Horvitz {RRTCS}R Documentation

Horvitz model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Horvitz model. The function can also return the transformed variable. The Horvitz model was proposed by Horvitz et al. (1967) and by Greenberg et al. (1969).

Usage

Horvitz(z,p,alpha,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)

Arguments

z

vector of the observed variable; its length is equal to nn (the sample size)

p

proportion of marked cards with the sensitive question

alpha

proportion of people with the innocuous attribute

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 Horvitz model, the randomized response device presents to the sampled person labelled ii a box containing a large number of identical cards, with a proportion p,(0<p<1)p,(0 <p < 1) bearing the mark AA and the rest marked BB (an innocuous attribute whose population proportion α\alpha is known). The response solicited denoted by ziz_i takes the value yiy_i if ii bears AA and the card drawn is marked AA or if ii bears BB and the card drawn is marked BB. Otherwise ziz_i takes the value 0.

The transformed variable is ri=zi(1p)αpr_i=\frac{z_i-(1-p)\alpha}{p} and the estimated variance is V^R(ri)=ri(ri1)\widehat{V}_R(r_i)=r_i(r_i-1).

Value

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

References

Greenberg, B.G., Abul-Ela, A.L., Simmons, W.R., Horvitz, D.G. (1969). The unrelated question RR model: Theoretical framework. Journal of the American Statistical Association, 64, 520-539.

Horvitz, D.G., Shah, B.V., Simmons, W.R. (1967). The unrelated question RR model. Proceedings of the Social Statistics Section of the American Statistical Association. 65-72. Alexandria, VA: ASA.

See Also

HorvitzData

HorvitzDataStCl

HorvitzDataRealSurvey

HorvitzUB

SoberanisCruz

ResamplingVariance

Examples

N=10777
data(HorvitzData)
dat=with(HorvitzData,data.frame(z,Pi))
p=0.5
alpha=0.6666667
cl=0.95
Horvitz(dat$z,p,alpha,dat$Pi,"mean",cl,N)

#Horvitz real survey
N=10777
n=710
data(HorvitzDataRealSurvey)
p=0.5
alpha=1/12
pi=rep(n/N,n)
cl=0.95
Horvitz(HorvitzDataRealSurvey$sex,p,alpha,pi,"mean",cl,N)

[Package RRTCS version 0.0.4 Index]