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 Gi 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.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1995.tb00338.x

Local Indicators of Spatial Association—LISA

Dengue is a systemic viral infection transmitted between humans by Aedes mosquitoes. For some patients, dengue is a life-threatening illness. There are currently no licensed vaccines or specific therapeutics, and substantial vector control efforts have not stopped its rapid emergence and global spread. The contemporary worldwide distribution of the risk of dengue virus infection and its public health burden are poorly known. Here we undertake an exhaustive assembly of known records of dengue occurrence worldwide, and use a formal modelling framework to map the global distribution of dengue risk. We then pair the resulting risk map with detailed longitudinal information from dengue cohort studies and population surfaces to infer the public health burden of dengue in 2010. We predict dengue to be ubiquitous throughout the tropics, with local spatial variations in risk influenced strongly by rainfall, temperature and the degree of urbanization. Using cartographic approaches, we estimate there to be 390 million (95% credible interval 284-528) dengue infections per year, of which 96 million (67-136) manifest apparently (any level of disease severity). This infection total is more than three times the dengue burden estimate of the World Health Organization. Stratification of our estimates by country allows comparison with national dengue reporting, after taking into account the probability of an apparent infection being formally reported. The most notable differences are discussed. These new risk maps and infection estimates provide novel insights into the global, regional and national public health burden imposed by dengue. We anticipate that they will provide a starting point for a wider discussion about the global impact of this disease and will help to guide improvements in disease control strategies using vaccine, drug and vector control methods, and in their economic evaluation.

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The global distribution and burden of dengue

Statistics for Spatial Data.

Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran’s I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i ∗ statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.

http://archive.nefmc.org/tech/cte_mtg_docs/130516/CATT%20Report/Getis-Ord%20statistic.pdf

The Analysis of Spatial Association by Use of Distance Statistics

ilbstract. Autocorrelation is a very general statistical property of ecological variables observed across geographic space; its most common forms are patches and gradients. Spatial autocorrelation. which comes either from the physical forcing of environmental variables or from community processes, presents a problem for statistical testing because autocorrelated data violate the assumption of independence of most standard statistical procedures. The paper discusses first how autocorrelation in ecological variables can be described and measured. with emphasis on mapping techniques. Then. proper statistical testing in the presence of autocorrelation is briefly discussed. Finally. ways are presented of explicitly introducing spatial structures into ecological models. Two approaches are proposed: in the raw-data approach, the spatial structure takes the form of a polynomial of the x and .v geographic coordinates of the sampling stations; in the matrix approach. the spatial structure is introduced in the form of a geographic distance matrix among locations. These two approaches are compared in the concluding section. A table provides a list of computer programs available for spatial analysis.

https://www.jstor.org/stable/pdfplus/1939924.pdf

Spatial Autocorrelation: Trouble or New Paradigm?

The statistics Gi(d) and Gi*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1995.tb00912.x

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W, based on the principle that spatial structure should be considered in a two-part framework, those units that evoke a distance effect, and those that do not. Our two-variable local statistics model (LSM) is based on the G i * local statistic. The local statistic concept depends on the designation of a critical distance, d c , defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well-known spatial weights matrix specifications – two different contiguity configurations, three different inverse distance formulations, and three semi-variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran’s I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.2004.tb01127.x

Constructing the Spatial Weights Matrix Using a Local Statistic

/pdf/handbook-of-applied-spatial-analysis-1k6br7vyi9.pdf

Handbook of Applied Spatial Analysis

In this paper, we discuss a number of general issues that pertain to the interface between GIS and spatial analysis. In particular, we focus on the various paradigms for spatial data analysis that follow from the existence of this interface. We outline a series of questions that need to be confronted in the analysis of spatial data, and the extent to which a GIS can facilitate their resolution. We also review a number of exploratory and confirmatory techniques that we feel should form the core of a spatial analysis module for a GIS.

Arthur Getis

Papers

The Analysis of Spatial Association by Use of Distance Statistics

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

Constructing the Spatial Weights Matrix Using a Local Statistic

Handbook of Applied Spatial Analysis

Spatial Statistical Analysis and Geographic Information Systems