Abstract:
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The Post Randomization Method (PRAM) is a disclosure avoidance method, where values of potentially identifying categorical variables are perturbed via some known probability mechanism. The main goal is to reduce the risk of identification, but the use of misclassified data raises issues about validity of statistical inference. We develop and implement an expectation-maximization (EM) algorithm to obtain unbiased parameter estimates of generalized linear models (GLMs) with data subject to PRAM, and thus account for the effects of PRAM and preserve data utility. The proposed technique improves on current methodology since it significantly reduces the bias that results from the unadjusted inference and enables PRAM to be applied to a larger set of models, thus increasing the applicability of PRAM to a wider range of official statistics products. We derive new standard errors of the estimates, and evaluate the effects of the level of perturbation and sample size on the reduction of bias through a number of simulation studies and by applying the proposed methodology to a dataset from the 1993 Current Population Survey.
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