/
shrinkage-based functions.R
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shrinkage-based functions.R
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########################################### magrginal analysis #####################################
## define magnitude-based shrinkage for marginal analysis
magnitude_marginal<-function(X,Y,lambda1,lambda2,gamma,specific)
{ change<-vector()
it = 0
maxit = 200
beta<-matrix(0,1,m); beta<-apply(beta,2,as.numeric)
a = 0
b = 0
eps=10
while ((it<=200) & (eps >10^(-3)) )
{ it<-it+1
Lold = beta
for ( k in 1:m)
{ x = X[[k]][,specific]
y = Y[[k]]
b3=0;b4=0
for (r in 1:m){ if(r != k & (sign(S[specific,k])==sign(S[specific,r]))){b3 <-b3+ beta[r];b4<-b4+1} }
a = t(y)%*%x /nrow(X[[k]])+ 2.0*lambda2*b3
b = t(x)%*%x/nrow(X[[k]]) + lambda2* (m-1+b4)
temp=a/b
if (abs(temp)>gamma*lambda1){ beta[k]=temp }
else
{ if (abs(a)>lambda1){ beta[k]=(a-sign(a)*lambda1)/(b-1/gamma)}
else { beta[k]=0 }
}
}
Lnew<-beta
change [it]<- sum(abs(Lold-Lnew))
eps<-change[it]
}
return(beta=beta)
}
## define sign-based shrinkage for marginal analysis
sign_marginal<-function(X,Y,lambda1,lambda2,gamma,specific)
{ change<-vector()
it = 0
maxit = 200
beta<-matrix(0,1,m);beta<-apply(beta,2,as.numeric)
a = 0
b = 0
eps=10
while ((it<=200) & (eps >10^(-3)) )
{ it<-it+1
Lold = beta
for ( k in 1:m)
{ x = X[[k]][,specific]
y = Y[[k]]
a5=0
for (r in 1:m) {if(r != k ) {a5 <-a5+ lambda2*sign(beta[r])/((abs(beta[k])+xi)) } }
a =t(y)%*%x /nrow(X[[k]])+ a5
b = t(x)%*%x/nrow(X[[k]])+lambda2*(m-1)/(abs(beta[k])+xi)^2
temp=a/b
if (abs(temp)>gamma*lambda1){ beta[k]=temp }
else
{ if (abs(a)>lambda1){ beta[k]=(a-sign(a)*lambda1)/(b-1/gamma)}
else { beta[k]=0 }
}
}
Lnew<-beta
change [it]<- sum(abs(Lold-Lnew))
eps<-change[it]
}
return(beta=beta)
}
########################################### joint analysis #####################################
## define magnitude-based shrinkage for joint analysis
magnitude_joint<-function(X,Y,lambda1,lambda2,gamma)
{
change<-vector()
it = 0
maxit = 200
a = 0;b = 0;eps=10
beta<-matrix(0,p,m);beta<-apply(beta,2,as.numeric)
while ((it<=200) & (eps >10^(-3)) )
{ it<-it+1
Lold = beta
for( k in 1:m)
{ x = X[[k]]; y = Y[[k]]
res_l=y - x %*% beta[,k]
for( l in 1:p)
{
res_l = res_l+x[,l]*beta[l,k]
b3=0;b4=0
for (r in 1:m){ if(r != k & (sign(S[l,k])==sign(S[l,r]))){b3 <-b3+ beta[l, r];b4<-b4+1} }
a = t(res_l)%*%x[,l] /nrow(x)+ 2.0*lambda2*b3
b = t(x[,l])%*%x[,l ]/nrow(x) + lambda2* (m-1+b4)
temp=a/b
if (abs(temp)>gamma*lambda1){ beta[l,k]=temp }
else{
if (abs(a)>lambda1){ beta[l,k]=(a-sign(a)*lambda1)/(b-1/gamma)}
else{beta[l,k]=0}
}
res_l = res_l - x[,l]*beta[l,k]
}
}
Lnew<-beta
change [it]<- sum(abs(Lold-Lnew))
eps<-change[it]
}
return(beta=beta)
}
## define sign-based shrinkage for joint analysis
sign_joint<-function(X,Y,lambda1,lambda2,gamma)
{
change<-vector()
it = 0
maxit = 200
m = length(X)
beta<-matrix(0,p,m)
beta<-apply(beta,2,as.numeric)
a = 0
b = 0
eps=10
while ((it<=200) & (eps >10^(-3)))
{
it<-it+1
Lold = beta
for ( k in 1:m)
{
x = X[[k]]
y = Y[[k]]
res_l=y - x%*%beta[,k]
for( l in 1:p)
{ res_l = res_l+x[,l]*beta[l,k]
a5=0
for (r in 1:m) {if(r != k ) {a5 <-a5+ lambda2*sign(beta[l,r])/((abs(beta[l,k])+xi)) } }
a = t(res_l)%*%x[,l] /nrow(x)+ a5
b = t(x[,l])%*%x[,l]/nrow(x) +lambda2*(m-1)/(abs(beta[l,k])+xi)^2
temp=a/b
if (abs(temp)>gamma*lambda1){ beta[l,k]=temp }
else
{
if (abs(a)>lambda1){ beta[l,k]=(a-sign(a)*lambda1)/(b-1/gamma)}
else{beta[l,k]=0}
}
res_l = res_l - x[,l]*beta[l,k]
}
}
Lnew<-beta
change [it]<- sum(abs(Lold-Lnew))
eps<-change[it]
}
return(beta=beta)
}