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emma.r
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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)) )
}
emma.MLE <- 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(ML=0,delta=0,ve=0,vg=0))
}
if ( is.null(Z) ) {
if ( is.null(eig.L) ) {
eig.L <- emma.eigen.L.wo.Z(K)
}
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)
Xis <- matrix(eig.L$values,n,m) + matrix(delta,n,m,byrow=TRUE)
Etasq <- matrix(etas*etas,n-q,m)
LL <- 0.5*(n*(log(n/(2*pi))-1-log(colSums(Etasq/Lambdas)))-colSums(log(Xis)))
dLL <- 0.5*delta*(n*colSums(Etasq/(Lambdas*Lambdas))/colSums(Etasq/Lambdas)-colSums(1/Xis))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(llim,eig.R$values,etas,eig.L$values))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(ulim,eig.R$values,etas,eig.L$values))
}
for( i in 1:(m-1) )
{
if ( ( dLL[i]*dLL[i+1] < 0-esp*esp ) && ( dLL[i] > 0 ) && ( dLL[i+1] < 0 ) )
{
r <- uniroot(emma.delta.ML.dLL.wo.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.R$values, etas=etas, xi=eig.L$values)
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(r$root,eig.R$values, etas, eig.L$values))
}
}
# optdelta <- exp(optlogdelta)
}
else {
if ( is.null(eig.L) ) {
eig.L <- emma.eigen.L.w.Z(Z,K)
}
if ( is.null(eig.R) ) {
eig.R <- emma.eigen.R.w.Z(Z,K,X)
}
etas <- crossprod(eig.R$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$values,t-q,m) + matrix(delta,t-q,m,byrow=TRUE)
Xis <- matrix(eig.L$values,t,m) + matrix(delta,t,m,byrow=TRUE)
Etasq <- matrix(etas.1*etas.1,t-q,m)
#LL <- 0.5*(n*(log(n/(2*pi))-1-log(colSums(Etasq/Lambdas)+etas.2.sq/delta))-colSums(log(Xis))+(n-t)*log(deltas))
dLL <- 0.5*delta*(n*(colSums(Etasq/(Lambdas*Lambdas))+etas.2.sq/(delta*delta))/(colSums(Etasq/Lambdas)+etas.2.sq/delta)-(colSums(1/Xis)+(n-t)/delta))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(llim,eig.R$values,etas.1,eig.L$values,n,etas.2.sq))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(ulim,eig.R$values,etas.1,eig.L$values,n,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.ML.dLL.w.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.R$values, etas.1=etas.1, xi.1=eig.L$values, n=n, etas.2.sq = etas.2.sq )
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(r$root,eig.R$values, etas.1, eig.L$values, n, 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$values+maxdelta))/n
}
else {
maxva <- (sum(etas.1*etas.1/(eig.R$values+maxdelta))+etas.2.sq/maxdelta)/n
}
maxve <- maxva*maxdelta
return (list(ML=maxLL,delta=maxdelta,ve=maxve,vg=maxva))
}
emma.MLE.noX <- function(y, K, Z=NULL, ngrids=100, llim=-10, ulim=10,
esp=1e-10, eig.L = NULL)
{
n <- length(y)
t <- nrow(K)
# stopifnot(nrow(K) == t)
stopifnot(ncol(K) == t)
if ( is.null(Z) ) {
if ( is.null(eig.L) ) {
eig.L <- emma.eigen.L.wo.Z(K)
}
etas <- crossprod(eig.L$vectors,y)
logdelta <- (0:ngrids)/ngrids*(ulim-llim)+llim
m <- length(logdelta)
delta <- exp(logdelta)
Xis <- matrix(eig.L$values,n,m) + matrix(delta,n,m,byrow=TRUE)
Etasq <- matrix(etas*etas,n,m)
LL <- 0.5*(n*(log(n/(2*pi))-1-log(colSums(Etasq/Xis)))-colSums(log(Xis)))
dLL <- 0.5*delta*(n*colSums(Etasq/(Xis*Xis))/colSums(Etasq/Xis)-colSums(1/Xis))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
#print(dLL)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(llim,eig.L$values,etas,eig.L$values))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(ulim,eig.L$values,etas,eig.L$values))
}
for( i in 1:(m-1) )
{
#if ( ( dLL[i]*dLL[i+1] < 0 ) && ( dLL[i] > 0 ) && ( dLL[i+1] < 0 ) )
if ( ( dLL[i]*dLL[i+1] < 0-esp*esp ) && ( dLL[i] > 0 ) && ( dLL[i+1] < 0 ) )
{
r <- uniroot(emma.delta.ML.dLL.wo.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.L$values, etas=etas, xi=eig.L$values)
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, emma.delta.ML.LL.wo.Z(r$root,eig.L$values, etas, eig.L$values))
}
}
# optdelta <- exp(optlogdelta)
}
else {
if ( is.null(eig.L) ) {
eig.L <- emma.eigen.L.w.Z(Z,K)
}
etas <- crossprod(eig.L$vectors,y)
etas.1 <- etas[1:t]
etas.2 <- etas[(t+1):n]
etas.2.sq <- sum(etas.2*etas.2)
logdelta <- (0:ngrids)/ngrids*(ulim-llim)+llim
m <- length(logdelta)
delta <- exp(logdelta)
Xis <- matrix(eig.L$values,t,m) + matrix(delta,t,m,byrow=TRUE)
Etasq <- matrix(etas.1*etas.1,t,m)
#LL <- 0.5*(n*(log(n/(2*pi))-1-log(colSums(Etasq/Lambdas)+etas.2.sq/delta))-colSums(log(Xis))+(n-t)*log(deltas))
dLL <- 0.5*delta*(n*(colSums(Etasq/(Xis*Xis))+etas.2.sq/(delta*delta))/(colSums(Etasq/Xis)+etas.2.sq/delta)-(colSums(1/Xis)+(n-t)/delta))
optlogdelta <- vector(length=0)
optLL <- vector(length=0)
if ( dLL[1] < esp ) {
optlogdelta <- append(optlogdelta, llim)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(llim,eig.L$values,etas.1,eig.L$values,n,etas.2.sq))
}
if ( dLL[m-1] > 0-esp ) {
optlogdelta <- append(optlogdelta, ulim)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(ulim,eig.L$values,etas.1,eig.L$values,n,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.ML.dLL.w.Z, lower=logdelta[i], upper=logdelta[i+1], lambda=eig.L$values, etas.1=etas.1, xi.1=eig.L$values, n=n, etas.2.sq = etas.2.sq )
optlogdelta <- append(optlogdelta, r$root)
optLL <- append(optLL, emma.delta.ML.LL.w.Z(r$root,eig.L$values, etas.1, eig.L$values, n, etas.2.sq ))
}
}
# optdelta <- exp(optlogdelta)
}
maxdelta <- exp(optlogdelta[which.max(optLL)])
maxLL <- max(optLL)
if ( is.null(Z) ) {
maxva <- sum(etas*etas/(eig.L$values+maxdelta))/n
}
else {
maxva <- (sum(etas.1*etas.1/(eig.L$values+maxdelta))+etas.2.sq/maxdelta)/n
}
maxve <- maxva*maxdelta
return (list(ML=maxLL,delta=maxdelta,ve=maxve,vg=maxva))
}
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.ML.LRT <- function(ys, xs, K, Z=NULL, X0 = NULL, ngrids=100, llim=-10, ulim=10, esp=1e-10, ponly = FALSE) {
if ( is.null(dim(ys)) || ncol(ys) == 1 ) {
ys <- matrix(ys,1,length(ys))
}
if ( is.null(dim(xs)) || ncol(xs) == 1 ) {
xs <- matrix(xs,1,length(xs))
}
if ( is.null(X0) ) {
X0 <- matrix(1,ncol(ys),1)
}
g <- nrow(ys)
n <- ncol(ys)
m <- nrow(xs)
t <- ncol(xs)
q0 <- ncol(X0)
q1 <- q0 + 1
if ( !ponly ) {
ML1s <- matrix(nrow=m,ncol=g)
ML0s <- matrix(nrow=m,ncol=g)
vgs <- matrix(nrow=m,ncol=g)
ves <- matrix(nrow=m,ncol=g)
}
stats <- matrix(nrow=m,ncol=g)
ps <- matrix(nrow=m,ncol=g)
ML0 <- vector(length=g)
stopifnot(nrow(K) == t)
stopifnot(ncol(K) == t)
stopifnot(nrow(X0) == n)
if ( sum(is.na(ys)) == 0 ) {
eig.L <- emma.eigen.L(Z,K)
eig.R0 <- emma.eigen.R(Z,K,X0)
for(i in 1:g) {
ML0[i] <- emma.MLE(ys[i,],X0,K,Z,ngrids,llim,ulim,esp,eig.L,eig.R0)$ML
}
x.prev <- vector(length=0)
for(i in 1:m) {
vids <- !is.na(xs[i,])
nv <- sum(vids)
xv <- xs[i,vids]
if ( ( mean(xv) <= 0 ) || ( mean(xv) >= 1 ) ) {
if (!ponly) {
stats[i,] <- rep(NA,g)
vgs[i,] <- rep(NA,g)
ves[i,] <- rep(NA,g)
ML1s[i,] <- rep(NA,g)
ML0s[i,] <- rep(NA,g)
}
ps[i,] = rep(1,g)
}
else if ( identical(x.prev, xv) ) {
if ( !ponly ) {
stats[i,] <- stats[i-1,]
vgs[i,] <- vgs[i-1,]
ves[i,] <- ves[i-1,]
ML1s[i,] <- ML1s[i-1,]
ML0s[i,] <- ML0s[i-1,]
}
ps[i,] <- ps[i-1,]
}
else {
if ( is.null(Z) ) {
X <- cbind(X0[vids,,drop=FALSE],xs[i,vids])
eig.R1 = emma.eigen.R.wo.Z(K[vids,vids],X)
}
else {
vrows <- as.logical(rowSums(Z[,vids]))
nr <- sum(vrows)
X <- cbind(X0[vrows,,drop=FALSE],Z[vrows,vids]%*%t(xs[i,vids,drop=FALSE]))
eig.R1 = emma.eigen.R.w.Z(Z[vrows,vids],K[vids,vids],X)
}
for(j in 1:g) {
if ( nv == t ) {
MLE <- emma.MLE(ys[j,],X,K,Z,ngrids,llim,ulim,esp,eig.L,eig.R1)
# MLE <- emma.MLE(ys[j,],X,K,Z,ngrids,llim,ulim,esp,eig.L,eig.R1)
if (!ponly) {
ML1s[i,j] <- MLE$ML
vgs[i,j] <- MLE$vg
ves[i,j] <- MLE$ve
}
stats[i,j] <- 2*(MLE$ML-ML0[j])
}
else {
if ( is.null(Z) ) {
eig.L0 <- emma.eigen.L.wo.Z(K[vids,vids])
MLE0 <- emma.MLE(ys[j,vids],X0[vids,,drop=FALSE],K[vids,vids],NULL,ngrids,llim,ulim,esp,eig.L0)
MLE1 <- emma.MLE(ys[j,vids],X,K[vids,vids],NULL,ngrids,llim,ulim,esp,eig.L0)
}
else {
if ( nr == n ) {
MLE1 <- emma.MLE(ys[j,],X,K,Z,ngrids,llim,ulim,esp,eig.L)
}
else {
eig.L0 <- emma.eigen.L.w.Z(Z[vrows,vids],K[vids,vids])
MLE0 <- emma.MLE(ys[j,vrows],X0[vrows,,drop=FALSE],K[vids,vids],Z[vrows,vids],ngrids,llim,ulim,esp,eig.L0)
MLE1 <- emma.MLE(ys[j,vrows],X,K[vids,vids],Z[vrows,vids],ngrids,llim,ulim,esp,eig.L0)
}
}
if (!ponly) {
ML1s[i,j] <- MLE1$ML
ML0s[i,j] <- MLE0$ML
vgs[i,j] <- MLE1$vg
ves[i,j] <- MLE1$ve
}
stats[i,j] <- 2*(MLE1$ML-MLE0$ML)
}
}
if ( ( nv == t ) && ( !ponly ) ) {
ML0s[i,] <- ML0
}
ps[i,] <- pchisq(stats[i,],1,lower.tail=FALSE)
}
}
}
else {
eig.L <- emma.eigen.L(Z,K)
eig.R0 <- emma.eigen.R(Z,K,X0)
for(i in 1:g) {
vrows <- !is.na(ys[i,])
if ( is.null(Z) ) {
ML0[i] <- emma.MLE(ys[i,vrows],X0[vrows,,drop=FALSE],K[vrows,vrows],NULL,ngrids,llim,ulim,esp)$ML
}
else {
vids <- colSums(Z[vrows,]>0)
ML0[i] <- emma.MLE(ys[i,vrows],X0[vrows,,drop=FALSE],K[vids,vids],Z[vrows,vids],ngrids,llim,ulim,esp)$ML
}
}
x.prev <- vector(length=0)
for(i in 1:m) {
vids <- !is.na(xs[i,])
nv <- sum(vids)
xv <- xs[i,vids]
if ( ( mean(xv) <= 0 ) || ( mean(xv) >= 1 ) ) {
if (!ponly) {
stats[i,] <- rep(NA,g)
vgs[i,] <- rep(NA,g)
ves[i,] <- rep(NA,g)
ML1s[i,] <- rep(NA,g)
ML0s[,i] <- rep(NA,g)
}
ps[i,] = rep(1,g)
}
else if ( identical(x.prev, xv) ) {
if ( !ponly ) {
stats[i,] <- stats[i-1,]
vgs[i,] <- vgs[i-1,]
ves[i,] <- ves[i-1,]
ML1s[i,] <- ML1s[i-1,]
}
ps[i,] = ps[i-1,]
}
else {
if ( is.null(Z) ) {
X <- cbind(X0,xs[i,])
if ( nv == t ) {
eig.R1 = emma.eigen.R.wo.Z(K,X)
}
}
else {
vrows <- as.logical(rowSums(Z[,vids]))
X <- cbind(X0,Z[,vids,drop=FALSE]%*%t(xs[i,vids,drop=FALSE]))
if ( nv == t ) {
eig.R1 = emma.eigen.R.w.Z(Z,K,X)
}
}
for(j in 1:g) {
# print(j)
vrows <- !is.na(ys[j,])
if ( nv == t ) {
nr <- sum(vrows)
if ( is.null(Z) ) {
if ( nr == n ) {
MLE <- emma.MLE(ys[j,],X,K,NULL,ngrids,llim,ulim,esp,eig.L,eig.R1)
}
else {
MLE <- emma.MLE(ys[j,vrows],X[vrows,],K[vrows,vrows],NULL,ngrids,llim,ulim,esp)
}
}
else {
if ( nr == n ) {
MLE <- emma.MLE(ys[j,],X,K,Z,ngrids,llim,ulim,esp,eig.L,eig.R1)
}
else {
vtids <- as.logical(colSums(Z[vrows,,drop=FALSE]))
MLE <- emma.MLE(ys[j,vrows],X[vrows,],K[vtids,vtids],Z[vrows,vtids],ngrids,llim,ulim,esp)
}
}
if (!ponly) {
ML1s[i,j] <- MLE$ML
vgs[i,j] <- MLE$vg
ves[i,j] <- MLE$ve
}
stats[i,j] <- 2*(MLE$ML-ML0[j])
}
else {
if ( is.null(Z) ) {
vtids <- vrows & vids
eig.L0 <- emma.eigen.L(NULL,K[vtids,vtids])
MLE0 <- emma.MLE(ys[j,vtids],X0[vtids,,drop=FALSE],K[vtids,vtids],NULL,ngrids,llim,ulim,esp,eig.L0)
MLE1 <- emma.MLE(ys[j,vtids],X[vtids,],K[vtids,vtids],NULL,ngrids,llim,ulim,esp,eig.L0)
}
else {
vtids <- as.logical(colSums(Z[vrows,])) & vids
vtrows <- vrows & as.logical(rowSums(Z[,vids]))
eig.L0 <- emma.eigen.L(Z[vtrows,vtids],K[vtids,vtids])
MLE0 <- emma.MLE(ys[j,vtrows],X0[vtrows,,drop=FALSE],K[vtids,vtids],Z[vtrows,vtids],ngrids,llim,ulim,esp,eig.L0)
MLE1 <- emma.MLE(ys[j,vtrows],X[vtrows,],K[vtids,vtids],Z[vtrows,vtids],ngrids,llim,ulim,esp,eig.L0)
}
if (!ponly) {
ML1s[i,j] <- MLE1$ML
vgs[i,j] <- MLE1$vg
ves[i,j] <- MLE1$ve
ML0s[i,j] <- MLE0$ML
}
stats[i,j] <- 2*(MLE1$ML-MLE0$ML)
}
}
if ( ( nv == t ) && ( !ponly ) ) {
ML0s[i,] <- ML0
}
ps[i,] <- pchisq(stats[i,],1,lower.tail=FALSE)
}
}
}
if ( ponly ) {
return (ps)
}
else {
return (list(ps=ps,ML1s=ML1s,ML0s=ML0s,stats=stats,vgs=vgs,ves=ves))
}
}
emma.test <- function(ys, xs, K, Z=NULL, x0s = NULL, X0 = NULL, dfxs = 1, dfx0s = 1, use.MLE = FALSE, use.LRT = FALSE, ngrids = 100, llim = -10, ulim = 10, esp=1e-10, ponly = FALSE)
{
stopifnot (dfxs > 0)
if ( is.null(dim(ys)) || ncol(ys) == 1 ) {
ys <- matrix(ys,1,length(ys))
}
if ( is.null(dim(xs)) || ncol(xs) == 1 ) {
xs <- matrix(xs,1,length(xs))
}
nx <- nrow(xs)/dfxs
if ( is.null(x0s) ) {
dfx0s = 0
x0s <- matrix(NA,0,ncol(xs))
}
# X0 automatically contains intercept. If no intercept is to be used,
# X0 should be matrix(nrow=ncol(ys),ncol=0)
if ( is.null(X0) ) {
X0 <- matrix(1,ncol(ys),1)
}
stopifnot(Z == NULL) # The case where Z is not null is not implemented
ny <- nrow(ys)
iy <- ncol(ys)
ix <- ncol(xs)
stopifnot(nrow(K) == ix)
stopifnot(ncol(K) == ix)
stopifnot(nrow(X0) == iy)
if ( !ponly ) {
LLs <- matrix(nrow=m,ncol=g)
vgs <- matrix(nrow=m,ncol=g)
ves <- matrix(nrow=m,ncol=g)
}
dfs <- matrix(nrow=m,ncol=g)
stats <- matrix(nrow=m,ncol=g)
ps <- matrix(nrow=m,ncol=g)
# The case with no missing phenotypes
if ( sum(is.na(ys)) == 0 ) {
if ( ( use.MLE ) || ( !use.LRT ) ) {
eig.L0 <- emma.eigen.L(Z,K)
}
if ( dfx0s == 0 ) {
eig.R0 <- emma.eigen.R(Z,K,X0)
}
x.prev <- NULL
for(i in 1:ix) {
x1 <- t(xs[(dfxs*(i-1)+1):(dfxs*i),,drop=FALSE])
if ( dfxs0 == 0 ) {
x0 <- X0
}
else {
x0 <- cbind(t(x0s[(dfx0s*(i-1)+1):(dfx0s*i),,drop=FALSE]),X0)
}
x <- cbind(x1,x0)
xvids <- rowSums(is.na(x) == 0)
nxv <- sum(xvids)
xv <- x[xvids,,drop=FALSE]
Kv <- K[xvids,xvids,drop=FALSE]
yv <- ys[j,xvids]
if ( identical(x.prev, xv) ) {
if ( !ponly ) {
vgs[i,] <- vgs[i-1,]
ves[i,] <- ves[i-1,]
dfs[i,] <- dfs[i-1,]
REMLs[i,] <- REMLs[i-1,]
stats[i,] <- stats[i-1,]
}
ps[i,] <- ps[i-1,]
}
else {
eig.R1 = emma.eigen.R.wo.Z(Kv,xv)
for(j in 1:iy) {
if ( ( use.MLE ) || ( !use.LRT ) ) {
if ( nxv < t ) {
# NOTE: this complexity can be improved by avoiding eigen computation for identical missing patterns
eig.L0v <- emma.eigen.L.wo.Z(Kv)
}
else {
eig.L0v <- eig.L0
}
}
if ( use.MLE ) {
MLE <- emma.REMLE(yv,xv,Kv,NULL,ngrids,llim,ulim,esp,eig.R1)
stop("Not implemented yet")
}
else {
REMLE <- emma.REMLE(yv,xv,Kv,NULL,ngrids,llim,ulim,esp,eig.R1)
if ( use.LRT ) {
stop("Not implemented yet")
}
else {
U <- eig.L0v$vectors * matrix(sqrt(1/(eig.L0v$values+REMLE$delta)),t,t,byrow=TRUE)
dfs[i,j] <- length(eig.R1$values)
yt <- crossprod(U,yv)
xt <- crossprod(U,xv)
ixx <- solve(crossprod(xt,xt))
beta <- ixx%*%crossprod(xt,yt)
if ( dfxs == 1 ) {
stats[i,j] <- beta[q1]/sqrt(iXX[q1,q1]*REMLE$vg)
}
else {
model.m <- c(rep(1,dfxs),rep(0,ncol(xv)-dfxs))
stats[i,j] <-
crossprod(crossprod(solve(crossprod(crossprod(iXX,model.m),
model.m)),
model.m*beta),model.m*beta)
}
if ( !ponly ) {
vgs[i,j] <- REMLE$vg
ves[i,j] <- REMLE$ve
REMLs[i,j] <- REMLE$REML
}
}
}
}
if ( dfxs == 1 ) {
ps[i,] <- 2*pt(abs(stats[i,]),dfs[i,],lower.tail=FALSE)
}
else {
ps[i,] <- pf(abs(stats[i,]),dfs[i,],lower.tail=FALSE)
}
}
}
}
# The case with missing genotypes - not implemented yet
else {
stop("Not implemented yet")
eig.L <- emma.eigen.L(Z,K)
eig.R0 <- emma.eigen.R(Z,K,X0)
x.prev <- vector(length=0)
for(i in 1:m) {
vids <- !is.na(xs[i,])
nv <- sum(vids)
xv <- xs[i,vids]
if ( ( mean(xv) <= 0 ) || ( mean(xv) >= 1 ) ) {
if (!ponly) {
vgs[i,] <- rep(NA,g)
ves[i,] <- rep(NA,g)
REMLs[i,] <- rep(NA,g)
dfs[i,] <- rep(NA,g)
}
ps[i,] = rep(1,g)
}
else if ( identical(x.prev, xv) ) {
if ( !ponly ) {
stats[i,] <- stats[i-1,]
vgs[i,] <- vgs[i-1,]
ves[i,] <- ves[i-1,]
REMLs[i,] <- REMLs[i-1,]
dfs[i,] <- dfs[i-1,]
}
ps[i,] = ps[i-1,]
}
else {
if ( is.null(Z) ) {
X <- cbind(X0,xs[i,])
if ( nv == t ) {
eig.R1 = emma.eigen.R.wo.Z(K,X)
}
}
else {
vrows <- as.logical(rowSums(Z[,vids,drop=FALSE]))
X <- cbind(X0,Z[,vids,drop=FALSE]%*%t(xs[i,vids,drop=FALSE]))
if ( nv == t ) {
eig.R1 = emma.eigen.R.w.Z(Z,K,X)
}
}
for(j in 1:g) {
vrows <- !is.na(ys[j,])
if ( nv == t ) {
yv <- ys[j,vrows]
nr <- sum(vrows)
if ( is.null(Z) ) {
if ( nr == n ) {
REMLE <- emma.REMLE(yv,X,K,NULL,ngrids,llim,ulim,esp,eig.R1)
U <- eig.L$vectors * matrix(sqrt(1/(eig.L$values+REMLE$delta)),n,n,byrow=TRUE)
}
else {
eig.L0 <- emma.eigen.L.wo.Z(K[vrows,vrows,drop=FALSE])
REMLE <- emma.REMLE(yv,X[vrows,,drop=FALSE],K[vrows,vrows,drop=FALSE],NULL,ngrids,llim,ulim,esp)
U <- eig.L0$vectors * matrix(sqrt(1/(eig.L0$values+REMLE$delta)),nr,nr,byrow=TRUE)
}
dfs[i,j] <- nr-q1
}
else {
if ( nr == n ) {
REMLE <- emma.REMLE(yv,X,K,Z,ngrids,llim,ulim,esp,eig.R1)
U <- eig.L$vectors * matrix(c(sqrt(1/(eig.L$values+REMLE$delta)),rep(sqrt(1/REMLE$delta),n-t)),n,n,byrow=TRUE)
}
else {
vtids <- as.logical(colSums(Z[vrows,,drop=FALSE]))
eig.L0 <- emma.eigen.L.w.Z(Z[vrows,vtids,drop=FALSE],K[vtids,vtids,drop=FALSE])
REMLE <- emma.REMLE(yv,X[vrows,,drop=FALSE],K[vtids,vtids,drop=FALSE],Z[vrows,vtids,drop=FALSE],ngrids,llim,ulim,esp)
U <- eig.L0$vectors * matrix(c(sqrt(1/(eig.L0$values+REMLE$delta)),rep(sqrt(1/REMLE$delta),nr-sum(vtids))),nr,nr,byrow=TRUE)
}
dfs[i,j] <- nr-q1
}
yt <- crossprod(U,yv)
Xt <- crossprod(U,X[vrows,,drop=FALSE])
iXX <- solve(crossprod(Xt,Xt))
beta <- iXX%*%crossprod(Xt,yt)
if ( !ponly ) {
vgs[i,j] <- REMLE$vg
ves[i,j] <- REMLE$ve
REMLs[i,j] <- REMLE$REML
}
stats[i,j] <- beta[q1]/sqrt(iXX[q1,q1]*REMLE$vg)
}
else {
if ( is.null(Z) ) {
vtids <- vrows & vids
eig.L0 <- emma.eigen.L.wo.Z(K[vtids,vtids,drop=FALSE])
yv <- ys[j,vtids]
nr <- sum(vtids)
REMLE <- emma.REMLE(yv,X[vtids,,drop=FALSE],K[vtids,vtids,drop=FALSE],NULL,ngrids,llim,ulim,esp)
U <- eig.L0$vectors * matrix(sqrt(1/(eig.L0$values+REMLE$delta)),nr,nr,byrow=TRUE)
Xt <- crossprod(U,X[vtids,,drop=FALSE])
dfs[i,j] <- nr-q1
}
else {
vtids <- as.logical(colSums(Z[vrows,,drop=FALSE])) & vids
vtrows <- vrows & as.logical(rowSums(Z[,vids,drop=FALSE]))
eig.L0 <- emma.eigen.L.w.Z(Z[vtrows,vtids,drop=FALSE],K[vtids,vtids,drop=FALSE])
yv <- ys[j,vtrows]
nr <- sum(vtrows)
REMLE <- emma.REMLE(yv,X[vtrows,,drop=FALSE],K[vtids,vtids,drop=FALSE],Z[vtrows,vtids,drop=FALSE],ngrids,llim,ulim,esp)
U <- eig.L0$vectors * matrix(c(sqrt(1/(eig.L0$values+REMLE$delta)),rep(sqrt(1/REMLE$delta),nr-sum(vtids))),nr,nr,byrow=TRUE)
Xt <- crossprod(U,X[vtrows,,drop=FALSE])
dfs[i,j] <- nr-q1
}
yt <- crossprod(U,yv)
iXX <- solve(crossprod(Xt,Xt))
beta <- iXX%*%crossprod(Xt,yt)
if ( !ponly ) {
vgs[i,j] <- REMLE$vg
ves[i,j] <- REMLE$ve
REMLs[i,j] <- REMLE$REML
}
stats[i,j] <- beta[q1]/sqrt(iXX[q1,q1]*REMLE$vg)