| Christofides {RRTCS} | R Documentation |
Christofides model
Description
Computes the randomized response estimation, its variance estimation and its confidence interval through the Christofides model. The function can also return the transformed variable. The Christofides model was proposed by Christofides in 2003.
Usage
Christofides(z,mm,pm,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)
Arguments
z |
vector of the observed variable; its length is equal to |
mm |
vector with the marks of the cards |
pm |
vector with the probabilities of previous marks |
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 Christofides randomized response technique, a sampled person i is given a box with identical cards, each bearing a separate mark as
1,\dots,k,\dots m with m\geq 2 but in known proportions p_1,\dots,p_k,\dots p_m with 0<p_k< 1 for k=1,\dots,m and
\sum_{k=1}^{m}p_k=1. The person sampled is requested to draw one of the cards and respond
z_i=\left \{\begin{array}{lcc}
k & \textrm{if a card marked } k \textrm{ is drawn and the person bears } A^c\\
m-k+1 & \textrm{if a card marked } k \textrm{ is drawn but the person bears } A
\end{array}
\right .
The transformed variable is r_i=\frac{z_i-\mu}{m+1-2\mu} where \mu=\sum_{k=1}^{m}kp_k and the estimated variance is
\widehat{V}_R(r_i)=\frac{V_R(k)}{(m+1-2\mu)^2}, where V_R(k)=\sum_{k=1}^{m}k^2p_k-\mu^2.
Value
Point and confidence estimates of the sensitive characteristics using the Christofides model. The transformed variable is also reported, if required.
References
Christofides, T.C. (2003). A generalized randomized response technique. Metrika, 57, 195-200.
See Also
Examples
N=802
data(ChristofidesData)
dat=with(ChristofidesData,data.frame(z,Pi))
mm=c(1,2,3,4,5)
pm=c(0.1,0.2,0.3,0.2,0.2)
cl=0.95
Christofides(dat$z,mm,pm,dat$Pi,"mean",cl,N)