# The Calibration Weights Computes the calibration weights (Chi-squared distance) for the estimation of the population total of several variables of interest. ```r Wk(x,tx,Pik,ck,b0) ``` ## Arguments - `x`: Vector, matrix or data frame containing the recollected auxiliary information for every unit in the selected sample - `tx`: Vector containing the populations totals of the auxiliary information - `Pik`: A vector containing inclusion probabilities for each unit in the sample - `ck`: A vector of weights induced by the structure of variance of the supposed model - `b0`: By default FALSE. The intercept of the regression model ## Details The calibration weights satisfy the following expression $$ \sum_{k\in S}w_kx_k=\sum_{k\in U}x_k $$ ## Returns The function returns a vector of calibrated weights. ## Author(s) Hugo Andres Gutierrez Rojas hagutierrezro@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. ## Examples ```r ############ ## Example 1 ############ # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # pik is some vector of inclusion probabilities in the sample # In this case the sample size is equal to the population size pik<-rep(1,5) w1<-Wk(x,tx=236,pik,ck=1,b0=FALSE) sum(x*w1) # Draws a sample size without replacement sam <- sample(5,2) pik <- c (0.8,0.2,0.2,0.5,0.3) # The auxiliary information an variable of interest in the selected smaple x.s<-x[sam] y.s<-y[sam] # The vector of inclusion probabilities in the selected smaple pik.s<-pik[sam] # Calibration weights under some specifics model w2<-Wk(x.s,tx=236,pik.s,ck=1,b0=FALSE) sum(x.s*w2) w3<-Wk(x.s,tx=c(5,236),pik.s,ck=1,b0=TRUE) sum(w3) sum(x.s*w3) w4<-Wk(x.s,tx=c(5,236),pik.s,ck=x.s,b0=TRUE) sum(w4) sum(x.s*w4) w5<-Wk(x.s,tx=236,pik.s,ck=x.s,b0=FALSE) sum(x.s*w5) ###################################################################### ## Example 2: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 Pik <- rep(n/N, n) sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common ratio model ################### estima<-data.frame(Income) x <- Employees tx <- sum(Lucy$Employees) w <- Wk(x, tx, Pik, ck=1, b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model without intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- sum(Lucy$Taxes) w<-Wk(x,tx,Pik,ck=x,b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model without intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model with intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- c(N,sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model with intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) #################################################################### ## Example 3: Linear models involving discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Vector of inclusion probabilities for units in the selected sample Pik<-rep(n/N,n) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model ################### estima<-data.frame(Income, Employees, Taxes) tx <- colSums(Domains(Lucy$Level)) w <- Wk(Doma,tx,Pik,ck=1,b0=FALSE) sum(Doma[,1]*w) sum(Doma[,2]*w) sum(Doma[,3]*w) tx # The calibration estimation colSums(estima*w) ########### Poststratified common ratio model ################### estima<-data.frame(Income, Employees) x<-Doma*Taxes tx <- colSums(Domains(Lucy$Level)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) sum(x[,3]*w) tx # The calibration estimation colSums(estima*w) ```

Wk.rd function