DianaPerri1 {RRTCS}

Diana-Perri-1 model

Description

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).

Usage

DianaPerri1(z,p,mu,pi,type=c("total","mean"),cl,N=NULL,method="srswr")

Arguments

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

Details

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)\mu_W\mu_U}{p+(1-p)\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(p+(1-p)\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(p+(1-p)\mu_W)^2}\left(1-\frac{n}{N}\right)

Value

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

DianaPerri1Data

DianaPerri2

ResamplingVariance

Examples

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")