Saha: Saha model

In RRTCS: Randomized Response Techniques for Complex Surveys

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Saha model. The function can also return the transformed variable. The Saha model was proposed by Saha in 2007.

Usage

Saha(z,mu,sigma,pi,type=c("total","mean"),cl,N=NULL,method="srswr")

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 W and U
sigma	vector with the standard deviations of the scramble variables W and U
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
method	method used to draw the sample: srswr or srswor. By default it is srswr

Details

In the Saha model, each respondent selected is asked to report the randomized response z_i=W(y_i+U) where W,U are scramble variables whose distribution is assumed to be known.

To estimate \bar{Y} a sample of respondents is selected according to simple random sampling with replacement. The transformed variable is

r_i=\frac{z_i-μ_Wμ_U}{μ_W}

where μ_W,μ_U are the means of W,U scramble variables respectively

The estimated variance in this model is

\widehat{V}(\widehat{\bar{Y}}_R)=\frac{s_z^2}{nμ_W^2}

where s_z^2=∑_{i=1}^n\frac{(z_i-\bar{z})^2}{n-1}.

If the sample is selected by simple random sampling without replacement, the estimated variance is

\widehat{V}(\widehat{\bar{Y}}_R)=\frac{s_z^2}{nμ_W^2}≤ft(1-\frac{n}{N}\right)

Value

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

References

Saha, A. (2007). A simple randomized response technique in complex surveys. Metron LXV, 59-66.

See Also

SahaData

ResamplingVariance

Examples

N=228
data(SahaData)
dat=with(SahaData,data.frame(z,Pi))
mu=c(1.5,5.5)
sigma=sqrt(c(1/12,81/12))
cl=0.95
Saha(dat$z,mu,sigma,dat$Pi,"mean",cl,N)

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