| ResamplingVariance {RRTCS} | R Documentation |
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 |
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
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))