A new visualization for Local Moran's I (seeking feedback and suggestions)

[Lee Mason]

Hello!

I have noticed that there isn't a single, unified plot design that captures all of the main elements involved in a Local Moran's I calculation and how they relate to each other. In an attempt to fill this gap I'd like to propose a new plot design: the Moran dual-density plot. 

I'd like to introduce this plot here, and if anybody is kind enough to provide feedback it would be much appreciated! For a quick, interactive introduction to the plot with many examples, please see this online Observable Notebook. 

Here is an example:

To explain the design, I've made a less dense, labelled version of the plot which:



In essence, the plot shows the value at the focal location, the value of the neighbors, the spatial lag, and the Local Moran's I value. At the top is are density plots of the target values and spatial lags across the dataset, and at the bottom is a density plot of the permuted statistic values (along with p-value cut-offs).

The aim of this plot design is to make the relationships between the various elements of Moran's I calculation clearer, especially in an exploratory context where information has to conveyed to the user quickly. The plot shows how the neighbor values contribute to the lag and how the lag is directly proportional to the resulting Local Moran's I value. It contextualizes the focal and neighbor values with the top density plot, and contextualizes the p-value and label with the bottom density plot. It also shows potentially useful information like the spread of a location's neighbor values: are they close together? Are there extreme values contributing to a significant result? I also think it indirectly shows one of the less intuitive (in my opinion) aspects of Local Moran's I: the magnitude of the focal value contributes to the Local Moran's I value but doesn't contribute to the p-value. 

Because the plot only shows a single location's value, it is most useful when used in tandem with other plots. To demonstrate the plot in this context, we have created a basic online dashboard here: https://episphere.github.io/moranplot/. 

I'd really love some feedback for the plot's design. Do you think it would be useful? Do you have any suggestions? Are there any confusing elements that should be modified or removed? Is the lag density plot useful or distracting?  Are there any useful elements missing? 

At present, the plot is only implemented in an open-source JS library called MoranPlot (with some other Moran's I plots). But I'd love to implement it for other software environments (especially GeoDa!) if there's interest.

Thanks!
Lee