A Mixture Model Approach for Compositional Data: Inferring Land-Use Influence on Point-Referenced Water Quality Measurements

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 sub-catchment, or a group of sub-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 is point-referenced data, measured at the exact location, whereas other such as land use is areal data often recorded in a compositional format at the catchment or sub-catchment level. The spatial change of support inherited by this data collection process breaks the natural link between the response variable and the predictors. In this paper, we present an approach to reconstruct this link by using a categorical latent variable that identifies the land use that most likely influences water quality in each sub-catchment. This constitutes the spatial clustering layer of the model. Each cluster is associated with an estimated temporal variability common to water quality measurements. The strength of this approach lies in the temporal variation identifying each cluster, allowing decision makers to make inform decision regarding land use and its influence over 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.