Assessing Identification Risk in Survey Microdata

This article considers the assessment of the risk of identification of respondents in survey microdata, in the context of applications at the United Kingdom (UK) Office for National Statistics (ONS). The threat comes from the matching of categorical ’key’ variables between microdata records and external data sources and from the use of log-linear models to facilitate matching. While the potential use of such statistical models is well-established in the literature, little consideration has been given to model specification nor to the sensitivity of risk assessment to this specification. In numerical work not reported here, we have found that standard techniques for selecting log-linear models, such as chi-squared goodness of fit tests, provide little guidance regarding the accuracy of risk estimation for the very sparse tables generated by typical applications at ONS, for example tables with millions of cells formed by cross-classifying six key variables, with sample sizes of 10 or 100 thousand. In this article we develop new criteria for assessing the specification of a log-linear model in relation to the accuracy of risk estimates. We find that, within a class of ’reasonable’ models, risk estimates tend to decrease as the complexity of the model increases. We ∗Chris Skinner is Professor, Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, United Kingdom. Natalie Shlomo is research student, S3RI, University of Southampton and Department of Statistics, Hebrew University, Jerusalem, Israel.