Modifying a local measure of spatial association to account for non-stationary spatial processes.




Mackenzie, Ian Kenneth

Journal Title

Journal ISSN

Volume Title



With an increasing number of large area data sets, many study areas exhibit spatial non-stationarity or spatial variation in mean and variance of observed phenomena. This poses issues for a number of spatial analysis methods which assume data are stationary. The Getis and Ord’s Gi* statistic is a popular measure that, like many others, is impacted by non stationarity. The Gi* is used for locating hot and cold spots in marked data through the detection of spatial autocorrelation in values that are extreme relative to the global mean value, or the mean entire study area. This thesis describes modifications of the Getis and Ord’s Gi* local measure of spatial association, in part to account for regional differences (spatial non-stationarity) in a dataset. Instead of using data from the entire study area to calculate the mean parameter, as is done for the standard Gi*, I capture points for calculation of the mean using a circular distance band centred on the pivot location, which I call the local region (similar to the Ord and Getis Oi statistic). This approach can be applied to a single instance of a local region or to multiple spatial scales of the local region. I explore both in this paper using simulated datasets and a case study on mountain pine beetle infestation data. I find that the local region, when of a similar size to a true region (homogeneous section of the study area where the mean is approximately the same across locations), obtains similar results to the standard Gi* calculated separately on distinct regions (simulated to be distinct), but has the advantage of not needing explicit delineation of regional boundaries or partitioning into separate subareas. The results of a probability score for a multi-scale approach include high and low scores that are more evenly distributed across the study area and that are thus able to pick out more subtle variations within different regions. Through the case study I demonstrate how the multi-scale approach may be applied to a real dataset.



Spatial analysis, Mountain pine beetle