DianaPerri2: Diana-Perri-2 model
In RRTCS: Randomized Response Techniques for Complex Surveys

Description Usage Arguments Details Value References See Also Examples

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).

1	DianaPerri2(z,mu,beta,pi,type=c("total","mean"),cl,N=NULL,method="srswr")

`z`	vector of the observed variable; its length is equal to n (the sample size)
`mu`	vector with the means of the scramble variables W and U
`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

In the Diana-Perri-2 model, each respondent is asked to report the scrambled response z_i=W(β U+(1-β)y_i) where β \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-βμ_Wμ_U}{(1-β)μ_W}

where μ_W,μ_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-β)^2μ_W^2}

where s_z^2=∑_{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-β)^2μ_W^2}≤ft(1-\frac{n}{N}\right)

Point and confidence estimates of the sensitive characteristics using the Diana-Perri-2 model. The transformed variable is also reported, if required.

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.

DianaPerri2Data

DianaPerri1

ResamplingVariance

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")