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# Fitting homoscedastic SAR models
#
hom_sar=function(formula,data,W,nsim,burn,step,prior,initial,kernel="normal",impacts=TRUE,seed=0){
y_n <- as.character(formula[[2]])
X0 <- as.character(formula[[3]])[-1]
X1 <- as.character(do.call("c",sapply(X0, function(x){strsplit(x,"\\+")})))
X_n <- gsub(" ","",X1)
y <- data[,which(names(data)==y_n)]
X <- as.matrix(data[,which(names(data)%in%X_n)])
b_pri <- prior$b_pri
B_pri <- prior$B_pri
r_pri <- prior$r_pri
lambda_pri <- prior$lambda_pri
beta_0 <- initial$beta_0
sigma2_0 <- initial$sigma2_0
rho_0 <- initial$rho_0
output <- hom_sar_int(y,X,W,nsim,burn,step,b_pri,B_pri,r_pri,lambda_pri,beta_0,sigma2_0,rho_0,kernel="normal",seed=seed,impacts=impacts)
return(output)
}
#' Hello
#'
#' @keywords internal
#'
hom_sar_int=function(y,X,W,nsim,burn,step,b_pri,B_pri,r_pri,lambda_pri,beta_0,sigma2_0,rho_0,kernel="normal",seed=0,impacts=TRUE)
{
set.seed(seed)
rowst=function(x){
x1=c()
x1=(x)/sum(x)}
########Lectura de la informacion
y=as.matrix(y)
if (is.null(X) | is.null(y) ){
stop("No data")
}
if(burn>nsim | burn<0){
stop("Burn must be between 0 and nsim")
}
if(nsim<=0){
stop("There must be more than 0 simulations")
}
if(step<0 | step > nsim){
stop("Jump length must not be lesser than 0 or greater than nsim")
}
if(class(W)[1]=="nb"){
matstand=nb2mat(W)
mat0=nb2listw(W,style="B")
mat=listw2mat(mat0)
}
else{
if(class(W)[1]=="listw"){
mat=listw2mat(W)
matstand=apply(mat,2,rowst)
matstand=t(matstand)
}
else{
if(sum(rowSums(W))==nrow(X))
{
matstand=W
mat=matrix(nrow=nrow(X),ncol=nrow(X))
for(i in 1:nrow(mat)){
for(j in 1:ncol(mat)){
if(matstand[i,j]==0){mat[i,j]=0}
else{mat[i,j]=1/matstand[i,j]}
}
}
}
else{
mat=W
matstand=apply(mat,2,rowst)
matstand=t(matstand)
}
}
}
dpost <- function(betas,sigma2,rho) {
A=diag(nrow(X))-rho*matstand
k=t(A%*%y-X%*%(betas))%*%(A%*%y-X%*%(betas))
fc.y=k
fc.beta=t(b_pri - betas)%*%solve(B_pri)%*%(b_pri-betas)
fc.sigma2=(lambda_pri^(r_pri))*(sigma2)^(-r_pri-1)*exp(-lambda_pri/sigma2)/gamma(r_pri)
#dp <- (sigma2^(-nrow(X)/2))*det(A)*exp(-0.5*fc.y/sigma2)*exp(-0.5*fc.beta)*fc.sigma2
logdp <- (-nrow(X)/2)*log(sigma2) + log(det(A)) -0.5*fc.y/sigma2 - 0.5*fc.beta + fc.sigma2
return(logdp)
}
dproposal <- function(rho) {
a=(sigma2.now)*t(y)%*%t(matstand)%*%matstand%*%y
b=(sigma2.now)*t(y)%*%t(matstand)%*%(y-X%*%betas.now)
dmvnorm(rho,b/a,1/sqrt(a),log = T)
}
ind=rep(0,nsim)
beta.mcmc=matrix(NA,nrow=nsim,ncol=ncol(X))
sigma2.mcmc=c()
rho.mcmc=c()
logV_DIC=c()
Sigma_0=(sigma2_0)*diag(nrow(X))
pb <- txtProgressBar(min = 0, max = nsim, style = 3)
if(kernel=="uniform"){
for(i in 1:nsim){
if(i==1){
Sigma=Sigma_0
Rho=rho_0
}
else{
Sigma=sigma2.now*diag(nrow(X))
}
B_pos=solve(solve(B_pri)+t(X)%*%solve(Sigma)%*%(X))
b_pos=B_pos%*%(solve(B_pri)%*%b_pri+t(X)%*%solve(Sigma)%*%y-Rho*t(X)%*%solve(Sigma)%*%matstand%*%y)
#Beta a posteriori condicional
betas.now=c(rmvnorm(1,b_pos,B_pos))
#A posteriori condicional completa para Sigma2
r_pos=+nrow(X)/2+r_pri
A=diag(nrow(X))-Rho*matstand
k=t(A%*%y-X%*%(betas.now))%*%(A%*%y-X%*%(betas.now))
lambda_pos=(k+2*lambda_pri)/2
sigma2.now=rigamma(1,r_pos,lambda_pos)
#A posteriori condicional completa para Rho
rho.now=runif(1,1/abs(min(eigen(mat)$values)),1)
p1=dpost(betas.now,sigma2.now,rho.now)
p2=dpost(betas.now,sigma2.now,Rho)
T.val=min(1,p1/p2)
u<-runif(1)
if (u <=T.val) {
Rho= rho.now
ind[i] = 1
}
beta.mcmc[i,]<-betas.now
sigma2.mcmc[i]<-sigma2.now
rho.mcmc[i]<-rho.now
Sigma=diag(sigma2.mcmc[i],nrow(X))
detS=det(Sigma)
detB=det(diag(nrow(X))-rho.mcmc[i]*matstand)
Yg=(diag(nrow(X))-rho.mcmc[i]*matstand)%*%(y-X%*%beta.mcmc[i,])
logV_DIC[i]=(-(nrow(X)/2)*log(pi))+log(detB)-0.5*log(detS)-0.5*t(Yg)%*%solve(Sigma)%*%Yg
Sys.sleep(0.000000001)
# update progress bar
setTxtProgressBar(pb, i)
}
}
if(kernel=="normal"){
for(i in 1:nsim){
#A posteriori condicional completa para Betas
if(i==1){
Sigma=Sigma_0
Rho=rho_0
}
else{
Sigma=sigma2.now*diag(nrow(X))
}
B_pos=solve(solve(B_pri)+t(X)%*%diag(1/diag(Sigma))%*%X)
b_pos=B_pos%*%(solve(B_pri)%*%b_pri+t(X)%*%diag(1/diag(Sigma))%*%y-Rho*t(X)%*%diag(1/diag(Sigma))%*%matstand%*%y)
betas.now=c(rmvnorm(1,b_pos,B_pos))
r_pos=nrow(X)/2+r_pri
A=diag(nrow(X))-Rho*matstand
k=t(A%*%y-X%*%(betas.now))%*%(A%*%y-X%*%(betas.now))
lambda_pos=(k-2*lambda_pri)/2
sigma2.now=rigamma(1,r_pos,lambda_pos)
a=(1/sigma2.now)*t(y)%*%t(matstand)%*%matstand%*%y
b=(1/sigma2.now)*t(y)%*%t(matstand)%*%(y-X%*%betas.now)
rho.now=rnorm(1,b/a,1/sqrt(a))
while(det(diag(nrow(X))-rho.now*matstand)<=0){
rho.now <- rnorm(1,b/a,1/sqrt(a))
}
p1=dpost(betas.now,sigma2.now,rho.now)
p2=dpost(betas.now,sigma2.now,Rho)
q1=dproposal(rho.now)
q2=dproposal(Rho)
#T.val=min(1,(p1*q1)/(p2*q2))
met.a <- ifelse(p1>p2,log(p1-p2),-log(p2-p1))
met.b <- ifelse(q1>q2,log(q1-q2),-log(q2-q1))
T.val=min(0,met.a+met.b)
u<-runif(1)
if (u <=exp(T.val)) {
Rho= rho.now
ind[i] = 1
}
beta.mcmc[i,]<-betas.now
sigma2.mcmc[i]<-sigma2.now
rho.mcmc[i]<-rho.now
Sigma=diag(sigma2.mcmc[i],nrow(X))
detS=det(Sigma)
detB=det(diag(nrow(X))-rho.mcmc[i]*matstand)
Yg=(diag(nrow(X))-rho.mcmc[i]*matstand)%*%(y-X%*%beta.mcmc[i,])
logV_DIC[i]=(-(nrow(X)/2)*log(pi))+log(detB)-0.5*log(detS)-0.5*t(Yg)%*%diag(1/diag(Sigma))%*%Yg
Sys.sleep(0.000000001)
# update progress bar
setTxtProgressBar(pb, i)
}
}
beta.mcmc_1=beta.mcmc[(burn+1):nsim,]
sigma2.mcmc_1=sigma2.mcmc[(burn+1):nsim]
rho.mcmc_1=rho.mcmc[(burn+1):nsim]
beta.mcmc_2=matrix(NA,nrow=(nsim-burn+1)/step,ncol(X))
sigma2.mcmc_2=c()
rho.mcmc_2=c()
for (i in 1:(nsim-burn+1))
{
if(i%%step==0)
{
beta.mcmc_2[i/step,]=beta.mcmc_1[i,]
sigma2.mcmc_2[i/step]=sigma2.mcmc_1[i]
rho.mcmc_2[i/step]=rho.mcmc_1[i]
}
}
Bestimado = colMeans(beta.mcmc_2)
Sigma2est = mean(sigma2.mcmc_2)
rho.mcmc_3=rho.mcmc_2[rho.mcmc_2<=1]
Rhoest=mean(rho.mcmc_3)
DesvBeta <- apply(beta.mcmc_2,2,sd)
DesvSigma2 <- sd(sigma2.mcmc_2)
DesvRho<-sd(rho.mcmc_3)
Betaquant <- t(apply(beta.mcmc_2,2,function(x){quantile(x,c(0.025,0.5,0.975))}))
Sigma2quant <- quantile(sigma2.mcmc_2,c(0.025,0.5,0.975))
Rhoquant <- quantile(rho.mcmc_3,c(0.025,0.5,0.975))
AccRate<-sum(ind)/nsim
Sigma=diag(Sigma2est,nrow(X))
detS=det(Sigma)
detB=det(diag(nrow(X))-Rhoest*matstand)
Yg=((diag(nrow(X))-Rhoest*matstand)%*%y)-X%*%Bestimado
Veros=detB*((detS)^(-0.5))*exp(-0.5*t(Yg)%*%solve(Sigma)%*%Yg)
logV=log(Veros)
#logV1=log(detB)-0.5*log(detS)-0.5*t(Yg)%*%solve(Sigma)%*%Yg
logV1=-(nrow(X)/2)*log(2*pi)+log(detB)-0.5*log(detS)-0.5*(1/Sigma2est)*t(Yg)%*%Yg
p=ncol(X)+2
BIC=-2*logV1+p*log(nrow(X))
logV_DIC=logV_DIC[is.nan(logV_DIC)==FALSE]
Dbar=mean(-2*logV_DIC)
logV1_DIC=(-(nrow(X)/2)*log(2*pi))+log(detB)-0.5*log(detS)-0.5*t(Yg)%*%solve(Sigma)%*%Yg
Dev=-2*logV1_DIC
DIC=2*Dbar+Dev
summary = data.frame( mean=c(Bestimado,Sigma2est,Rhoest),
sd = c(DesvBeta,DesvSigma2,DesvRho),
q0.025=c(Betaquant[,1],Sigma2quant[1],Rhoquant[1]),
q0.5=c(Betaquant[,2],Sigma2quant[2],Rhoquant[2]),
q0.975=c(Betaquant[,3],Sigma2quant[3],Rhoquant[3]))
rownames(summary) = c("x0","x1","x2","sigma2","rho")
if(impacts){
n <- nrow(X)
V <- pblapply(1:(nsim-burn),function(x){solve(diag(n)-rho.mcmc_1[x]*matstand)})
S <- lapply(1:ncol(X),function(y){
pblapply(1:(nsim-burn), function(x){
beta.mcmc_1[x,y]*V[[x]]},cl=2)})
retain <- rep(c(rep(0,step-1),1),(nsim-burn)/step)
S <- lapply(S,function(x){x[which(retain>0)]})
impact.df <- lapply(S, function(x){
lapply(x, function(y){
impact.direct <- sum(diag(y))/n
impact.total<- sum((y))/n
impact.indirect <- impact.total - impact.direct
return(data.frame(Direct=impact.direct,Total=impact.total,Indirect=impact.indirect))
})})
impacts <- t(sapply(impact.df, function(x){tmp <- do.call("rbind",x)
colMeans(tmp)
}))
rownames(impacts) <- rownames(summary)[1:ncol(X)]
impacts <- impacts[-1,]
}
out<- list(summary=summary, Acceptance_Rate=AccRate,Criteria=list(BIC=BIC,DIC=DIC),
chains=mcmc(data.frame(beta_chain=beta.mcmc,sigma2_chain=sigma2.mcmc,rho_chain=rho.mcmc)),
impacts=impacts)
class(out) <- "out"
return(out)
}
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