On integrating the number of synthetic data sets m into the 'a priori' synthesis approach
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Until recently, multiple synthetic data sets were always released to analysts, to allow valid inferences to be obtained. However, under certain conditions - including when saturated count models are used to synthesize categorical data - single imputation (m=1) is sufficient. Nevertheless, increasing m causes utility to improve, but at the expense of higher risk, an example of the risk-utility trade-off. The question, therefore, is: which value of m is optimal with respect to the risk-utility trade-off? Moreover, the paper considers two ways of analysing categorical data sets: as they have a contingency table representation, multiple categorical data sets can be averaged before being analysed, as opposed to the usual way of averaging post-analysis. This paper also introduces a pair of metrics, τ_3(k,d) and τ_4(k,d), that are suited for assessing disclosure risk in multiple categorical synthetic data sets. Finally, the synthesis methods are demonstrated empirically.
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