Horvitz: Horvitz model

In RRTCS: Randomized Response Techniques for Complex Surveys

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 n (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 i a box containing a large number of identical cards, with a proportion p,(0 <p < 1) bearing the mark A and the rest marked B (an innocuous attribute whose population proportion α is known). The response solicited denoted by z_i takes the value y_i if i bears A and the card drawn is marked A or if i bears B and the card drawn is marked B. Otherwise z_i takes the value 0.

The transformed variable is r_i=\frac{z_i-(1-p)α}{p} and the estimated variance is \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)

RRTCS documentation built on April 21, 2021, 9:06 a.m.