calibev {sampling}R Documentation

Calibration estimator and its variance estimation

Description

Computes the calibration estimator and its variance estimation using the residuals' technique. The function returns two values: cest (the calibration estimator) and evar (its estimated variance).

Usage

calibev(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)), with=FALSE,EPS=1e-6)

Arguments

Ys vector of interest variable; its size is n, the sample size.
Xs matrix of sample calibration variables.
total vector of population totals for calibration.
pikl matrix of joint inclusion probabilities of the sample units.
d vector of initial weights of the sample units.
g vector of g-weights; its size is n, the sample size.
q vector of positive values accounting for heteroscedasticity; its size is n, the sample size.
with if TRUE, the variance estimation takes into account the initial weights d; otherwise, the final weights w=g*d are taken into account; by default, its value is FALSE. If TRUE, the following formula is used $$hat{Var}(hat{Ys})= sum_{kin s}sum_{ellin s} ((π_{kell}-π_kπ_{ell})/π_{kell})(d_ke_k)(d_ell e_ell)$$ else $$hat{Var}(hat{Ys})= sum_{kin s}sum_{ellin s} ((π_{kell}-π_kπ_{ell})/π_{kell})(w_ke_k)(w_ell e_ell)$$ where $e_k$ denotes the residual for unit k.
EPS the tolerance in checking the calibration; by default, its value is 1e-6.

References

Deville, J.-C. and Säarndal, C.-E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87:376–382.
Deville, J.-C., Särndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. Journal of the American Statistical Association, 88:1013–1020.

See Also

calib

Examples

############
## Example
############
# Example of g-weights (linear, raking, truncated, logit),
# with the data of Belgian municipalities as population.
# Firstly, a sample is selected by means of Poisson sampling.
# Secondly, the g-weights are calculated.
data(belgianmunicipalities)
attach(belgianmunicipalities)
# matrix of calibration variables for the population
X=cbind(
Men03/mean(Men03),
Women03/mean(Women03),
Diffmen,
Diffwom,
TaxableIncome/mean(TaxableIncome),
Totaltaxation/mean(Totaltaxation),
averageincome/mean(averageincome),
medianincome/mean(medianincome))
# selection of a sample with expectation size equal to 200
# by means of Poisson sampling
# the inclusion probabilities are proportional to the average income 
pik=inclusionprobabilities(averageincome,200)
N=length(pik)               # population size
s=UPsystematic(pik)         # draws a sample s using systematic sampling        
Xs=X[s==1,]                 # matrix of sample calibration variables
piks=pik[s==1]              # sample inclusion probabilities
n=length(piks)              # sample size
# vector of population totals of the calibration variables
total=c(t(rep(1,times=N))%*%X)  
g1=calib(Xs,d=1/piks,total,method="linear") # computes the g-weights
pikl=UPsystematicpi2(pik)   # computes the matrix of the joint inclusion probabilities 
pikls=pikl[s==1,s==1]       # the same matrix for the units in s
Ys=Tot04[s==1]              # the variable of interest is Tot04 (for the units in s)
calibev(Ys,Xs,total,pikls,d=1/piks,g1,with=FALSE,EPS=1e-6)

[Package sampling version 2.1 Index]