MangatUB {RRTCS}

Mangat-UB model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Mangat model (Mangat, 1992) when the proportion of people bearing the innocuous attribute is unknown. The function can also return the transformed variable. The Mangat-UB model can be seen in Chaudhuri (2011, page 53).

Usage

MangatUB(I,J,p1,p2,t,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 second box

p2

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

t

probability of response to the sensitive questions without using random response in the first 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

In Mangat's extended scheme, three boxes containing cards are presented to the sampled person, labelled i. The first box contains cards marked "True" and "RR" in proportions t and 1-t, the second one contains A and B-marked cards in proportions p_1 and (1-p_1),(0<p_1<1) and the third box contains A and B-marked cards in proportions p_2 and 1-p_2,(0<p_2<1),p_1\neq p_2. The subject is requested to draw a card from the first box. The sample respondent i is then instructed to tell the truth, using "the first box and if necessary also the second box" and next, independently, to give a second truthful response also using "the first box and if necessary, the third box." Let I_i represent the first response and J_i the second response for 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-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. (1992). Two stage randomized response sampling procedure using unrelated question. Journal of the Indian Society of Agricultural Statistics, 44, 82-87.

See Also

Mangat

ResamplingVariance