#' @export
E.2SI<-function(NI,nI,Ni,ni,y,PSU){
y<-cbind(1,y)
y<-as.data.frame(y)
names(y)[1] <- "N"
PSU<-as.factor(PSU)
Total<-matrix(NA,nrow=4,ncol=dim(y)[2])
rownames(Total)=c("Estimation", "Standard Error","CVE","DEFF")
colnames(Total)<-names(y)
f<-ni/Ni
F<-nI/NI
for(k in 1:dim(y)[2]){
ysum<- tapply(y[,k],PSU,sum)
s2i <- tapply(y[,k],PSU,var)
ti <- (1/f)*ysum
ty <- (1/F)*sum(ti)
part.1 <- NI^2/nI*(1-F)*var(ti)
part.2 <- NI/nI*sum(Ni^2/ni*(1-f)*s2i)
Vty <- part.1+part.2
CVe<-100*sqrt(Vty)/ty
n<-length(y[,k])
N<-(NI/nI)*sum(Ni)
VMAS<-(N^2)*(1-(n/N))*var(y[,k])/(n)
DEFF<-Vty/VMAS
Total[,k]<-c(ty,sqrt(Vty),CVe,DEFF)
}
return(Total)
}
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