Demystifying Spatial Dependence: Interactive Visualizations for Interpreting Local Spatial Autocorrelation

TL;DR

Local Moran's I is a key tool for identifying localized spatial autocorrelation, but its interpretation is hindered by multiple interacting calculation elements and neighbor relationships. Local Moran's I for a location is $I_i = \frac{z_i \cdot lag_i}{n-1}$ with $lag_i = \sum_j W'_{ij} z_j$, and significance is determined via permutation to yield a pseudo p-value. The paper presents three interactive visualizations—the Moran Dual-Density Plot, Moran Network Scatterplot, and Spatial Lag Radial Plot—implemented in an open-source JavaScript library and demonstrated in a browser dashboard, with plots linked through shared axes and overlays. This in-browser toolkit enhances interpretability and supports rapid exploratory analysis of local spatial autocorrelation, demonstrated on US cancer mortality data and designed for both novice and expert geospatial analysts.

Abstract

The Local Moran's I statistic is a valuable tool for identifying localized patterns of spatial autocorrelation. Understanding these patterns is crucial in spatial analysis, but interpreting the statistic can be difficult. To simplify this process, we introduce three novel visualizations that enhance the interpretation of Local Moran's I results. These visualizations can be interactively linked to one another, and to established visualizations, to offer a more holistic exploration of the results. We provide a JavaScript library with implementations of these new visual elements, along with a web dashboard that demonstrates their integrated use.

Figures (4)

• Figure 1: The Moran dual-density plot showing a negative z-score normalized attribute value and a negative spatial lag. The blue points are within the positive significance area, indicating that the statistic exhibits significant positive spatial autocorrelation.
• Figure 2: The Moran network scatterplot showing a high-high result connected to three other high-high results, a low-high result, and a non significant result.
• Figure 3: A spatial lag radial plot (right) showing a location with positive spatial autocorrelation. Note how the the substantially high value to the North West is primarily responsible for the lag exceeding the threshold for significance.
• Figure 4: A screenshot of the MoranPlot dashboard which provides an integrated example of the plots introduced in this work. Here, the user has hovered over the US county of Freestone, Texas and the corresponding result is conveyed in the other plots. The dashboard can be accessed at https://episphere.github.io/moranplot.