Wk {TeachingSampling}

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

Details

The calibration weights satisfy the following expression

\sum_{k\in S}w_kx_k=\sum_{k\in U}x_k

Value

The function returns a vector of calibrated weights.

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: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

Examples

############
## 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)