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.
SinghJoarder(z,p,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)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
the estimator type: total or mean
confidence level
size of the population. By default it is NULL
matrix of the second-order inclusion probabilities. By default it is NULL
Point and confidence estimates of the sensitive characteristics using the Singh-Joarder model. The transformed variable is also reported, if required.
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 \(\widehat{V}_R(r_i)=r_i(r_i-1)\).
Singh, S., Joarder, A.H. (1997). Unknown repeated trials in randomized response sampling. Journal of the Indian Statistical Association, 30, 109-122.
# 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)
# }
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