RRTCS (version 0.0.4)

Kuk: Kuk model

Description

Computes the randomized response estimation, its variance estimation and its confidence through the Kuk model. The function can also return the transformed variable. The Kuk model was proposed by Kuk in 1990.

Usage

Kuk(z,p1,p2,k,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)

p1

proportion of red cards in the first box

p2

proportion of red cards in the second box

k

total number of cards drawn

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 Kuk model. The transformed variable is also reported, if required.

Details

In the Kuk randomized response technique, the sampled person \(i\) is offered two boxes. Each box contains cards that are identical exception colour, either red or white, in sufficiently large numbers with proportions \(p_1\) and \(1-p_1\) in the first and \(p_2\) and \(1-p_2\), in the second (\(p_1\neq p_2\)). The person sampled is requested to use the first box, if his/her trait is \(A\) and the second box if his/her trait is \(A^c\) and to make \(k\) independent draws of cards, with replacement each time. The person is asked to reports \(z_i=f_i\), the number of times a red card is drawn.

The transformed variable is \(r_i=\frac{f_i/k-p_2}{p_1-p_2}\) and the estimated variance is \(\widehat{V}_R(r_i)=br_i+c\), where \(b=\frac{1-p_1-p_2}{k(p_1-p_2)}\) and \(c=\frac{p_2(1-p_2)}{k(p_1-p_2)^2}\).

References

Kuk, A.Y.C. (1990). Asking sensitive questions indirectly. Biometrika, 77, 436-438.

See Also

KukData

ResamplingVariance

Examples

# NOT RUN {
N=802
data(KukData)
dat=with(KukData,data.frame(z,Pi))
p1=0.6
p2=0.2
k=25
cl=0.95
Kuk(dat$z,p1,p2,k,dat$Pi,"mean",cl,N)
# }