17.5 Which Local Statistic to Use?

In practice, the choice between the three main classes of local spatial autocorrelation statistics covered so far may seem a bit bewildering. They each provide a slightly different perspective on the notion of clusters and spatial outliers. The main difference is between the Local Moran and the Local Geary, with the latter potentially picking up nonlinear relationships which the Local Moran is not able to. However, the extent to which this matters in practice depends on the particular application.

When the results between the two approaches differ much, a closer examination is in order. For example, this could consist of inspecting the values of identified clusters and their neighbors to look for the potential impact of outliers. Such an investigation may also be in order when the results for the conventional and Median Local Moran differ much.

The Getis-Ord statistics are different in that they do not account for spatial outliers. Whether this matters depends on the particular context. In general, they tend to identify the same locations as significant as the Local Moran.

For all the local statistics, a careful consideration of significance is in order. Locations that remain identified as clusters or outliers under different criteria (as well as using different statistics) are likely interesting locations. On the other hand, observations that move in and out of significance as the criteria change are likely spurious. The only way to address this problem confidently is though a careful sensitivity analysis.