gencalib {sampling}

g-weights of the generalized calibration estimator

Description

Computes the g-weights of the generalized calibration estimator. The g-weights should lie in the specified bounds for the truncated and logit methods.

Usage

gencalib(Xs,Zs,d,total,q=rep(1,length(d)),method=c("linear","raking","truncated","logit"),
bounds=c(low=0,upp=10),description=FALSE,max_iter=500,C=1)

Arguments

Xs

matrix of calibration variables.

Zs

matrix of instrumental variables with same dimension as Xs.

d

vector of initial weights.

total

vector of population totals.

q

vector of positive values accounting for heteroscedasticity; the variation of the g-weights is reduced for small values of q.

method

calibration method (linear, raking, logit, truncated).

bounds

vector of bounds for the g-weights used in the truncated and logit methods; 'low' is the smallest value and 'upp' is the largest value.

description

if description=TRUE, summary of initial and final weights are printed, and their boxplots and histograms are drawn; by default, its value is FALSE.

max_iter

maximum number of iterations in the Newton's method.

C

value of the centering constant, by default equals 1.

Details

The generalized calibration or the instrument vector method computes the g-weights g_k=F(\lambda'z_k), where z_k is a vector with values defined for k\in s (or k\in r where r is the set of respondents) and sharing the dimension of the specified auxiliary vector x_k. The vectors z_k and x_k have to be stronlgy correlated. The vector \lambda is determined from the calibration equation \sum_{k\in s} d_kg_k x_k=\sum_{k\in U} x_k or \sum_{k\in r} d_kg_k x_k=\sum_{k\in U} x_k. The function F plays the same role as in the calibration method (see calib). If Xs=Zs the calibration method is obtain. If the method is "logit" the g-weights will be centered around the constant C, with low<C<upp. In the calibration method C=1 (see calib).

Value

The function returns the vector of g-weights.

References

Deville, J.-C. (1998). La correction de la nonréponse par calage ou par échantillonnage équilibré. Paper presented at the Congrès de l'ACFAS, Sherbrooke, Québec.
Deville, J.-C. (2000). Generalized calibration and application for weighting for non-response, COMPSTAT 2000: proceedings in computational statistics, p. 65–76.
Estevao, V.M., and Särndal, C.E. (2000). A functional form approach to calibration. Journal of Official Statistics, 16, 379–399.
Kott, P.S. (2006). Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32, 133–142.

See Also

checkcalibration, calib

Examples

############
## Example 1
############
# matrix of sample calibration variables 
Xs=cbind(
c(1,1,1,1,1,0,0,0,0,0),
c(0,0,0,0,0,1,1,1,1,1),
c(1,2,3,4,5,6,7,8,9,10))
# inclusion probabilities
piks=rep(0.2,times=10)
# vector of population totals
total=c(24,26,290)
# matrix of instrumental variables
Zs=Xs+matrix(runif(nrow(Xs)*ncol(Xs)),nrow(Xs),ncol(Xs))
# the g-weights using the truncated method
g=gencalib(Xs,Zs,d=1/piks,total,method="truncated",bounds=c(0.5,1.5))
# the calibration estimator of X is equal to the 'total' vector
t(g/piks)%*%Xs
# the g-weights are between lower and upper bounds
summary(g)
############
## Example 2
############
# Example of generalized 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(Totaltaxation/mean(Totaltaxation),medianincome/mean(medianincome))
# selection of a sample with expected 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=UPpoisson(pik)            # sample
Xs=X[s==1,]                 # sample calibration variable matrix 
piks=pik[s==1]              # sample inclusion probabilities
n=length(piks)              # expected sample size
# vector of population totals of the calibration variables
total=c(t(rep(1,times=N))%*%X)  
Z=cbind(TaxableIncome/mean(TaxableIncome),averageincome/mean(averageincome))
# defines the instrumental variables (sample level)
Zs=Z[s==1,]
# computation of the generalized g-weights
# by means of different generalized calibration methods
g1=gencalib(Xs,Zs,d=1/piks,total,method="linear")
g2=gencalib(Xs,Zs,d=1/piks,total,method="raking")
g3=gencalib(Xs,Zs,d=1/piks,total,method="truncated",bounds=c(0.5,8))
g4=gencalib(Xs,Zs,d=1/piks,total,method="logit",bounds=c(0.5,1.5))
# In some cases, the calibration is not possible
# particularly when bounds are used.
# if the calibration is possible, the calibration estimator of X total is printed
if(checkcalibration(Xs,d=1/piks,total,g1)$result) print(c((g1/piks)%*% Xs)) else print("error")
if(!is.null(g2))
if(checkcalibration(Xs,d=1/piks,total,g2)$result) print(c((g2/piks)%*% Xs)) else print("error")
if(!is.null(g3))
if(checkcalibration(Xs,d=1/piks,total,g3)$result) print(c((g3/piks)%*% Xs)) else print("error")
if(!is.null(g4))
if(checkcalibration(Xs,d=1/piks,total,g4)$result) print(c((g4/piks)%*% Xs)) else print("error")
detach(belgianmunicipalities)
############
## Example 3
############
# Generalized calibration and adjustment for unit nonresponse in the 'calibration' vignette
# vignette("calibration", package="sampling")