Development and application of multivariate spatial clustering statistics

Abstract

In spatial statistics, several methods have been developed to measure the extent of local and global spatial dependence (clustering) in measured data across areas in a region of research interest. These methods are now routinely implemented in most Geographical Information Systems (GIS) and statistical computer packages. However, spatial statistics for measuring joint spatial dependence of multiple spatial measurement and outcome data have not been well developed. A naive analysis would simply apply univariate spatial dependence methods to each data separately. Though this is simple and straightforward, it ignores possible relationships between multiple spatial data because they may be measuring the same phenomena. Limited work has been done on extending the Moran’s index, a commonly used and applied univariate measure of spatial clustering, to bivariate Moran’s index in order to assess spatial dependence for two spatial data. The overall aim of this PhD was to develop multivariate spatial clustering methods for multiple spatial data, especially in the health sciences. Our proposed multivariate spatial clustering statistic is based on the fundamental theory regarding canonical correlations. We firstly reviewed and applied univariate and bivariate Moran’s indexes to spatial analyses of multiple non-communicable diseases and related risk factors in South Africa. Then we derived our proposed multivariate spatial clustering method, which was evaluated by simulation studies and applied to a spatial analysis of multiple non-communicable diseases and related risk factors in South Africa. Simulation studies showed that our proposed multivariate spatial statistic was able to identify correctly clusters of areas with high risks as well as clusters with low risk.