Estimating uncertainty in spatial microsimulation approaches to small area estimation: a new approach to solving an old problem

A wide range of user groups from policy makers to media commentators demand ever more spatially detailed information yet the desired data are often not available at fine spatial scales. Increasingly, small area estimation (SAE) techniques are called upon to fill in these informational gaps by downscaling survey outcome variables of interest based on the relationships seen with key covariate data. In the process SAE techniques both rely extensively on small area Census data to enable their estimation and offer potential future substitute data sources in the event of Census data becoming unavailable. Whilst statistical approaches to SAE routinely incorporate intervals of uncertainty around central point estimates in order to indicate their likely accuracy, the continued absence of such intervals from spatial microsimulation SAE approaches severely limits their utility and arguably represents their key methodological weakness. The present article presents an innovative approach to resolving this key methodological gap based on the estimation of variance of the between-area error term from a multilevel regression specification of the constraint selection for iterative proportional fitting (IPF). The performance of the estimated credible intervals are validated against known Census data at the target small area and show an extremely high level of performance. As well as offering an innovative solution to this long-standing methodological problem, it is hoped more broadly that the research will stimulate the spatial microsimulation community to adopt and build on these foundations so that we can collectively move to a position where intervals of uncertainty are delivered routinely around spatial microsimulation small area point estimates.