ChaudhuriChristofides: Chaudhuri-Christofides model

In RRTCS: Randomized Response Techniques for Complex Surveys

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Chaudhuri-Christofides model. The function can also return the transformed variable. The Chaudhuri-Christofides model can be seen in Chaudhuri and Christofides (2013, page 97).

Usage

ChaudhuriChristofides(z,mu,sigma,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)

Arguments

z	vector of the observed variable; its length is equal to n (the sample size)
mu	vector with the means of the scramble variables
sigma	vector with the standard deviations of the scramble variables
pi	vector of the first-order inclusion probabilities
type	the estimator type: total or mean
cl	confidence level
N	size of the population. By default it is NULL
pij	matrix of the second-order inclusion probabilities. By default it is NULL

Details

The randomized response given by the person i is z_i=y_iS_1+S_2 where S_1,S_2 are scramble variables, whose mean μ and standard deviation σ are known.

Value

Point and confidence estimates of the sensitive characteristics using the Chaudhuri-Christofides model. The transformed variable is also reported, if required.

References

Chaudhuri, A., and Christofides, T.C. (2013) Indirect Questioning in Sample Surveys. Springer-Verlag Berlin Heidelberg.

See Also

ChaudhuriChristofidesData

ChaudhuriChristofidesDatapij

ResamplingVariance

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)
ChaudhuriChristofides(dat$z,mu,sigma,dat$Pi,"mean",cl,pij=ChaudhuriChristofidesDatapij)

Example output

Call:
ChaudhuriChristofides(z = dat$z, mu = mu, sigma = sigma, pi = dat$Pi, 
    type = "mean", cl = cl, pij = ChaudhuriChristofidesDatapij)

Quantitative model
Chaudhuri and Christofides model for the mean estimator
Parameters: mu1=6; mu2=6; sigma1=3.2; sigma2=3.2

Estimation: 6479.657
Variance: 257283.4
Confidence interval (95%)
    Lower bound: 5485.503 
    Upper bound: 7473.812 

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