R/Gibbs.R
In zhanglj37/blcfa: Bayesian Covariance Lasso Prior Confirmatory Factor Analysis
Defines functions
gibbs_fun
gibbs_fun<-function(MCMAX, NZ, NY, N, Y, LY_int, IDY0, IDY,
nthin, N.burn, CIR)
{
#### def_rec ###################################################################
#vector indicating whether MU should be added to each measurement equation or not.
#Added(1), remove(0).
IDMU<-rep(1,NY) # now MU is estimated
IDMUA<-any(as.logical(IDMU))
#source("def_rec.R")
NM<-0 #dimension of eta (q_1)
NK<-NM+NZ #dimension of latent variables (eta+xi); number of factors
############################## Automatic done
#Y<-array(0,dim=c(NY,N)) #observed data Y
xi<-array(dim=c(NZ,N)) #independent latent variable xi
#eta<-array(dim=c(NM,N)) #dependent latent variable eta
TUE<-Omega<-array(dim=c(NK,N)) #latent variable omega
NMU<-sum(IDMU) #number of Mu in measurement equation.
NLY<-sum(IDY!=0) #number of free lambda need to be estimated in Lambda.
Nrec<-MCMAX/nthin #number of samples after burn-in.
EMU<-array(0,dim=c(Nrec,NMU)) #Store retained trace of MU
ELY<-array(0,dim=c(Nrec,NLY)) #Store retained trace of Lambda
#ELY<-array(0,dim=c(Nrec,NY*NZ))
EPSX<-array(0,dim=c(Nrec,NY,NY)) #Store retained trace of PSX
EinvPSX<-array(0,dim=c(Nrec,NY,NY)) #Store retained trace of inv(PSX)
EPHI<-array(0,dim=c(Nrec,(NZ*NZ))) #Store retained trace of PHI
EXI<-array(0,dim=c(Nrec,NZ,N)) #Store retained trace of xi
Elambda<-array(0,dim=c(Nrec,1)) #Store retained trace of shrinkage paraemter lambda
Lj=rowSums(IDY==-1)>0 #lasso items
lj=sum(Lj) #no. of lasso items
Elamsq<-array(0,dim=c(Nrec,lj)) #Store retained trace of shrinkage paraemter lamsq
indmx<-matrix(1:NY^2, nrow=NY, ncol=NY)
temp<-indmx[upper.tri(indmx)]
upperind<-temp[temp>0]
indmx_t<-t(indmx)
temp<-indmx_t[upper.tri(indmx_t)]
lowerind<-temp[temp>0]
tau<-array(0,dim=c(NY,NY))
tausq<-array(0,dim=c(NY,NZ))
tausq[IDY==-1]=1
ind_noi_all<-array(0,dim=c(NY-1,NY))
for(i in 1:NY){
if(i==1) {ind_noi<-2:NY}
else if(i==NY) {ind_noi<-1:(NY-1)}
else ind_noi<-c(1:(i-1),(i+1):NY)
ind_noi_all[,i]<-ind_noi
} # end of i
Empostp<-numeric(2) ## numeric(CNUM)
chainpsx<-array(0,dim=c(Nrec,NY*(NY+1)/2))
set.seed(1)
### prior ##########################################################
#Prior mean of Lambda, NY*NZ
PLY<-array(0,dim=c(NY,NZ))
PLY[which(IDY0==9)] = 1
#Prior mean of MU, NY*1
PMU<-rep(0.0,NY)
#Inverse prior variance of unknown parameters in factor loading matrix
sigly<-0.25
#Inverse prior variance of unknown parameters in intercept
sigmu<-0.25
rou.scale<-6.0
#rho_0, hyperparameters of Wishart distribution
rou.zero<-rou.scale+NZ+1
#Matrix R_0, hyperparameters of Wishart distribution
R.zero<-rou.scale*diag(1,NZ)
#R.zero<-matrix(.1,nrow=NZ,ncol=NZ)
#diag(R.zero)<-rou.scale
#Hyperparameters of Gamma distribution for the shrinkage parameter
a_lambda<-1
b_lambda<-0.01
NLY1<-sum(IDY==-1) #number of lasso lambda.
a_lamsq<-1
b_lamsq<-.01
stau<-0
LY_eps<-0 #threhods for LY sign change
#initial value of Lambda,
LY<-LY_int
#LY<-matrix(0,ncol=NK,nrow=NY)
#LY[IDY==1]=.7
#LY[IDY==-1]=.1
#initial value of MU
MU<-rep(1.0,NY)
#initial value of PHI
PHI<-matrix(0.3,nrow=NZ,ncol=NZ)
if(NZ>1){
diag(PHI[,])<-1.0
}
#initial value of PSX
xi<-t(mvrnorm(N,mu=rep(0,NZ),Sigma=PHI)) # NZ*N
#xi<-matrix(runif(NZ*N),nrow=NZ)+2# NZ*N
PSX<-matrix(0.0,nrow=NY,ncol=NY)
diag(PSX)<-1.0
#initial value of PHI^(-1)
#inv.PHI<-chol2inv(chol(PHI))
inv.PHI<-chol2inv(chol(PHI))
#initial value of PHI^(-1/2)
#c.inv.PHI<-chol(inv.PHI)
#initial value of PSX^(-1)
inv.PSX<-chol2inv(chol(PSX))
#initial value of PSX^(-1/2)
inv.sqrt.PSX<-chol(inv.PSX)
if(IDMUA==F) MU<-rep(0,NY)
#source("Gibbs.R")
Epostp<-array(0, dim=c(MCMAX-N.burn,1))
# Creat the matrix of missing indicators where 1 represents missing
missing_ind = array(0, dim=c(NY, N))
Y_missing = array(0, dim=c(NY,N,MCMAX))
for(i in 1:NY)
for(j in 1:N)
if(is.na(Y[i,j])) missing_ind[i,j]<-1
# initial values for missing data in Y
for(i in 1:NY)
for(j in 1:N)
if(is.na(Y[i,j])) Y[i,j]<-rnorm(1)
### gibbs sampling ##########################################################
for(g in 1:MCMAX){
gm<-g
gm2<-g-N.burn
#Generate the latent factors from its conditinal distribution
#source("Gibbs_Omega.R")
################## update Omega ##############################################################
ISG<-crossprod(inv.sqrt.PSX%*%LY)+inv.PHI
SIG<-chol2inv(chol(ISG))
Ycen<-Y
if(IDMUA==T) Ycen<-Y-MU
Mean<-SIG%*%t(LY)%*%inv.PSX%*%Ycen
for(i in 1:N) Omega[,i]<-xi[,i]<-mvrnorm(1, Mean[,i], Sigma=SIG)
################## end of update Omega #######################################################
#Generate the unknown parameter of intercept in CFA from its conditinal distribution
#source("Gibbs_MU.R")
################### update MU #################################################################
if(IDMUA==T){
calsm<-chol2inv(chol(N*inv.PSX+diag(rep(sigmu,NY)))) # inv[sigma0^(-1)+N*inv.PSX]
Ycen<-Y-LY%*%Omega
temp<-rowSums(Ycen)
mumu<-calsm%*%(inv.PSX%*%temp+rep(sigmu,NY)*PMU)
MU<-mvrnorm(1,mumu,Sigma=calsm)
}
################### end of update MU ##########################################################
################### update PSX #################################################################
temp<-Y-MU-LY%*%Omega # NY*N
S<-temp%*%t(temp) # NY*NY
apost<-a_lambda+NY*(NY+1)/2;
#sample lambda
bpost<-b_lambda + sum(abs(inv.PSX))/2 # C is the presicion matrix
lambda<- rgamma(1, shape=apost, rate=bpost)
#sample tau off-diagonal
Cadjust<-pmax(abs(inv.PSX[upperind]),10^(-6))
mu_prime<-pmin(lambda/Cadjust, 10^12)
lambda_prime<-lambda^2
tau_temp<-rep(0,length(mu_prime))
for(i in 1:length(mu_prime)){
tau_temp[i]<-1/rinvgauss(1, mean=mu_prime[i], dispersion=1/lambda_prime)
}
tau[upperind]<-tau_temp
tau[lowerind]<-tau_temp
#sample PSX and inv(PSX)
for(i in 1:NY){
#i=1
ind_noi<-ind_noi_all[,i]
tau_temp1<-tau[ind_noi,i]
Sig11<-PSX[ind_noi, ind_noi]
Sig12<-PSX[ind_noi,i]
invC11<-Sig11-Sig12%*%t(Sig12)/PSX[i,i]
Ci<-(S[i,i]+lambda)*invC11+diag(1/tau_temp1)
Sigma<-chol2inv(chol(Ci))
mu_i<--Sigma%*%S[ind_noi,i]
beta<-mvrnorm(1,mu_i,Sigma)
inv.PSX[ind_noi,i]<-beta
inv.PSX[i,ind_noi]<-beta
gam<-rgamma(1, shape=N/2+1, rate=(S[i,i]+lambda)/2)
inv.PSX[i,i]<-gam+t(beta)%*%invC11%*%beta
# below updating covariance matrix according to one-column change of precision matrix
invC11beta<-invC11%*%beta
PSX[ind_noi,ind_noi]<-invC11+invC11beta%*%t(invC11beta)/gam
Sig12<--invC11beta/gam
PSX[ind_noi, i]<-Sig12
PSX[i,ind_noi]<-t(Sig12)
PSX[i,i]<-1/gam
} # end of i, sample Sig and C=inv(Sig)
inv.sqrt.PSX<-chol(inv.PSX)
################## end of update PSX ##########################################################
apost1<-a_lamsq+NLY1;
#sample lambda
bpost1<-b_lamsq + stau/2 # C is the presicion matrix
lamsq<- rgamma(1, shape=apost1, rate=bpost1)
stau<-0
#count.n<-1
for(j in 1:NY){
#j=1
temp1<-chol2inv(chol(PSX[-j,-j]))
convar<-PSX[j,j]-PSX[j,-j]%*%temp1%*%PSX[-j,j]
#invconvar<-chol2inv(chol(convar))
invconvar<-1/convar[1,1]
subs<-(IDY[j,]==1)
len<-length(LY[j,subs])
if(len>0){
Ycen<-Y[j,]-MU[j] # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs),drop=F],nrow=1)%*%matrix(Omega[(!subs),,drop=F],ncol=N) # 1*N
Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)-PSX[j,-j]%*%temp1%*%(Y[-j,]-MU[-j]-LY[-j,]%*%Omega) # 1*N
Ycen<-as.vector(Ycen) # vector
if(len==1){omesub<-matrix(Omega[subs,],nrow=1)
}else{omesub<-Omega[subs,]}
PSiginv<-diag(len)
diag(PSiginv)<-rep(sigly,len)
Pmean<-PLY[j,subs]
#calsmnpsx<-chol2inv(chol(invconvar%*%tcrossprod(omesub)+PSiginv))
#temp<-(omesub%*%Ycen%*%invconvar+PSiginv*Pmean)
calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+PSiginv))
temp<-(omesub%*%Ycen*invconvar+PSiginv%*%Pmean)
LYnpsx<-calsmnpsx%*%temp
LY[j,subs]<-mvrnorm(1,LYnpsx,Sigma=(calsmnpsx))
#if((gm>0)&&(gm%%nthin==0)){ELY[gm/nthin,count.n:(count.n+len-1)]<-LY[j,subs]}
# count.n<-count.n+len
} # end len>0
subs<-(IDY[j,]==-1)
len<-length(LY[j,subs])
if(len>0){
Ycen<-Y[j,]-MU[j] # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs),drop=F],nrow=1)%*%matrix(Omega[(!subs),,drop=F],ncol=N) # 1*N
#temp1<-chol2inv(chol(PSX[-j,-j]))
Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)-PSX[j,-j]%*%temp1%*%(Y[-j,]-MU[-j]-LY[-j,]%*%Omega) # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)
Ycen<-as.vector(Ycen) # vector
#convar<-PSX[j,j]
#invconvar<-1/convar
Cadj1<-pmax((LY[j,subs])^2,10^(-6))
mu_p1<-pmin(sqrt(lamsq/Cadj1), 10^12)
#mu_p1<-pmin(sqrt(lamsq*PSX[j,j]/Cadj1), 10^12)
#lambda_prime<-lambda^2
tausq<-rep(0,length(mu_p1))
for(i in 1:length(mu_p1)){
tausq[i]<-1/rinvgauss(1, mean=mu_p1[i], dispersion=1/lamsq)
}
if(len==1){
omesub<-matrix(Omega[subs,],nrow=1)
invD_tau=1/tausq
}else{
omesub<-Omega[subs,]
invD_tau=diag(1/tausq)
}
stau<-stau+sum(tausq)
#calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+invD_tau))
#temp<-(omesub%*%Ycen*invconvar)
calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+invD_tau))
temp<-(omesub%*%Ycen*invconvar)
LYnpsx<-calsmnpsx%*%temp
LY[j,subs]<-mvrnorm(1,LYnpsx,Sigma=(calsmnpsx))
} # end len>0
for(k in 1:NZ){
#k=2
ind=!(IDY[,k]==0)
if(mean(LY[ind,k])<LY_eps){
LY[ind,k]<--LY[ind,k]
Omega[k,]<--Omega[k,]
}
}
} # end of NY
################## end of update LY ########################################################
#Generate the unknown parameter of covariance matrix of latent factors in CFA from its conditinal distribution
#source("Gibbs_PHI.R")
######## update PHI ########################################################
inv.PHI<-rwish(rou.zero+N, solve(tcrossprod(Omega)+R.zero))
PHI<-chol2inv(chol(inv.PHI))
c.inv.PHI<-chol(inv.PHI)
#Generate the missing reponse in CFA from its conditinal distribution
#source("Gibbs_MISY.R")
for(j in 1:NY)
for(i in 1:N)
if(missing_ind[j,i]==1){
mean<-MU[j]+LY[j,]%*%Omega[,i]+PSX[j,-j]%*%chol2inv(chol(PSX[-j,-j]))%*%(Y[-j,i]-MU[-j]-LY[-j,]%*%Omega[,i])
var<-PSX[j,j]-PSX[j,-j]%*%chol2inv(chol(PSX[-j,-j]))%*%PSX[-j,j]
Y[j,i]<-rnorm(1, mean, var)
}
#Save results
if((gm>0)&&(gm%%nthin==0)){
gm<-gm/nthin
EPHI[gm,]<-as.vector(PHI[,])
EPSX[gm,,]<-PSX
#EinvPSX[gm,,]<-inv.PSX
EMU[gm,]<-MU
#Elambda[gm,]<-lambda
#Elamsq[gm,]<-lamsq
ELY[gm,]<-LY[IDY!=0]
k<-1
for(i in 1:NY){
for(j in 1:NY){
if(i>=j) {chainpsx[gm,k]<-PSX[i,j];k<-k+1}
}
}
if (gm2>0)
{
#Calculate PP p-value
# source("Postp.R")
postp1<-0.0
postp2<-0.0
Y.temp<-array(0, dim=c(NY,N))
Y.cen<-Y-MU-LY%*%Omega # NY*N
for(i in 1:N){
postp1<-postp1+t(Y.cen[,i])%*%inv.PSX%*%Y.cen[,i]
}
xi.temp<-t(mvrnorm(N,mu=rep(0,NZ),Sigma=PHI))
theta.temp<-MU+LY%*%xi.temp # NY*N
for(i in 1:N) Y.temp[,i]<-mvrnorm(1, theta.temp[,i], Sigma=PSX)
Y.cen<-Y.temp-MU-LY%*%xi.temp # NY*N
Y_missing[,,gm] = Y.temp[,]
for(i in 1:N){
postp2<-postp2+t(Y.cen[,i])%*%inv.PSX%*%Y.cen[,i]
}
if(postp1<=postp2) Epostp[gm2]<-1.0;
}
}
if(g%%100==0 && CIR == 1)cat(paste("Num of Iterations: ",g,"\n"),file="log.txt",append=T)
}#end of g MCMAX
chainlist<-list(EMU=EMU,ELY=ELY,EPHI=EPHI,EPSX=EPSX,Epostp=Epostp,chainpsx=chainpsx,
missing_ind=missing_ind,Y_missing=Y_missing)
return(chainlist)
}
zhanglj37/blcfa documentation built on Oct. 6, 2023, 5:43 a.m.
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Defines functions gibbs_fun
gibbs_fun<-function(MCMAX, NZ, NY, N, Y, LY_int, IDY0, IDY,
nthin, N.burn, CIR)
{
#### def_rec ###################################################################
#vector indicating whether MU should be added to each measurement equation or not.
#Added(1), remove(0).
IDMU<-rep(1,NY) # now MU is estimated
IDMUA<-any(as.logical(IDMU))
#source("def_rec.R")
NM<-0 #dimension of eta (q_1)
NK<-NM+NZ #dimension of latent variables (eta+xi); number of factors
############################## Automatic done
#Y<-array(0,dim=c(NY,N)) #observed data Y
xi<-array(dim=c(NZ,N)) #independent latent variable xi
#eta<-array(dim=c(NM,N)) #dependent latent variable eta
TUE<-Omega<-array(dim=c(NK,N)) #latent variable omega
NMU<-sum(IDMU) #number of Mu in measurement equation.
NLY<-sum(IDY!=0) #number of free lambda need to be estimated in Lambda.
Nrec<-MCMAX/nthin #number of samples after burn-in.
EMU<-array(0,dim=c(Nrec,NMU)) #Store retained trace of MU
ELY<-array(0,dim=c(Nrec,NLY)) #Store retained trace of Lambda
#ELY<-array(0,dim=c(Nrec,NY*NZ))
EPSX<-array(0,dim=c(Nrec,NY,NY)) #Store retained trace of PSX
EinvPSX<-array(0,dim=c(Nrec,NY,NY)) #Store retained trace of inv(PSX)
EPHI<-array(0,dim=c(Nrec,(NZ*NZ))) #Store retained trace of PHI
EXI<-array(0,dim=c(Nrec,NZ,N)) #Store retained trace of xi
Elambda<-array(0,dim=c(Nrec,1)) #Store retained trace of shrinkage paraemter lambda
Lj=rowSums(IDY==-1)>0 #lasso items
lj=sum(Lj) #no. of lasso items
Elamsq<-array(0,dim=c(Nrec,lj)) #Store retained trace of shrinkage paraemter lamsq
indmx<-matrix(1:NY^2, nrow=NY, ncol=NY)
temp<-indmx[upper.tri(indmx)]
upperind<-temp[temp>0]
indmx_t<-t(indmx)
temp<-indmx_t[upper.tri(indmx_t)]
lowerind<-temp[temp>0]
tau<-array(0,dim=c(NY,NY))
tausq<-array(0,dim=c(NY,NZ))
tausq[IDY==-1]=1
ind_noi_all<-array(0,dim=c(NY-1,NY))
for(i in 1:NY){
if(i==1) {ind_noi<-2:NY}
else if(i==NY) {ind_noi<-1:(NY-1)}
else ind_noi<-c(1:(i-1),(i+1):NY)
ind_noi_all[,i]<-ind_noi
} # end of i
Empostp<-numeric(2) ## numeric(CNUM)
chainpsx<-array(0,dim=c(Nrec,NY*(NY+1)/2))
set.seed(1)
### prior ##########################################################
#Prior mean of Lambda, NY*NZ
PLY<-array(0,dim=c(NY,NZ))
PLY[which(IDY0==9)] = 1
#Prior mean of MU, NY*1
PMU<-rep(0.0,NY)
#Inverse prior variance of unknown parameters in factor loading matrix
sigly<-0.25
#Inverse prior variance of unknown parameters in intercept
sigmu<-0.25
rou.scale<-6.0
#rho_0, hyperparameters of Wishart distribution
rou.zero<-rou.scale+NZ+1
#Matrix R_0, hyperparameters of Wishart distribution
R.zero<-rou.scale*diag(1,NZ)
#R.zero<-matrix(.1,nrow=NZ,ncol=NZ)
#diag(R.zero)<-rou.scale
#Hyperparameters of Gamma distribution for the shrinkage parameter
a_lambda<-1
b_lambda<-0.01
NLY1<-sum(IDY==-1) #number of lasso lambda.
a_lamsq<-1
b_lamsq<-.01
stau<-0
LY_eps<-0 #threhods for LY sign change
#initial value of Lambda,
LY<-LY_int
#LY<-matrix(0,ncol=NK,nrow=NY)
#LY[IDY==1]=.7
#LY[IDY==-1]=.1
#initial value of MU
MU<-rep(1.0,NY)
#initial value of PHI
PHI<-matrix(0.3,nrow=NZ,ncol=NZ)
if(NZ>1){
diag(PHI[,])<-1.0
}
#initial value of PSX
xi<-t(mvrnorm(N,mu=rep(0,NZ),Sigma=PHI)) # NZ*N
#xi<-matrix(runif(NZ*N),nrow=NZ)+2# NZ*N
PSX<-matrix(0.0,nrow=NY,ncol=NY)
diag(PSX)<-1.0
#initial value of PHI^(-1)
#inv.PHI<-chol2inv(chol(PHI))
inv.PHI<-chol2inv(chol(PHI))
#initial value of PHI^(-1/2)
#c.inv.PHI<-chol(inv.PHI)
#initial value of PSX^(-1)
inv.PSX<-chol2inv(chol(PSX))
#initial value of PSX^(-1/2)
inv.sqrt.PSX<-chol(inv.PSX)
if(IDMUA==F) MU<-rep(0,NY)
#source("Gibbs.R")
Epostp<-array(0, dim=c(MCMAX-N.burn,1))
# Creat the matrix of missing indicators where 1 represents missing
missing_ind = array(0, dim=c(NY, N))
Y_missing = array(0, dim=c(NY,N,MCMAX))
for(i in 1:NY)
for(j in 1:N)
if(is.na(Y[i,j])) missing_ind[i,j]<-1
# initial values for missing data in Y
for(i in 1:NY)
for(j in 1:N)
if(is.na(Y[i,j])) Y[i,j]<-rnorm(1)
### gibbs sampling ##########################################################
for(g in 1:MCMAX){
gm<-g
gm2<-g-N.burn
#Generate the latent factors from its conditinal distribution
#source("Gibbs_Omega.R")
################## update Omega ##############################################################
ISG<-crossprod(inv.sqrt.PSX%*%LY)+inv.PHI
SIG<-chol2inv(chol(ISG))
Ycen<-Y
if(IDMUA==T) Ycen<-Y-MU
Mean<-SIG%*%t(LY)%*%inv.PSX%*%Ycen
for(i in 1:N) Omega[,i]<-xi[,i]<-mvrnorm(1, Mean[,i], Sigma=SIG)
################## end of update Omega #######################################################
#Generate the unknown parameter of intercept in CFA from its conditinal distribution
#source("Gibbs_MU.R")
################### update MU #################################################################
if(IDMUA==T){
calsm<-chol2inv(chol(N*inv.PSX+diag(rep(sigmu,NY)))) # inv[sigma0^(-1)+N*inv.PSX]
Ycen<-Y-LY%*%Omega
temp<-rowSums(Ycen)
mumu<-calsm%*%(inv.PSX%*%temp+rep(sigmu,NY)*PMU)
MU<-mvrnorm(1,mumu,Sigma=calsm)
}
################### end of update MU ##########################################################
################### update PSX #################################################################
temp<-Y-MU-LY%*%Omega # NY*N
S<-temp%*%t(temp) # NY*NY
apost<-a_lambda+NY*(NY+1)/2;
#sample lambda
bpost<-b_lambda + sum(abs(inv.PSX))/2 # C is the presicion matrix
lambda<- rgamma(1, shape=apost, rate=bpost)
#sample tau off-diagonal
Cadjust<-pmax(abs(inv.PSX[upperind]),10^(-6))
mu_prime<-pmin(lambda/Cadjust, 10^12)
lambda_prime<-lambda^2
tau_temp<-rep(0,length(mu_prime))
for(i in 1:length(mu_prime)){
tau_temp[i]<-1/rinvgauss(1, mean=mu_prime[i], dispersion=1/lambda_prime)
}
tau[upperind]<-tau_temp
tau[lowerind]<-tau_temp
#sample PSX and inv(PSX)
for(i in 1:NY){
#i=1
ind_noi<-ind_noi_all[,i]
tau_temp1<-tau[ind_noi,i]
Sig11<-PSX[ind_noi, ind_noi]
Sig12<-PSX[ind_noi,i]
invC11<-Sig11-Sig12%*%t(Sig12)/PSX[i,i]
Ci<-(S[i,i]+lambda)*invC11+diag(1/tau_temp1)
Sigma<-chol2inv(chol(Ci))
mu_i<--Sigma%*%S[ind_noi,i]
beta<-mvrnorm(1,mu_i,Sigma)
inv.PSX[ind_noi,i]<-beta
inv.PSX[i,ind_noi]<-beta
gam<-rgamma(1, shape=N/2+1, rate=(S[i,i]+lambda)/2)
inv.PSX[i,i]<-gam+t(beta)%*%invC11%*%beta
# below updating covariance matrix according to one-column change of precision matrix
invC11beta<-invC11%*%beta
PSX[ind_noi,ind_noi]<-invC11+invC11beta%*%t(invC11beta)/gam
Sig12<--invC11beta/gam
PSX[ind_noi, i]<-Sig12
PSX[i,ind_noi]<-t(Sig12)
PSX[i,i]<-1/gam
} # end of i, sample Sig and C=inv(Sig)
inv.sqrt.PSX<-chol(inv.PSX)
################## end of update PSX ##########################################################
apost1<-a_lamsq+NLY1;
#sample lambda
bpost1<-b_lamsq + stau/2 # C is the presicion matrix
lamsq<- rgamma(1, shape=apost1, rate=bpost1)
stau<-0
#count.n<-1
for(j in 1:NY){
#j=1
temp1<-chol2inv(chol(PSX[-j,-j]))
convar<-PSX[j,j]-PSX[j,-j]%*%temp1%*%PSX[-j,j]
#invconvar<-chol2inv(chol(convar))
invconvar<-1/convar[1,1]
subs<-(IDY[j,]==1)
len<-length(LY[j,subs])
if(len>0){
Ycen<-Y[j,]-MU[j] # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs),drop=F],nrow=1)%*%matrix(Omega[(!subs),,drop=F],ncol=N) # 1*N
Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)-PSX[j,-j]%*%temp1%*%(Y[-j,]-MU[-j]-LY[-j,]%*%Omega) # 1*N
Ycen<-as.vector(Ycen) # vector
if(len==1){omesub<-matrix(Omega[subs,],nrow=1)
}else{omesub<-Omega[subs,]}
PSiginv<-diag(len)
diag(PSiginv)<-rep(sigly,len)
Pmean<-PLY[j,subs]
#calsmnpsx<-chol2inv(chol(invconvar%*%tcrossprod(omesub)+PSiginv))
#temp<-(omesub%*%Ycen%*%invconvar+PSiginv*Pmean)
calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+PSiginv))
temp<-(omesub%*%Ycen*invconvar+PSiginv%*%Pmean)
LYnpsx<-calsmnpsx%*%temp
LY[j,subs]<-mvrnorm(1,LYnpsx,Sigma=(calsmnpsx))
#if((gm>0)&&(gm%%nthin==0)){ELY[gm/nthin,count.n:(count.n+len-1)]<-LY[j,subs]}
# count.n<-count.n+len
} # end len>0
subs<-(IDY[j,]==-1)
len<-length(LY[j,subs])
if(len>0){
Ycen<-Y[j,]-MU[j] # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs),drop=F],nrow=1)%*%matrix(Omega[(!subs),,drop=F],ncol=N) # 1*N
#temp1<-chol2inv(chol(PSX[-j,-j]))
Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)-PSX[j,-j]%*%temp1%*%(Y[-j,]-MU[-j]-LY[-j,]%*%Omega) # 1*N
#Ycen<-Ycen-matrix(LY[j,(!subs)],nrow=1)%*%matrix(Omega[(!subs),],ncol=N)
Ycen<-as.vector(Ycen) # vector
#convar<-PSX[j,j]
#invconvar<-1/convar
Cadj1<-pmax((LY[j,subs])^2,10^(-6))
mu_p1<-pmin(sqrt(lamsq/Cadj1), 10^12)
#mu_p1<-pmin(sqrt(lamsq*PSX[j,j]/Cadj1), 10^12)
#lambda_prime<-lambda^2
tausq<-rep(0,length(mu_p1))
for(i in 1:length(mu_p1)){
tausq[i]<-1/rinvgauss(1, mean=mu_p1[i], dispersion=1/lamsq)
}
if(len==1){
omesub<-matrix(Omega[subs,],nrow=1)
invD_tau=1/tausq
}else{
omesub<-Omega[subs,]
invD_tau=diag(1/tausq)
}
stau<-stau+sum(tausq)
#calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+invD_tau))
#temp<-(omesub%*%Ycen*invconvar)
calsmnpsx<-chol2inv(chol(invconvar*tcrossprod(omesub)+invD_tau))
temp<-(omesub%*%Ycen*invconvar)
LYnpsx<-calsmnpsx%*%temp
LY[j,subs]<-mvrnorm(1,LYnpsx,Sigma=(calsmnpsx))
} # end len>0
for(k in 1:NZ){
#k=2
ind=!(IDY[,k]==0)
if(mean(LY[ind,k])<LY_eps){
LY[ind,k]<--LY[ind,k]
Omega[k,]<--Omega[k,]
}
}
} # end of NY
################## end of update LY ########################################################
#Generate the unknown parameter of covariance matrix of latent factors in CFA from its conditinal distribution
#source("Gibbs_PHI.R")
######## update PHI ########################################################
inv.PHI<-rwish(rou.zero+N, solve(tcrossprod(Omega)+R.zero))
PHI<-chol2inv(chol(inv.PHI))
c.inv.PHI<-chol(inv.PHI)
#Generate the missing reponse in CFA from its conditinal distribution
#source("Gibbs_MISY.R")
for(j in 1:NY)
for(i in 1:N)
if(missing_ind[j,i]==1){
mean<-MU[j]+LY[j,]%*%Omega[,i]+PSX[j,-j]%*%chol2inv(chol(PSX[-j,-j]))%*%(Y[-j,i]-MU[-j]-LY[-j,]%*%Omega[,i])
var<-PSX[j,j]-PSX[j,-j]%*%chol2inv(chol(PSX[-j,-j]))%*%PSX[-j,j]
Y[j,i]<-rnorm(1, mean, var)
}
#Save results
if((gm>0)&&(gm%%nthin==0)){
gm<-gm/nthin
EPHI[gm,]<-as.vector(PHI[,])
EPSX[gm,,]<-PSX
#EinvPSX[gm,,]<-inv.PSX
EMU[gm,]<-MU
#Elambda[gm,]<-lambda
#Elamsq[gm,]<-lamsq
ELY[gm,]<-LY[IDY!=0]
k<-1
for(i in 1:NY){
for(j in 1:NY){
if(i>=j) {chainpsx[gm,k]<-PSX[i,j];k<-k+1}
}
}
if (gm2>0)
{
#Calculate PP p-value
# source("Postp.R")
postp1<-0.0
postp2<-0.0
Y.temp<-array(0, dim=c(NY,N))
Y.cen<-Y-MU-LY%*%Omega # NY*N
for(i in 1:N){
postp1<-postp1+t(Y.cen[,i])%*%inv.PSX%*%Y.cen[,i]
}
xi.temp<-t(mvrnorm(N,mu=rep(0,NZ),Sigma=PHI))
theta.temp<-MU+LY%*%xi.temp # NY*N
for(i in 1:N) Y.temp[,i]<-mvrnorm(1, theta.temp[,i], Sigma=PSX)
Y.cen<-Y.temp-MU-LY%*%xi.temp # NY*N
Y_missing[,,gm] = Y.temp[,]
for(i in 1:N){
postp2<-postp2+t(Y.cen[,i])%*%inv.PSX%*%Y.cen[,i]
}
if(postp1<=postp2) Epostp[gm2]<-1.0;
}
}
if(g%%100==0 && CIR == 1)cat(paste("Num of Iterations: ",g,"\n"),file="log.txt",append=T)
}#end of g MCMAX
chainlist<-list(EMU=EMU,ELY=ELY,EPHI=EPHI,EPSX=EPSX,Epostp=Epostp,chainpsx=chainpsx,
missing_ind=missing_ind,Y_missing=Y_missing)
return(chainlist)
}
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