  In low and middle income countries, household surveys are a valuable source
of information for a range of health and demographic indicators. Increasingly,
subnational estimates are required for targeting interventions and evaluating
progress towards targets. In the majority of cases, stratified cluster sampling
is used, with clusters corresponding to enumeration areas. The reported
geographical information varies. A common procedure, to preserve
confidentiality, is to give a jittered location with the true centroid of the
cluster is displaced under a known algorithm. An alternative situation, which
was used for older surveys in particular, is to report the geographical region
within the cluster lies. In this paper, we describe a spatial hierarchical
model in which we account for inaccuracies in the cluster locations. The
computational algorithm we develop is fast and avoids the heavy computation of
a pure MCMC approach. We illustrate by simulation the benefits of the model,
over naive alternatives.
