E.2SI: Estimation of the Population Total under Two Stage Simple...

In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

Description

Computes the Horvitz-Thompson estimator of the population total according to a 2SI sampling design

Usage

E.2SI(NI, nI, Ni, ni, y, PSU)

Arguments

NI	Population size of Primary Sampling Units
nI	Sample size of Primary Sampling Units
Ni	Vector of population sizes of Secundary Sampling Units selected in the first draw
ni	Vector of sample sizes of Secundary Sampling Units
y	Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample
PSU	Vector identifying the membership to the strata of each unit in the population

Details

Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation

Value

The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest

Author(s)

Hugo Andres Gutierrez Rojas [e-mail]

References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Dise?o de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

See Also

S.SI

Examples

############
## Example 1
############
# Uses Lucy data to draw a twostage simple random sample 
# accordind to a 2SI design. Zone is the clustering variable
data(Lucy)
attach(Lucy)
summary(Zone)
# The population of clusters or Primary Sampling Units
UI<-c("A","B","C","D","E")
NI <- length(UI)
# The sample size is nI=3
nI <- 3
# Selects the sample of PSUs
samI<-S.SI(NI,nI)
dataI<-UI[samI]
dataI   
# The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy3
Lucy1<-Lucy[which(Zone==dataI[1]),]
Lucy2<-Lucy[which(Zone==dataI[2]),]
Lucy3<-Lucy[which(Zone==dataI[3]),]
# The size of every single PSU
N1<-dim(Lucy1)[1]
N2<-dim(Lucy2)[1]
N3<-dim(Lucy3)[1]
Ni<-c(N1,N2,N3)
# The sample size in every PSI is 135 Secondary Sampling Units
n1<-135
n2<-135
n3<-135
ni<-c(n1,n2,n3)
# Selects a sample of Secondary Sampling Units inside the PSUs
sam1<-S.SI(N1,n1)
sam2<-S.SI(N2,n2)
sam3<-S.SI(N3,n3)
# The information about each Secondary Sampling Unit in the PSUs
# is saved in data1 ... data3
data1<-Lucy1[sam1,]
data2<-Lucy2[sam2,]
data3<-Lucy3[sam3,]
# The information about each unit in the final selected sample is saved in data
data<-rbind(data1, data2, data3)
attach(data)
# The clustering variable is Zone
Cluster <- as.factor(as.integer(Zone))
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
# Estimation of the Population total
E.2SI(NI,nI,Ni,ni,estima,Cluster)

########################################################
## Example 2 Total Census to the entire population
########################################################
# Uses Lucy data to draw a cluster random sample
# accordind to a SI design ...
# Zone is the clustering variable
data(Lucy)
attach(Lucy)
summary(Zone)
# The population of clusters
UI<-c("A","B","C","D","E")
NI <- length(UI)
# The sample size equals to the population size of PSU
nI <- NI
# Selects every single PSU
samI<-S.SI(NI,nI)
dataI<-UI[samI]
dataI   
# The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy5
Lucy1<-Lucy[which(Zone==dataI[1]),]
Lucy2<-Lucy[which(Zone==dataI[2]),]
Lucy3<-Lucy[which(Zone==dataI[3]),]
Lucy4<-Lucy[which(Zone==dataI[4]),]
Lucy5<-Lucy[which(Zone==dataI[5]),]
# The size of every single PSU
N1<-dim(Lucy1)[1]
N2<-dim(Lucy2)[1]
N3<-dim(Lucy3)[1]
N4<-dim(Lucy4)[1]
N5<-dim(Lucy5)[1]
Ni<-c(N1,N2,N3,N4,N5)
# The sample size of Secondary Sampling Units equals to the size of each PSU
n1<-N1
n2<-N2
n3<-N3
n4<-N4
n5<-N5
ni<-c(n1,n2,n3,n4,n5)
# Selects every single Secondary Sampling Unit inside the PSU
sam1<-S.SI(N1,n1)
sam2<-S.SI(N2,n2)
sam3<-S.SI(N3,n3)
sam4<-S.SI(N4,n4)
sam5<-S.SI(N5,n5)
# The information about each unit in the cluster is saved in Lucy1 ... Lucy5
data1<-Lucy1[sam1,]
data2<-Lucy2[sam2,]
data3<-Lucy3[sam3,]
data4<-Lucy4[sam4,]
data5<-Lucy5[sam5,]
# The information about each Secondary Sampling Unit
# in the sample (census) is saved in data
data<-rbind(data1, data2, data3, data4, data5)
attach(data)
# The clustering variable is Zone
Cluster <- as.factor(as.integer(Zone))
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
# Estimation of the Population total
E.2SI(NI,nI,Ni,ni,estima,Cluster)
# Sampling error is null

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