Nothing
#######################################################################
#emma.REMLE function was taken from the EMMA package by Hyun Min Kang
# http://mouse.cs.ucla.edu/emma/install.html
# We have put it here instead of using the EMMA
# package to make it easier to install fassoc.
########################################################################
.emma.REMLE <- function(y, X, K, Z=NULL, ngrids=100, llim=-10, ulim=10,
esp=1e-10, eig.L = NULL, eig.R = NULL) {
n <- length(y)
t <- nrow(K)
q <- ncol(X)
# stopifnot(nrow(K) == t)
stopifnot(ncol(K) == t)
stopifnot(nrow(X) == n)
if ( det(crossprod(X,X)) == 0 ) {
warning("X is singular")
return (list(REML=0,delta=0,ve=0,vg=0))
}
if ( is.null(Z) ) {
if ( is.null(eig.R) ) {
eig.R <- .emma.eigen.R.wo.Z(K,X)
}
etas <- crossprod(eig.R$vectors,y)
logdelta <- (0:ngrids)/ngrids*(ulim-llim)+llim
m <- length(logdelta)
delta <- exp(logdelta)
Lambdas <- matrix(eig.R$values,n-q,m) + matrix(delta,n-q,m,byrow=TRUE)
Etasq <- matrix(etas*etas,n-q,m)
LL <- 0.5*((n-q)*(log((n-q)/(2*pi))-1-log(colSums(Etasq/Lambdas)))-colSums(log(Lambdas)))
dLL <- 0.5*delta*((n-q)*colSums(Etasq/(Lambdas*Lambdas))/colSums(Etasq/Lambdas)-colSums(1/Lambdas))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, .emma.delta.REML.LL.wo.Z(llim,eig.R$values,etas))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, .emma.delta.REML.LL.wo.Z(ulim,eig.R$values,etas))
}
for( i in 1:(m-1) )
{
if ( ( dLL[i]*dLL[i+1] < 0-esp*esp ) && ( dLL[i] > 0 ) && ( dLL[i+1] < 0 ) )
{
r <- uniroot(.emma.delta.REML.dLL.wo.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.R$values, etas=etas)
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, .emma.delta.REML.LL.wo.Z(r$root,eig.R$values, etas))
}
}
# optdelta <- exp(optlogdelta)
}
else {
if ( is.null(eig.R) ) {
eig.R <- .emma.eigen.R.w.Z(Z,K,X)
}
etas <- crossprod(eig.R$vectors,y)
etas.1 <- etas[1:(t-q)]
etas.2 <- etas[(t-q+1):(n-q)]
etas.2.sq <- sum(etas.2*etas.2)
logdelta <- (0:ngrids)/ngrids*(ulim-llim)+llim
m <- length(logdelta)
delta <- exp(logdelta)
Lambdas <- matrix(eig.R$values,t-q,m) + matrix(delta,t-q,m,byrow=TRUE)
Etasq <- matrix(etas.1*etas.1,t-q,m)
dLL <- 0.5*delta*((n-q)*(colSums(Etasq/(Lambdas*Lambdas))+etas.2.sq/(delta*delta))/(colSums(Etasq/Lambdas)+etas.2.sq/delta)-(colSums(1/Lambdas)+(n-t)/delta))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, .emma.delta.REML.LL.w.Z(llim,eig.R$values,etas.1,n,t,etas.2.sq))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, .emma.delta.REML.LL.w.Z(ulim,eig.R$values,etas.1,n,t,etas.2.sq))
}
for( i in 1:(m-1) )
{
if ( ( dLL[i]*dLL[i+1] < 0-esp*esp ) && ( dLL[i] > 0 ) && ( dLL[i+1] < 0 ) )
{
r <- uniroot(.emma.delta.REML.dLL.w.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.R$values, etas.1=etas.1, n=n, t1=t, etas.2.sq = etas.2.sq )
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, .emma.delta.REML.LL.w.Z(r$root,eig.R$values, etas.1, n, t, etas.2.sq ))
}
}
# optdelta <- exp(optlogdelta)
}
maxdelta <- exp(optlogdelta[which.max(optLL)])
maxLL <- max(optLL)
if ( is.null(Z) ) {
maxva <- sum(etas*etas/(eig.R$values+maxdelta))/(n-q)
}
else {
maxva <- (sum(etas.1*etas.1/(eig.R$values+maxdelta))+etas.2.sq/maxdelta)/(n-q)
}
maxve <- maxva*maxdelta
return (list(REML=maxLL,delta=maxdelta,ve=maxve,vg=maxva))
}
.emma.kinship <- function(snps, method="additive", use="all") {
n0 <- sum(snps==0,na.rm=TRUE)
nh <- sum(snps==0.5,na.rm=TRUE)
n1 <- sum(snps==1,na.rm=TRUE)
nNA <- sum(is.na(snps))
stopifnot(n0+nh+n1+nNA == length(snps))
if ( method == "dominant" ) {
flags <- matrix(as.double(rowMeans(snps,na.rm=TRUE) > 0.5),nrow(snps),ncol(snps))
snps[!is.na(snps) & (snps == 0.5)] <- flags[!is.na(snps) & (snps == 0.5)]
}
else if ( method == "recessive" ) {
flags <- matrix(as.double(rowMeans(snps,na.rm=TRUE) < 0.5),nrow(snps),ncol(snps))
snps[!is.na(snps) & (snps == 0.5)] <- flags[!is.na(snps) & (snps == 0.5)]
}
else if ( ( method == "additive" ) && ( nh > 0 ) ) {
dsnps <- snps
rsnps <- snps
flags <- matrix(as.double(rowMeans(snps,na.rm=TRUE) > 0.5),nrow(snps),ncol(snps))
dsnps[!is.na(snps) & (snps==0.5)] <- flags[!is.na(snps) & (snps==0.5)]
flags <- matrix(as.double(rowMeans(snps,na.rm=TRUE) < 0.5),nrow(snps),ncol(snps))
rsnps[!is.na(snps) & (snps==0.5)] <- flags[!is.na(snps) & (snps==0.5)]
snps <- rbind(dsnps,rsnps)
}
if ( use == "all" ) {
mafs <- matrix(rowMeans(snps,na.rm=TRUE),nrow(snps),ncol(snps))
snps[is.na(snps)] <- mafs[is.na(snps)]
}
else if ( use == "complete.obs" ) {
snps <- snps[rowSums(is.na(snps))==0,]
}
n <- ncol(snps)
K <- matrix(nrow=n,ncol=n)
diag(K) <- 1
for(i in 2:n) {
for(j in 1:(i-1)) {
x <- snps[,i]*snps[,j] + (1-snps[,i])*(1-snps[,j])
K[i,j] <- sum(x,na.rm=TRUE)/sum(!is.na(x))
K[j,i] <- K[i,j]
}
}
return(K)
}
.emma.eigen.L <- function(Z,K,complete=TRUE) {
if ( is.null(Z) ) {
return(.emma.eigen.L.wo.Z(K))
}
else {
return(.emma.eigen.L.w.Z(Z,K,complete))
}
}
.emma.eigen.L.wo.Z <- function(K) {
eig <- eigen(K,symmetric=TRUE)
return(list(values=eig$values,vectors=eig$vectors))
}
.emma.eigen.L.w.Z <- function(Z,K,complete=TRUE) {
if ( complete == FALSE ) {
vids <- colSums(Z)>0
Z <- Z[,vids]
K <- K[vids,vids]
}
eig <- eigen(K%*%crossprod(Z,Z),symmetric=FALSE,EISPACK=TRUE)
return(list(values=eig$values,vectors=qr.Q(qr(Z%*%eig$vectors),complete=TRUE)))
}
.emma.eigen.R <- function(Z,K,X,complete=TRUE) {
if ( ncol(X) == 0 ) {
return(.emma.eigen.L(Z,K))
}
else if ( is.null(Z) ) {
return(.emma.eigen.R.wo.Z(K,X))
}
else {
return(.emma.eigen.R.w.Z(Z,K,X,complete))
}
}
.emma.eigen.R.wo.Z <- function(K, X) {
n <- nrow(X)
q <- ncol(X)
S <- diag(n)-X%*%solve(crossprod(X,X))%*%t(X)
eig <- eigen(S%*%(K+diag(1,n))%*%S,symmetric=TRUE)
stopifnot(!is.complex(eig$values))
return(list(values=eig$values[1:(n-q)]-1,vectors=eig$vectors[,1:(n-q)]))
}
.emma.eigen.R.w.Z <- function(Z, K, X, complete = TRUE) {
if ( complete == FALSE ) {
vids <- colSums(Z) > 0
Z <- Z[,vids]
K <- K[vids,vids]
}
n <- nrow(Z)
t <- ncol(Z)
q <- ncol(X)
SZ <- Z - X%*%solve(crossprod(X,X))%*%crossprod(X,Z)
eig <- eigen(K%*%crossprod(Z,SZ),symmetric=FALSE,EISPACK=TRUE)
if ( is.complex(eig$values) ) {
eig$values <- Re(eig$values)
eig$vectors <- Re(eig$vectors)
}
qr.X <- qr.Q(qr(X))
return(list(values=eig$values[1:(t-q)],
vectors=qr.Q(qr(cbind(SZ%*%eig$vectors[,1:(t-q)],qr.X)),
complete=TRUE)[,c(1:(t-q),(t+1):n)]))
}
.emma.delta.ML.LL.wo.Z <- function(logdelta, lambda, etas, xi) {
n <- length(xi)
delta <- exp(logdelta)
return( 0.5*(n*(log(n/(2*pi))-1-log(sum((etas*etas)/(lambda+delta))))-sum(log(xi+delta))) )
}
.emma.delta.ML.LL.w.Z <- function(logdelta, lambda, etas.1, xi.1, n, etas.2.sq ) {
t <- length(xi.1)
delta <- exp(logdelta)
# stopifnot(length(lambda) == length(etas.1))
return( 0.5*(n*(log(n/(2*pi))-1-log(sum(etas.1*etas.1/(lambda+delta))+etas.2.sq/delta))-(sum(log(xi.1+delta))+(n-t)*logdelta)) )
}
.emma.delta.ML.dLL.wo.Z <- function(logdelta, lambda, etas, xi) {
n <- length(xi)
delta <- exp(logdelta)
etasq <- etas*etas
ldelta <- lambda+delta
return( 0.5*(n*sum(etasq/(ldelta*ldelta))/sum(etasq/ldelta)-sum(1/(xi+delta))) )
}
.emma.delta.ML.dLL.w.Z <- function(logdelta, lambda, etas.1, xi.1, n, etas.2.sq ) {
t <- length(xi.1)
delta <- exp(logdelta)
etasq <- etas.1*etas.1
ldelta <- lambda+delta
return( 0.5*(n*(sum(etasq/(ldelta*ldelta))+etas.2.sq/(delta*delta))/(sum(etasq/ldelta)+etas.2.sq/delta)-(sum(1/(xi.1+delta))+(n-t)/delta) ) )
}
.emma.delta.REML.LL.wo.Z <- function(logdelta, lambda, etas) {
nq <- length(etas)
delta <- exp(logdelta)
return( 0.5*(nq*(log(nq/(2*pi))-1-log(sum(etas*etas/(lambda+delta))))-sum(log(lambda+delta))) )
}
.emma.delta.REML.LL.w.Z <- function(logdelta, lambda, etas.1, n, t, etas.2.sq ) {
tq <- length(etas.1)
nq <- n - t + tq
delta <- exp(logdelta)
return( 0.5*(nq*(log(nq/(2*pi))-1-log(sum(etas.1*etas.1/(lambda+delta))+etas.2.sq/delta))-(sum(log(lambda+delta))+(n-t)*logdelta)) )
}
.emma.delta.REML.dLL.wo.Z <- function(logdelta, lambda, etas) {
nq <- length(etas)
delta <- exp(logdelta)
etasq <- etas*etas
ldelta <- lambda+delta
return( 0.5*(nq*sum(etasq/(ldelta*ldelta))/sum(etasq/ldelta)-sum(1/ldelta)) )
}
.emma.delta.REML.dLL.w.Z <- function(logdelta, lambda, etas.1, n, t1, etas.2.sq ) {
t <- t1
tq <- length(etas.1)
nq <- n - t + tq
delta <- exp(logdelta)
etasq <- etas.1*etas.1
ldelta <- lambda+delta
return( 0.5*(nq*(sum(etasq/(ldelta*ldelta))+etas.2.sq/(delta*delta))/(sum(etasq/ldelta)+etas.2.sq/delta)-(sum(1/ldelta)+(n-t)/delta)) )
}
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