Recover a population rate from deliberately noised answers

The respondent answers one of two questions chosen by a private randomiser, so no individual answer reveals anything – which is what makes people answer honestly. The rate is still identified because the noise mechanism is known. The estimator blows up as p nears one half, where the answer carries no information at all.

Usage

Randres(y, truth = NULL, p = 0.7)

Arguments

y

Observed yes/no answers.

truth

True statuses when known; reported only.

p

Probability the randomiser selected the sensitive question.

Value

List with estimate, se, lambda, truth_rate, n.

Details

Formula: pi = (lambda - (1 - p))/(2p - 1), Var = lambda(1 - lambda)/(n (2p - 1)^2).

References

Warner, S. L. (1965). JASA 60:63-69, equations (1), (3).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Randres(V)
#> $estimate
#> [1] 10.5
#> 
#> $se
#> [1] NaN
#> 
#> $lambda
#> [1] 4.5
#> 
#> $truth_rate
#> [1] NaN
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Warner randomized response estimator"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"