# Estimation of the Population Total and its variance using the Ultimate Cluster technique 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. ```r 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. ## Returns 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. ## Details The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest. ## Examples ```r ############################# ## 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) ``` ## 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` ## Author(s) Hsugo Andres Gutierrez Rojas

E.UC function