Each respondent answers truthfully with probability
\(p = e^\epsilon/(1+e^\epsilon)\) and flips otherwise. This is LOCAL
differential privacy: there is no trusted curator, and the raw data
never leaves the respondent.
Usage
morie_randomized_response_dp(truth, epsilon = 1, seed = NULL)
Arguments
- truth
binary vector of true responses (0/1).
- epsilon
privacy budget.
- seed
optional integer seed.
Value
list with responses, p_truth,
raw_proportion, estimate (debiased), se.
Details
The raw proportion of 1s is biased toward 1/2 by construction. Use
estimate, which inverts the flip; reporting the raw proportion
is the standard misreading and understates any real effect.
References
Warner, S. L. (1965). Randomized response: a survey
technique for eliminating evasive answer bias. JASA, 60(309),
63-69.
Examples
set.seed(1)
r <- morie_randomized_response_dp(rbinom(2000, 1, 0.3), epsilon = 2)
round(r$estimate, 2)
#> [1] 0.31
