What values of Moran’s I and Theil index decomposition really mean under different conditions: on the issue of interpretation

Abstract

In recent decades, improved methodological apparatuses and increased data availability have enhanced data analyses in social sciences. Moreover, complex analyses using sophisticated methods take just a matter of seconds nowadays thanks to highly powerful software. However, such methods are often poorly understood from a methodological point of view despite the fact that knowledge of their specific properties is crucial to accurately interpreting the results. In this paper we study methods of spatial aspects of variability and examine a specific property of such methods to demonstrate how it can affect the final interpretation. By modelling data in a regular 100 by 100 grid as well as empirical examples from Czechia based on data from the 2011 Czech census, this paper presents possible interpretation-biases and recommendations for how to avoid them. We use the example of spatial autocorrelation (measured by Moran’s I) and variability decomposition (measured by the Theil index); two basic methods which enable us to measure variability in regions and in space.