A simplified perspective on the index of spatial autocorrelation

Abstract

Context

A recent article in Landscape Ecology presented a method to true Moran’s I to its conceptual ideals and existing intuition regarding correlations. It’s scope included multiple methods, exploration of designed and empirical datasets, sensitivity analyses, and extensive mathematical treatment. The editor, reviewers, and lead author feared that the article due to complexity would not be accessible to empirical landscape ecologists.

Objectives

This perspective aims to highlight critical problems with the traditional autocorrelation metric and make standout material from the larger analysis accessible by paring to essentials and presenting a simple recipe to calculate an improved metric that also serves as a statistic.

Methods

Desirable traits for an autocorrelation metric were reviewed followed by distillation of best practices discerned in the larger project to attain those traits. A minimal method to obtain the superior metric was formulated.

Results

Moran’s I met only 2 of 14 desirable qualities for indexing autocorrelation. An improved metric was found to be achievable in 7 steps. The new metric, now a statistic, realized 14 of 14 desirable traits. The new statistic fit existing intuition for regular correlation and facilitated comparisons across disparate contexts.

Conclusions

Spatial autocorrelation is a common focus in landscape ecology. The new statistic enabled intuitive interpretation and meaningful comparison within and among studies. It provided for meta-analysis and meta-research, such as co-use with other spatial pattern statistics. These improvements should foster sustained use and impact of the new autocorrelation statistic I_r.