# Kuk: Kuk model In RRTCS: Randomized Response Techniques for Complex Surveys

## 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

 1 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

## 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}.

## Value

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

## References

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

KukData

ResamplingVariance

## Examples

 1 2 3 4 5 6 7 8 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) 

### Example output

Call:
Kuk(z = dat$z, p1 = p1, p2 = p2, k = k, pi = dat$Pi, type = "mean",
cl = cl, N = N)

Qualitative model
Kuk model for the mean estimator
Parameters: p1=0.6; p2=0.2; k=25

Estimation: 0.1335
Variance: 0.0006541851
Confidence interval (95%)
Lower bound: 0.08336992
Upper bound: 0.1836301


RRTCS documentation built on May 29, 2017, 9:43 a.m.