TeachingSampling (version 4.1.1)

Wk: The Calibration Weights

Description

Computes the calibration weights (Chi-squared distance) for the estimation of the population total of several variables of interest.

Usage

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

Value

The function returns a vector of calibrated weights.

Details

The calibration weights satisfy the following expression $$\sum_{k\in S}w_kx_k=\sum_{k\in U}x_k$$

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

# NOT RUN {
############
## 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)

# }