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Last data update: 2014.03.03

R: Calibration estimator and its variance estimation

calibev

R Documentation

Calibration estimator and its variance estimation

Description

Computes the calibration estimator of the population total and its variance estimation using the residuals' method.

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.
`EPS`	the tolerance in checking the calibration; by default, its value is 1e-6.

Details

If with is TRUE, the following formula is used

hat{Var}(hat{Ys})=∑_{kin s}∑_{ellin s}((π_{kell}-π_kπ_{ell})/π_{kell})(d_ke_k)(d_ell e_ell)

else

hat{Var}(hat{Ys})=∑_{kin s}∑_{ellin s}((π_{kell}-π_kπ_{ell})/π_{kell})(w_ke_k)(w_ell e_ell)

where e_k denotes the residual of unit k.

Value

The function returns two values:

`cest`	the calibration estimator,
`evar`	its estimated variance.

References

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

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 systematic 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 of size 200
# using systematic 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)