MangatSinghSinghUB {RRTCS}

Mangat-Singh-Singh-UB model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Mangat-Singh-Singh model (Mangat el al., 1992) when the proportion of people bearing the innocuous attribute is unknown. The function can also return the transformed variable. The Mangat-Singh-Singh-UB model can be seen in Chauduri (2011, page 54).

Usage

MangatSinghSinghUB(I,J,p1,p2,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)

Arguments

I

first vector of the observed variable; its length is equal to n (the sample size)

J

second vector of the observed variable; its length is equal to n (the sample size)

p1

proportion of marked cards with the sensitive attribute in the first box

p2

proportion of marked cards with the sensitive attribute in the second box

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

A person labelled i who is chosen, is instructed to say "yes" if he/she bears A, and if not, to randomly take a card from a box containing cards marked A,B in proportions p_1 and (1-p_1),(0<p_1<1); they are then told to report the value x_i if a B-type card is chosen and he/she bears B; otherwise he/she is told to report "No". This entire exercise is to be repeated independently with the second box with A and B-marked cards in proportions p_2 and (1-p_2),(0<p_2<1,p_2\neq p_1). Let I_i the first response and J_i the second response for the respondent i.

The transformed variable is r_i=\frac{(1-p_2)I_i-(1-p_1)J_i}{p_1-p_2} 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-UB model. The transformed variable is also reported, if required.

References

Chaudhuri, A. (2011). Randomized response and indirect questioning techniques in surveys. Boca Raton: Chapman and Hall, CRC Press.

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

See Also

MangatSinghSinghUBData

MangatSinghSingh

ResamplingVariance

Examples

N=802
data(MangatSinghSinghUBData)
dat=with(MangatSinghSinghUBData,data.frame(I,J,Pi))
p1=0.6
p2=0.8
cl=0.95
MangatSinghSinghUB(dat$I,dat$J,p1,p2,dat$Pi,"mean",cl,N)