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Measuring the Disclosure Risk for Multiway Tables with Fixed Marginals Corresponding to Decomposable Loglinear Models

Adrian Dobra

Abstract:

The underlying connection between disclosure avoidance techniques for categorical data and sampling from the exact conditional distribution associated with a loglinear model is the data swaps necessary to link all the contingency tables having a set of fixed marginal totals. In this paper we show that simple data swaps are the only swaps needed when the set of fixed margins define a decomposable graph. Furthermore, we characterize the set of data swaps associated with more general graphical structures.

Keywords: Contingency tables; Decomposable loglinear models; Reducible loglinear models; Disclosure limitation; Exact distributions; Markov chain Monte Carlo

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