(E==n)],
S=STATES[,2],E=tt$edge[,2]),tt$tip.label))
if(nsim>1) X[,i]<-x else X<-x
}
X
}
## constant-rate Mk model simulator
## written by Liam J. Revell 2018
sim.Mk<-function(tree,Q,anc=NULL,nsim=1,...){
if(hasArg(as.list)) as.list<-list(...)$as.list
else as.list<-FALSE
ss<-rownames(Q)
tt<-reorder(tree)
P<-vector(mode="list",length=nrow(tt$edge))
for(i in 1:nrow(tt$edge))
P[[i]]<-expm(Q*tt$edge.length[i])
if(nsim>1) X<- if(as.list) vector(mode="list",length=nsim) else
data.frame(row.names=tt$tip.label)
for(i in 1:nsim){
a<-if(is.null(anc)) sample(ss,1) else anc
STATES<-matrix(NA,nrow(tt$edge),2)
root<-Ntip(tt)+1
STATES[which(tt$edge[,1]==root),1]<-a
for(j in 1:nrow(tt$edge)){
new<-ss[which(rmultinom(1,1,P[[j]][STATES[j,1],])[,1]==1)]
STATES[j,2]<-new
ii<-which(tt$edge[,1]==tt$edge[j,2])
if(length(ii)>0) STATES[ii,1]<-new
}
x<-as.factor(
setNames(sapply(1:Ntip(tt),function(n,S,E) S[which(E==n)],
S=STATES[,2],E=tt$edge[,2]),tt$tip.label))
if(nsim>1) X[[i]]<-x else X<-x
}
X
}