RRTCS (version 0.0.4)

ResamplingVariance: Resampling variance of randomized response models

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

Value

The resampling variance of the randomized response technique

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 L<U+00F3>pez, 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.

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.

L<U+00F3>pez, 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

# NOT RUN {
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))
# }