Local Indicators of Spatial Association—LISA

TLDR

GIS capabilities have spurred the need for new exploratory spatial analysis techniques that focus on local patterns of spatial association. The paper proposes a new class of local indicators of spatial association (LISA) that decompose global statistics like Moran’s I into per‑observation contributions. LISA statistics serve as local nonstationarity indicators or hot spots, assess individual location influence on global metrics, and identify outliers, as demonstrated by evaluating the local Moran statistic on African conflict data and Monte Carlo simulations. Initial evaluation of the local Moran statistic shows its applicability to African conflict patterns and validates its properties through Monte Carlo simulations.

Abstract

The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the G i and G* i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.