Both Ripley's k-function and Moran's index measure the statistically significant clustering within data. However, how to know, which method is performing better for our data?
What are the advantages and disadvantages of each method which can help to choose a better method?
Maybe of minor concern, but let me note that it is kind of misleading to call Ripley's K and Moran's I methods of 'cluster analysis'. I know that ArcGIS does so, but still. Traditionally, 'cluster analysis' means making groups of initially ungrouped observations within a sample. In contrast, Ripley's K and Moran's I analyse the spatial structure of the sample. They do not create groups, but describe/test aggregation of a point pattern or spatial autocorrelation of a variable.
Ripley's K and Moran's I serve different purposes. Ripley's K describes the expected number of neighbours of any point in a point pattern across different radii. You can use it to analyse point patterns in the space, whether they are aggregated, random, or systematic. The only information you use is the coordinates (or distances between them). Moran's I analyses how a measured variable is structured in space. It uses a spatial neighbourhood matrix between the observations and a measured variable for each observation. It has a global and a local variant; with the latter, you can step across different distance classes to reveal scale-dependency in the spatial correlation. If reasonable null-hypotheses are provided, both can be used for hypothesis testing.
Anyway, it would be interesting to outline a real clustering method based on the Ripley's K or Moran's I. Maybe such a method exists already.
I tried to investigate this research question and recently published an article on it. Using empirical data on traffic crashes of vulnerable road users, I worked on a comparison of two methods. I tried to explain these 2 methods as much as possible. Both have their advantages and disadvantages and therefore the selection of the right analysis method depends on our research question and hypothesis.
One thing that is very clear and mentioned by another researcher in the answer is that Ripley's K-function is not a cluster analysis. So yes, Ripley's k-function (and G-function) are point pattern analysis whereas Moran's Index method is a cluster analysis.
The complete article can be accessed at:
Article Exploring the Robustness of Alternative Cluster Detection an...
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