| 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 |
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
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)