J. Gouweleeuw, P. Kooiman, L. Willenborg and P.-P. de Wolf Statistics Netherlands. Division Research and Development. Department of Statistical Methods. Applying PRAM means that for each record in the data file according to a specified probability mechanism the score on a number of variables is changed. Since this probability mechanism is known, the characteristics of the latent true data can unbiasedly be estimated from the observed data moments in the perturbed file.
PRAM is applied to categorical variables.
It only requires pre-multiplication by the transpose of the inverted Markov transition matrix, specifying the randomisation process. Also, estimates for the additional variance introduced by PRAM are given. By a proper choice of the transition probabilities, PRAM can be applied in such a way that certain chosen marginal distributions in the original data file are left invariant in expectation. In that case the perturbed data can be used as if it were the original data. We describe how to obtain such an invariant PRAM process.