DianaPerri1: Diana-Perri-1 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-1 model. The function can also return the transformed variable. The Diana-Perri-1 model was proposed by Diana and Perri (2010, page 1877).

1	DianaPerri1(z,p,mu,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)
`p`	probability of direct response
`mu`	vector with the means of the scramble variables W and U
`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-1 model let p\in [0,1] be a design parameter, controlled by the experimenter, which is used to randomize the response as follows: with probability p the interviewer responds with the true value of the sensitive variable, whereas with probability 1-p the respondent gives a coded value, z_i=W(y_i+U) where 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-(1-p)μ_Wμ_U}{p+(1-p)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(p+(1-p)μ_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(p+(1-p)μ_W)^2}≤ft(1-\frac{n}{N}\right)

Point and confidence estimates of the sensitive characteristics using the Diana-Perri-1 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.

DianaPerri1Data

DianaPerri2

ResamplingVariance

N=417
data(DianaPerri1Data)
dat=with(DianaPerri1Data,data.frame(z,Pi))
p=0.6
mu=c(5/3,5/3)
cl=0.95
DianaPerri1(dat$z,p,mu,dat$Pi,"mean",cl,N,"srswor")