SinghJoarder: Singh-Joarder model

In RRTCS: Randomized Response Techniques for Complex Surveys

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=≤ft \{\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)

Example output

Call:
SinghJoarder(z = dat$z, p = p, pi = dat$Pi, type = "mean", cl = cl, 
    N = N)

Qualitative model
Singh and Joarder model for the mean estimator
Parameters: p=0.6

Estimation: 0.3342246
Variance: 0.007286378
Confidence interval (95%)
    Lower bound: 0.1669215 
    Upper bound: 0.5015277 

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