Description Usage Arguments Details Value References See Also Examples
Computes the randomized response estimation, its variance estimation and its confidence interval through the Warner model. The function can also return the transformed variable. The Warner model was proposed by Warner in 1965.
1 |
z |
vector of the observed variable; its length is equal to n (the sample size) |
p |
proportion of marked cards with the sensitive attribute |
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 |
Warner's randomized response device works as follows. A sampled person labelled i is offered a box of a considerable number of identical cards with a proportion p,(0<p<1,p\neq 0.5) of them marked A and the rest marked A^c. The person is requested, randomly, to draw one of them, to observe the mark on the card, and to give the response
z_i=≤ft\{\begin{array}{lcc} 1 & \textrm{if card type "matches" the trait } A \textrm{ or } A^c \\ 0 & \textrm{if a "no match" results } \end{array} \right.
The randomized response is given by r_i=\frac{z_i-(1-p)}{2p-1} 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 Warner model. The transformed variable is also reported, if required.
Warner, S.L. (1965). Randomized Response: a survey technique for eliminating evasive answer bias. Journal of the American Statistical Association 60, 63-69.
1 2 3 4 5 6 | N=802
data(WarnerData)
dat=with(WarnerData,data.frame(z,Pi))
p=0.7
cl=0.95
Warner(dat$z,p,dat$Pi,"total",cl)
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