GIS and Spatial Autocorrelation

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Spatial autocorrelation is simply looking at how well objects correlate with other nearby objects across a spatial area. Positive autocorrelation occurs when many similar values are located near each other, while negative correlation is common where very different results are found near each other. The importance of spatial autocorrelation is it helps to define how important spatial characteristics in affecting a given object in space and if there is a clear relationship (i.e., dependency) of objects with spatial properties. Strongly positive or negative results indicate that a clear spatial property is found in the object with a high correlation. The method gained increasing prominence in the 1980s as a spatial analytical approach, but had been developed already by the early 1950s.[1]

Types of Common Spatial Autocorrelation in GIS Software

Perhaps the most common way in which autocorrelation is measured is using Moran’s I, which now has become incorporated in commonly used packages such as ArcGIS as well as open source software such as GRASS and QGIS. Moran’s I allows the correlation measure to measure how well something correlates based on multiple dimensions across a given space. Results are generally used to measure how well an object correlates globally, that is across a given defined space for a dataset. Geary’s ratio (or C) is another similar measure, where this measure is more sensitive to local variations and can be used to define local patterning within a dataset.[2]

Spatial Autocorrelation is Used to Understand Associations

Studies applying spatial autocorrelation have shown strong association with factors such as language and species diversity.[3] Land use and land cover types show strong correlation results.[4] Autocorrelation has also been utilized to look at the effects of health care and survival rates based on spatial-based factors.[5] More recently, economists, who have been relatively late in utilizing spatial regression and autocorrelation techniques in econometric measures, have now also utilized spatial autocorrelation to investigate a variety of econometric indicators, including where traditional regression analyses would have been used.[6]

Spatial distributions of (a) language richness, (b) mammal richness and (c) elevation across the New Guinea mainland. From Turvey & Pettorelli, 2014).

Spatial distributions of (a) language richness, (b) mammal richness and (c) elevation across the New Guinea mainland. From Turvey & Pettorelli, 2014).

Issues with Spatial Autocorrelation in GIS

In general, spatial autocorrelation has a lot of utility for GIS users as it provides an indication of clear spatial correlation for given data. However, studies have noted there are faults with using standard autocorrelation methods such as Moran’s I. For instance, most method assume an initial independence of datasets.[7] This assumption may not be valid and techniques might be needed to adjust assumptions so that autocorrelation is determined based on initial bias as well. Alternative techniques adjust for biases.[8] Studies have shown that assumptions for statistical tests need to be investigated prior to applying spatial autocorrelation. With such adjustments and application along with more typical autocorrelation techniques, spatial dependency of data are better assessed for their empirical qualities.

References

[1] For more on the basics of spatial autocorrelation, see:  Griffith, D. A. (2011). Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Berlin: Springer.

[2] For more on Morran’s I and Gary’s ratio, see:  O’Sullivan, D., & Unwin, D. (2010). Geographic information analysis (2nd ed). Hoboken, N.J: John Wiley & Sons, pg. 167.

[3] For more on species and language diversity, see:  Turvey, S. T., & Pettorelli, N. (2014). Spatial congruence in language and species richness but not threat in the world’s top linguistic hotspot. Proceedings of the Royal Society B: Biological Sciences, 281(1796), 20141644–20141644.

[4] For studies on autocorrelation on landscape and land use studies, see:  Fan, C., & Myint, S. (2014). A comparison of spatial autocorrelation indices and landscape metrics in measuring urban landscape fragmentation. Landscape and Urban Planning, 121, 117–128.

[5] For example of a spatial autocorrelation approach, see:  Prudhomme O’Meara, W., Platt, A., Naanyu, V., Cole, D., & Ndege, S. (2013). Spatial autocorrelation in uptake of antenatal care and relationship to individual, household and village-level factors: results from a community-based survey of pregnant women in six districts in western Kenya. International Journal of Health Geographics, 12(1), 55.

[6] For more on econometric measures used in spatial autocorrelation, see:  Anselin, L. (2010). Spatial Econometrics: Methods and Models. Dordrecht: Springer Netherlands.

[7] For an example problem of interpretation using autocorrelation techniques, see:  Cardillo, M., Bromham, L., & Greenhill, S. J. (2015). Links between language diversity and species richness can be confounded by spatial autocorrelation: Table 1. Proceedings of the Royal Society B: Biological Sciences, 282(1809), 20142986.

[8] For an example in adjusting to bias in autocorrelation application, see:  Piani, C., Haerter, J. O., & Coppola, E. (2010). Statistical bias correction for daily precipitation in regional climate models over Europe. Theoretical and Applied Climatology, 99(1–2), 187–192.

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