ResamplingVariance: Resampling variance of randomized response models

In RRTCS: Randomized Response Techniques for Complex Surveys

Description

To estimate the variance of the randomized response estimators using resampling methods.

Usage

ResamplingVariance(output,pi,type=c("total","mean"),option=1,N=NULL,pij=NULL,str=NULL,
clu=NULL,srswr=FALSE)

Arguments

output	output of the qualitative or quantitative method depending on the variable of interest
pi	vector of the first-order inclusion probabilities. By default it is NULL
type	the estimator type: total or mean
option	method used to calculate the variance (1: Jackknife, 2: Escobar-Berger, 3: Campbell-Berger-Skinner). By default it is 1
N	size of the population
pij	matrix of the second-order inclusion probabilities. This matrix is necessary for the Escobar-Berger and Campbell-Berger-Skinner options. By default it is NULL
str	strata ID. This vector is necessary for the Jackknife option. By default it is NULL
clu	cluster ID. This vector is necessary for the Jackknife option. By default it is NULL
srswr	variable indicating whether sampling is with replacement. By default it is NULL

Details

Functions to estimate the variance under stratified, cluster and unequal probability sampling by resampling methods (Wolter, 2007). The function ResamplingVariance allows us to choose from three models:

- The Jackknife method (Quenouille, 1949)

- The Escobar-Berger method (Escobar and Berger, 2013)

- The Campbell-Berger-Skinner method (Campbell, 1980; Berger and Skinner, 2005).

The Escobar-Berger and Campbell-Berger-Skinner methods are implemented using the functions defined in samplingVarEst package:

VE.EB.SYG.Total.Hajek, VE.EB.SYG.Mean.Hajek;

VE.Jk.CBS.SYG.Total.Hajek, VE.Jk.CBS.SYG.Mean.Hajek

(see López, E., Barrios, E., 2014, for a detailed description of its use).

Note: Both methods require the matrix of the second-order inclusion probabilities. When this matrix is not an input, the program will give a warning and, by default, a jackknife method is used.

Value

The resampling variance of the randomized response technique

References

Berger, Y.G., Skinner, C.J. (2005). A jackknife variance estimator for unequal probability sampling. Journal of the Royal Statistical Society B, 67, 79-89.

Campbell, C. (1980). A different view of finite population estimation. Proceedings of the Survey Research Methods Section of the American Statistical Association, 319-324.

Escobar, E.L., Berger, Y.G. (2013). A new replicate variance estimator for unequal probability sampling without replacement. Canadian Journal of Statistics 41, 3, 508-524.

López, E., Barrios, E. (2014). samplingVarEst: Sampling Variance Estimation. R package version 0.9-9. Online http://cran.r-project.org/web/packages/survey/index.html

Quenouille, M.H. (1949). Problems in Plane Sampling. The Annals of Mathematical Statistics 20, 355-375.

Wolter, K.M. (2007). Introduction to Variance Estimation. 2nd Edition. Springer.

See Also

Warner

ChaudhuriChristofides

EichhornHayre

SoberanisCruz

Horvitz

Examples

N=417
data(ChaudhuriChristofidesData)
dat=with(ChaudhuriChristofidesData,data.frame(z,Pi))
mu=c(6,6)
sigma=sqrt(c(10,10))
cl=0.95
data(ChaudhuriChristofidesDatapij)
out=ChaudhuriChristofides(dat$z,mu,sigma,dat$Pi,"mean",cl,pij=ChaudhuriChristofidesDatapij)
out
ResamplingVariance(out,dat$Pi,"mean",2,N,ChaudhuriChristofidesDatapij)

#Resampling with strata
data(EichhornHayreData)
dat=with(EichhornHayreData,data.frame(ST,z,Pi))
mu=1.111111
sigma=0.5414886
cl=0.95
out=EichhornHayre(dat$z,mu,sigma,dat$Pi,"mean",cl)
out
ResamplingVariance(out,dat$Pi,"mean",1,str=dat$ST)

#Resampling with cluster
N=1500
data(SoberanisCruzData)
dat=with(SoberanisCruzData, data.frame(CL,z,Pi))
p=0.7
alpha=0.5
cl=0.90
out=SoberanisCruz(dat$z,p,alpha,dat$Pi,"total",cl)
out
ResamplingVariance(out,dat$Pi,"total",2,N,samplingVarEst::Pkl.Hajek.s(dat$Pi))

#Resampling with strata and cluster
N=1500
data(HorvitzDataStCl)
dat=with(HorvitzDataStCl, data.frame(ST,CL,z,Pi))
p=0.6
alpha=0.5
cl=0.95
out=Horvitz(dat$z,p,alpha,dat$Pi,"mean",cl,N)
out
ResamplingVariance(out,dat$Pi,"mean",3,N,samplingVarEst::Pkl.Hajek.s(dat$Pi))

RRTCS documentation built on April 21, 2021, 9:06 a.m.