MatReg_QC_RE <-
function(Y,X,Phi0,max.itr=1000,tol=1e-4,trace=FALSE,score.return=TRUE)
{
n<-length(Y)
p<-ncol(Y[[1]])
Tvec<-rep(NA,n)
q<-ncol(X)
# Estimate covariance matrix for each subject
Sigma<-array(NA,c(p,p,n))
for(i in 1:n)
{
Tvec[i]<-nrow(Y[[i]])
Sigma[,,i]<-t(scale(Y[[i]],center=TRUE,scale=FALSE))%*%(scale(Y[[i]],center=TRUE,scale=FALSE))/nrow(Y[[i]])
}
beta0<-rep(0,q)
if(trace)
{
gamma.trace<-NULL
beta.trace<-beta0
}
s<-0
diff<-100
while(s<=max.itr&diff>tol)
{
s<-s+1
# update gamma
A<-matrix(0,p,p)
for(i in 1:n)
{
A<-A+Tvec[i]*Sigma[,,i]/(exp(X[i,]%*%beta0)[1,1])
}
B<-apply(Sigma,c(1,2),mean)
B.inv<-solve(B)
P<-Phi0%*%ginv(t(Phi0)%*%B.inv%*%Phi0)%*%t(Phi0)%*%B.inv
B.inv.eigen<-eigen(B.inv)
B.inv.rt<-B.inv.eigen$vectors%*%diag(sqrt(B.inv.eigen$values))%*%solve(B.inv.eigen$vectors)
re.eigen<-eigen(B.inv.rt%*%(diag(rep(1,p))-P)%*%A%*%B.inv.rt)
re.eigen.vec<-Re(re.eigen$vectors)
x.tmp<-B.inv.rt%*%re.eigen.vec
# diag(t(x.tmp)%*%B%*%x.tmp)
# which.min(diag(t(x.tmp)%*%A%*%x.tmp))
# gamma.new<-x.tmp[,which.min(diag(t(x.tmp)%*%A%*%x.tmp))]
gamma.new.mat<-x.tmp
# update beta
# Q1<-t(X)%*%diag(Tvec)%*%X
beta.new.mat<-NULL
objfunc.tmp<-NULL
for(j in 1:ncol(gamma.new.mat))
{
gamma.new<-gamma.new.mat[,j]
Q1<-matrix(0,q,q)
Q2<-rep(0,q)
for(i in 1:n)
{
# Q1<-Q1+Tvec[i]*X[i,]%*%t(X[i,])
Q1<-Q1+(Tvec[i]*(t(gamma.new)%*%Sigma[,,i]%*%gamma.new)[1,1]*exp(-t(X[i,])%*%beta0)[1,1])*(X[i,]%*%t(X[i,]))
Q2<-Q2+Tvec[i]*(1-(t(gamma.new)%*%Sigma[,,i]%*%gamma.new)[1,1]*(exp(-t(X[i,])%*%beta0)[1,1]))*X[i,]
}
beta.new.mat<-cbind(beta.new.mat,beta0-ginv(Q1)%*%Q2)
objfunc.tmp<-c(objfunc.tmp,objfunc(Y,X,gamma.new,beta.new.mat[,j]))
}
beta.new<-beta.new.mat[,which.min(objfunc.tmp)]
gamma.new<-gamma.new.mat[,which.min(objfunc.tmp)]
if(trace)
{
gamma.trace<-cbind(gamma.trace,gamma.new)
beta.trace<-cbind(beta.trace,beta.new)
}
diff<-max(abs(beta.new-beta0))
beta0<-beta.new
# print(diff)
}
# scale gamma
gamma.new<-gamma.new/sqrt(sum(gamma.new^2))
if(gamma.new[1]<0)
{
gamma.new<--gamma.new
}
beta.new<-MatReg_QC_beta(Y,X,gamma=gamma.new,max.itr=max.itr,tol=tol,trace=trace,score.return=score.return)$beta
if(score.return)
{
score<-rep(NA,n)
for(i in 1:n)
{
score[i]<-t(gamma.new)%*%Sigma[,,i]%*%gamma.new
}
}
if(trace)
{
colnames(v.trace)<-NULL
colnames(beta.trace)<-NULL
if(score.return)
{
re<-list(gamma=c(gamma.new),beta=c(beta.new),convergence=(s<max.itr),score=score,gamma.trace=gamma.trace,beta.trace=beta.trace)
}else
{
re<-list(gamma=c(gamma.new),beta=c(beta.new),convergence=(s<max.itr),gamma.trace=gamma.trace,beta.trace=beta.trace)
}
}else
{
if(score.return)
{
re<-list(gamma=c(gamma.new),beta=c(beta.new),convergence=(s<max.itr),score=score)
}else
{
re<-list(gamma=c(gamma.new),beta=c(beta.new),convergence=(s<max.itr))
}
}
return(re)
}
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