SinghJoarder {RRTCS}R Documentation

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

z

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

p

proportion of marked cards with the sensitive question

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 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=\left \{\begin{array}{lcc} 1 & \textrm{if person } i \textrm{ responds "Yes"}\\ 0 & \textrm{if person } i \textrm{ responds "No"} \end{array} \right .

The transformed variable is r_i=\frac{z_i-(1-p)}{(2p-1)+p(1-p)} and the estimated variance is \widehat{V}_R(r_i)=r_i(r_i-1).

Value

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

References

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

See Also

SinghJoarderData

ResamplingVariance

Examples

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)

[Package RRTCS version 0.0.4 Index]