SinghJoarder: Singh-Joarder model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Singh-Joarder model. The function can also return the transformed variable. The Singh-Joarder model was proposed by Singh and Joarder in 1997.

Usage

SinghJoarder(z,p,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)

Arguments

vector of the observed variable; its length is equal to $n$ (the sample size)

proportion of marked cards with the sensitive question

vector of the first-order inclusion probabilities

type

the estimator type: total or mean

confidence level

size of the population. By default it is NULL

pij

matrix of the second-order inclusion probabilities. By default it is NULL

Value

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

Details

The basics of the Singh-Joarder scheme are similar to Warner's randomized response device, with the following difference. If a person labelled $i$ bears $A^{c}$ he/she is told to say so if so guided by a card drawn from a box of $A$ and $A^{c}$ marked cards in proportions $p$ and $(1 - p), (0 < p < 1)$ . However, if he/she bears $A$ and is directed by the card to admit it, he/she is told to postpone the reporting based on the first draw of the card from the box but to report on the basis of a second draw. Therefore, $z_{i} = {\begin{array}{lcc} 1 & if person i responds "Yes" \\ 0 & if person i responds "No" \end{array}$ The transformed variable is $r_{i} = \frac{z_{i} - (1 - p)}{(2 p - 1) + p (1 - p)}$ and the estimated variance is ${\hat{V}}_{R} (r_{i}) = r_{i} (r_{i} - 1)$ .

References

Singh, S., Joarder, A.H. (1997). Unknown repeated trials in randomized response sampling. Journal of the Indian Statistical Association, 30, 109-122.

Examples

Run this code

# NOT RUN {
N=802
data(SinghJoarderData)
dat=with(SinghJoarderData,data.frame(z,Pi))
p=0.6
cl=0.95
SinghJoarder(dat$z,p,dat$Pi,"mean",cl,N)
# }

Run the code above in your browser using DataLab

Get 50% off unlimited learning