MangatSinghSingh {RRTCS}

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

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).

Value

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

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

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)