On Integrating the Number of Synthetic Data Sets m into the a priori Synthesis Approach

The synthesis mechanism given in [4] uses saturated models, along with overdispersed count distributions, to generate synthetic categorical data. The mechanism is controlled by tuning parameters, which can be tuned according to a specific risk or utility metric. Thus expected properties of synthetic data sets can be determined analytically a priori, that is, before they are generated. While [4] considered the case of generating m = 1 data set, this paper considers generating m > 1 data sets. In effect, m becomes a tuning parameter and the role of m in relation to the risk-utility trade-off can be shown analytically. The paper introduces a pair of risk metrics, tau(3)(k, d) and tau(4)(k, d), that are suited to m > 1 data sets; and also considers the more general issue of how best to analyse m > 1 categorical data sets: average the data sets pre-analysis or average results post-analysis. Finally, the methods are demonstrated empirically with the synthesis of a constructed data set which is used to represent the English School Census.