E.UC {TeachingSampling}

Estimation of the Population Total and its variance using the Ultimate Cluster technique

Description

This function computes a weighted estimator of the population total and estimates its variance by using the Ultimate Cluster technique. This approximation performs well in many sampling designs. The user specifically needs to declare the variables of interest, the primary sampling units, the strata, and the sampling weights for every singlt unit in the sample.

Usage

E.UC(S, PSU, dk, y)

Arguments

S

Vector identifying the membership to the strata of each unit in selected sample.

PSU

Vector identifying the membership to the strata of each unit in the population.

dk

Sampling weights of the units in the sample.

y

Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample.

Details

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

Value

This function returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation.

Author(s)

Hsugo Andres Gutierrez Rojas <hugogutierrez at gmail.com>

References

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

See Also

E.2SI

Examples

#############################
## Example 1:              ##
## Stratified Two-stage SI ##
#############################

data('BigCity')
FrameI <- BigCity %>% group_by(PSU) %>%
summarise(Stratum = unique(Stratum),
          Persons = n(),
          Income = sum(Income),
          Expenditure = sum(Expenditure))
            
attach(FrameI)

sizes = FrameI %>% group_by(Stratum) %>%
        summarise(NIh = n(),
        nIh = 2,
        dI = NIh/nIh)
        
NIh <- sizes$NIh
nIh <- sizes$nIh

samI <- S.STSI(Stratum, NIh, nIh)
UI <- levels(as.factor(FrameI$PSU))
sampleI <- UI[samI]
          
FrameII <- left_join(sizes, BigCity[which(BigCity$PSU %in% sampleI), ])
attach(FrameII)

HHdb <- FrameII %>% 
        group_by(PSU) %>%
        summarise(Ni = length(unique(HHID)))
        
Ni <- as.numeric(HHdb$Ni)
ni <- ceiling(Ni * 0.1)
ni
sum(ni)

sam = S.SI(Ni[1], ni[1])
clusterII = FrameII[which(FrameII$PSU == sampleI[1]), ]
sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam])
clusterHH <- left_join(sam.HH, clusterII, by = "HHID") 
clusterHH$dki <- Ni[1]/ni[1]
clusterHH$dk <- clusterHH$dI * clusterHH$dki
data = clusterHH
for (i in 2:length(Ni)) {
      sam = S.SI(Ni[i], ni[i])
      clusterII = FrameII[which(FrameII$PSU == sampleI[i]), ]
      sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam])
      clusterHH <- left_join(sam.HH, clusterII, by = "HHID") 
      clusterHH$dki <- Ni[i]/ni[i]
      clusterHH$dk <- clusterHH$dI * clusterHH$dki
      data1 = clusterHH
      data = rbind(data, data1)
}

sum(data$dk)
attach(data)
estima <- data.frame(Income, Expenditure)
area <- as.factor(PSU)
stratum <- as.factor(Stratum)

E.UC(stratum, area, dk, estima)

################################
## Example 2:                 ##
## Self weighted Two-stage SI ##
################################

data('BigCity')
FrameI <- BigCity %>% group_by(PSU) %>%
summarise(Stratum = unique(Stratum),
          Households = length(unique(HHID)),
          Income = sum(Income),
          Expenditure = sum(Expenditure))
            
attach(FrameI)

sizes = FrameI %>% group_by(Stratum) %>%
        summarise(NIh = n(),
        nIh = 2)
        
NIh <- sizes$NIh
nIh <- sizes$nIh

resI <- S.STpiPS(Stratum, Households, nIh)
head(resI)
samI <- resI[, 1]
piI <- resI[, 2]
UI <- levels(as.factor(FrameI$PSU))
sampleI <- data.frame(PSU = UI[samI], dI = 1/piI) 
 
FrameII <- left_join(sampleI, 
           BigCity[which(BigCity$PSU %in% sampleI[,1]), ])
           
attach(FrameII)

HHdb <- FrameII %>% 
        group_by(PSU) %>%
        summarise(Ni = length(unique(HHID)))
Ni <- as.numeric(HHdb$Ni)
ni <- 5

sam = S.SI(Ni[1], ni)
clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[1]), ]
sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam])
clusterHH <- left_join(sam.HH, clusterII, by = "HHID") 
clusterHH$dki <- Ni[1]/ni
clusterHH$dk <- clusterHH$dI * clusterHH$dki
data = clusterHH
for (i in 2:length(Ni)) {
      sam = S.SI(Ni[i], ni)
      clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[i]), ]
      sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam])
      clusterHH <- left_join(sam.HH, clusterII, by = "HHID") 
      clusterHH$dki <- Ni[i]/ni
      clusterHH$dk <- clusterHH$dI * clusterHH$dki
      data1 = clusterHH
      data = rbind(data, data1)
}

sum(data$dk)
attach(data)
estima <- data.frame(Income, Expenditure)
area <- as.factor(PSU)
stratum <- as.factor(Stratum)

E.UC(stratum, area, dk, estima)