A Comparison of Synthetic Reconstruction and Combinatorial Optimisation Approaches to the Creation of Small-area Microdata

The work reported here offers for the first time a thorough comparison of two established methodologies for the creation of small area synthetic microdata, synthetic reconstruction and combinatorial optimisation. Two computer models, Pop91SR and Pop91CO, have been developed for the reconstruction of ED level populations drawing upon 1991 Census data. The adequacy of their outputs has been assessed at cellular, tabular and overall levels. Consideration has also been given to the impact on outputs of aggregating ED estimates into wards. Compared with previous synthetic reconstruction models, Pop91SR employs the following new techniques: (a) use of the SAR to examine relationships between variables and determine the ordering of conditional probabilities; (b) a three-level modelling approach to create the conditional distributions, combining data from the SAS, LBS and SAR; and (c) adoption of a modified Monte Carlo sampling procedure. These techniques maximise the use of information and greatly reduce the sampling error, thereby increasing estimation accuracy. The major improvements in Pop91CO are: (a) using a new criterion (RSSZm) for the selection of household combinations; (b) selection of households from the relevant SAR region, where possible; and (c) a revised set of stopping rules to control the number of iterations and improve the consistency of outputs. Using RSSZm as the selection criterion yields significant improvements in the quality of the synthetic data generated. An assessment of outputs from the two rival approaches, produced using the same smallarea constraints, suggests that both can produce synthetic microdata that fit constraining tables extremely well. But further examination reveals that the variability of datasets generated by combinatorial optimisation is considerably less than that for datasets created by synthetic reconstruction, at both ED and ward levels, making combinatorial optimisation the approach of choice for the creation of a single set of synthetic microdata. Acknowledgements The work reported in this paper was undertaken as part of an ESRC-funded project on ‘The creation of a national set of validated small-area microdata’, award no. R000237744.