RRTCS (version 0.0.4)

MangatSinghSingh: Mangat-Singh-Singh model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Mangat-Singh-Singh model. The function can also return the transformed variable. The Mangat-Singh-Singh model was proposed by Mangat, Singh and Singh in 1992.

Usage

MangatSinghSingh(z,p,alpha,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 attribute in the box

alpha

proportion of people with the innocuous attribute

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

Value

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

Details

In the Mangat-Singh-Singh scheme, a person labelled \(i\), if sampled, is offered a box and told to answer "yes" if the person bears \(A\). But if the person bears \(A^c\) then the person is to draw a card from the box with a proportion \(p(0<p< 1)\) of cards marked \(A\) and the rest marked \(B\); if the person draws a card marked \(B\) he/she is told to say "yes" again if he/she actually bears \(B\); in any other case, "no" is to be answered.

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

References

Mangat, N.S., Singh, R., Singh, S. (1992). An improved unrelated question randomized response strategy. Calcutta Statistical Association Bulletin, 42, 277-281.

See Also

MangatSinghSinghData

MangatSinghSinghUB

ResamplingVariance

Examples

# NOT RUN {
data(MangatSinghSinghData)
dat=with(MangatSinghSinghData,data.frame(z,Pi))
p=0.6
alpha=0.5
cl=0.95
MangatSinghSingh(dat$z,p,alpha,dat$Pi,"total",cl)
# }