Mangat: Mangat model

Description

Computes the randomized response estimation, its variance estimation and its confidence interval through the Mangat model. The function can also return the transformed variable. The Mangat model was proposed by Mangat in 1992.

Usage

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

Arguments

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

proportion of marked cards with the sensitive attribute in the second box

alpha

proportion of people with the innocuous attribute

proportion of marked cards with "True" in the first box

vector of the first-order inclusion probabilities

type

the estimator type: total or mean

confidence level

size of the population. By default it is NULL

pij

matrix of the second-order inclusion probabilities. By default it is NULL

Value

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

Details

In Mangat's method, there are two boxes, the first containing cards marked "True" and "RR" in proportions $t$ and $(1 - t), (0 < t < 1)$ . A person drawing a "True" marked card is asked to tell the truth about bearing $A$ or $A^{c}$ . A person drawing and <U+201C>RR<U+201D> marked card is then asked to apply Horvitz<U+2019>s device by drawing a card from a second box with cards marked $A$ and $B$ in proportions $p$ and $(1 - p)$ . If an $A$ marked card is now drawn the truthful response will be about bearing the sensitive attribute $A$ and otherwise about $B$ . The true proportion of people bearing $A$ is to be estimated but $α$ , the proportion of people bearing the innocuous trait $B$ unrelated to $A$ , is assumed to be known. The observed variable is $z_{i} = {\begin{array}{lcc} y_{i} & if a card marked "True" is drawn from the first box \\ I_{i} & if a card marked "RR" is drawn \end{array}$ where $I_{i} = {\begin{array}{lcc} 1 & if the type of card drawn from the second box matches trait A or B \\ 0 & if the type of card drawn from the second box does not match trait A or B . \end{array}$

The transformed variable is $r_{i} = \frac{z_{i} - (1 - t) (1 - p) α}{t + (1 - t) p}$ and the estimated variance is ${\hat{V}}_{R} (r_{i}) = r_{i} (r_{i} - 1)$ .

References

Mangat, N.S. (1992). Two stage randomized response sampling procedure using unrelated question. Journal of the Indian Society of Agricultural Statistics, 44, 82-87.

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