| DianaPerri2 {RRTCS} | R Documentation |
Diana-Perri-2 model
Description
Computes the randomized response estimation, its variance estimation and its confidence interval through the Diana-Perri-2 model. The function can also return the transformed variable. The Diana-Perri-2 model was proposed by Diana and Perri (2010, page 1879).
Usage
DianaPerri2(z,mu,beta,pi,type=c("total","mean"),cl,N=NULL,method="srswr")
Arguments
z |
vector of the observed variable; its length is equal to |
mu |
vector with the means of the scramble variables |
beta |
the constant of weighting |
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 |
method |
method used to draw the sample: srswr or srswor. By default it is srswr |
Details
In the Diana-Perri-2 model, each respondent is asked to report the scrambled response z_i=W(\beta U+(1-\beta)y_i) where \beta \in [0,1) is a suitable constant
controlled by the researcher and W,U are scramble variables whose distribution is assumed to be known.
To estimate \bar{Y} a sample of respondents is selected according to simple random sampling with replacement.
The transformed variable is
r_i=\frac{z_i-\beta\mu_W\mu_U}{(1-\beta)\mu_W}
where \mu_W,\mu_U are the means of W,U scramble variables, respectively.
The estimated variance in this model is
\widehat{V}(\widehat{\bar{Y}}_R)=\frac{s_z^2}{n(1-\beta)^2\mu_W^2}
where s_z^2=\sum_{i=1}^n\frac{(z_i-\bar{z})^2}{n-1}.
If the sample is selected by simple random sampling without replacement, the estimated variance is
\widehat{V}(\widehat{\bar{Y}}_R)=\frac{s_z^2}{n(1-\beta)^2\mu_W^2}\left(1-\frac{n}{N}\right)
Value
Point and confidence estimates of the sensitive characteristics using the Diana-Perri-2 model. The transformed variable is also reported, if required.
References
Diana, G., Perri, P.F. (2010). New scrambled response models for estimating the mean of a sensitive quantitative character. Journal of Applied Statistics 37 (11), 1875-1890.
See Also
Examples
N=100000
data(DianaPerri2Data)
dat=with(DianaPerri2Data,data.frame(z,Pi))
beta=0.8
mu=c(50/48,5/3)
cl=0.95
DianaPerri2(dat$z,mu,beta,dat$Pi,"mean",cl,N,"srswor")