  The assessment of water quality across space and time is of considerable
interest for both agricultural and public health reasons. The standard method
to assess the water quality of a catchment, or a group of catchments, usually
involves collecting point measurements of water quality and other additional
information such as the date and time of measurements, rainfall amounts, the
land-use and soil-type of the catchment and the elevation. Some of this
auxiliary information will be point data, measured at the exact location,
whereas other such as land-use will be areal data often in a compositional
format. Two problems arise if analysts try to incorporate this information into
a statistical model in order to predict (for example) the influence of land-use
on water quality. First is the spatial change of support problem that arises
when using areal data to predict outcomes at point locations. Secondly, the
physical process driving water quality is not compositional, rather it is the
observation process that provides compositional data. In this paper we present
an approach that accounts for these two issues by using a latent variable to
identify the land-use that most likely influences water quality. This latent
variable is used in a spatial mixture model to help estimate the influence of
land-use on water quality. We demonstrate the potential of this approach with
data from a water quality research study in the Mount Lofty range, in South
Australia.
