knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
library(BayesSampling)
In a simple model, where there is no auxiliary variable, and a Stratified Simple Random Sample was taken from the population, we can calculate the Bayes Linear Estimator for the individuals of each strata of the population with the BLE_SSRS() function, which receives the following parameters:
data(BigCity) end <- dim(BigCity)[1] s <- seq(from = 1, to = end, by = 1) set.seed(3) samp <- sample(s, size = 10000, replace = FALSE) ordered_samp <- sort(samp) BigCity_red <- BigCity[ordered_samp,] Rural <- BigCity_red[which(BigCity_red$Zone == "Rural"),] Rural_Exp <- Rural$Expenditure length(Rural_Exp) Rural_ys <- sample(Rural_Exp, size = 30, replace = FALSE) Urban <- BigCity_red[which(BigCity_red$Zone == "Urban"),] Urban_Exp <- Urban$Expenditure length(Urban_Exp) Urban_ys <- sample(Urban_Exp, size = 30, replace = FALSE)
The real expenditure means will be the values we want to estimate. In this example we know their real values:
mean(Rural_Exp) mean(Urban_Exp)
Our design-based estimator for the mean will be the sample mean for each strata:
mean(Rural_ys) mean(Urban_ys)
Applying the prior information about the population we can get a better estimate, especially in cases when only a small sample is available:
ys <- c(Rural_ys, Urban_ys) h <- c(30,30) N <- c(length(Rural_Exp), length(Urban_Exp)) m <- c(280, 420) v=c(4*(10.1^4), 10.1^5) sigma = c(sqrt(4*10^4), sqrt(10^5)) Estimator <- BLE_SSRS(ys, h, N, m, v, sigma)
Our Bayes Linear Estimator for the mean expenditure of each strata:
Estimator$est.beta Estimator$Vest.beta
ys <- c(2,-1,1.5, 6,10, 8,8) h <- c(3,2,2) N <- c(5,5,3) m <- c(0,9,8) v <- c(3,8,1) sigma <- c(1,2,0.5) Estimator <- BLE_SSRS(ys, h, N, m, v, sigma) Estimator
y1 <- mean(c(2,-1,1.5)) y2 <- mean(c(6,10)) y3 <- mean(c(8,8)) ys <- c(y1, y2, y3) h <- c(3,2,2) N <- c(5,5,3) m <- c(0,9,8) v <- c(3,8,1) sigma <- c(1,2,0.5) Estimator <- BLE_SSRS(ys, h, N, m, v, sigma) Estimator
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