Description Usage Arguments Details Value References See Also Examples
View source: R/ForcedResponse.R
Computes the randomized response estimation, its variance estimation and its confidence interval through the Forced-Response model. The function can also return the transformed variable. The Forced-Response model was proposed by Boruch in 1972.
1 |
z |
vector of the observed variable; its length is equal to n (the sample size) |
p1 |
proportion of cards marked "Yes" |
p2 |
proportion of cards marked "No" |
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 |
In the Forced-Response scheme, the sampled person i is offered a box with cards: some are marked "Yes" with a proportion p_1, some are marked "No" with a proportion p_2 and the rest are marked "Genuine", in the remaining proportion p_3=1-p_1-p_2, where 0<p_1,p_2<1,p_1\neq p_2,p_1+p_2<1. The person is requested to randomly draw one of them, to observe the mark on the card, and to respond
z_i=≤ft \{\begin{array}{lccc} 1 & \textrm{if the card is type "Yes"}\\ 0 & \textrm{if the card is type "No"}\\ y_i & \textrm{if the card is type "Genuine"} \end{array} \right .
The transformed variable is r_i=\frac{z_i-p_1}{1-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 Forced-Response model. The transformed variable is also reported, if required.
Boruch, R.F. (1972). Relations among statistical methods for assuring confidentiality of social research data. Social Science Research, 1, 403-414.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | data(ForcedResponseData)
dat=with(ForcedResponseData,data.frame(z,Pi))
p1=0.2
p2=0.2
cl=0.95
ForcedResponse(dat$z,p1,p2,dat$Pi,"total",cl)
#Forced Response with strata
data(ForcedResponseDataSt)
dat=with(ForcedResponseDataSt,data.frame(ST,z,Pi))
p1=0.2
p2=0.2
cl=0.95
ForcedResponse(dat$z,p1,p2,dat$Pi,"total",cl)
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