MangatSinghSinghUB: Mangat-Singh-Singh-UB model
In RRTCS: Randomized Response Techniques for Complex Surveys

Description Usage Arguments Details Value References See Also Examples

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).

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

`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

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).

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

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.

MangatSinghSinghUBData

MangatSinghSingh

ResamplingVariance

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)