lisa {elsa}R Documentation

Local indicators of Spatial Associations


Calculate local indicators of spatial association (LISA) for a continuous (numeric) variable at each location in a Raster layer or a SpatialPointsDataFrame or a SpatialPolygonsDataFrame.





a raster object (RasterLayer or SpatialPointsDataFrame or SpatialPolygonsDataFrame


numeric lower bound of local distance (default=0), or an object of class neighbours created by dneigh when x is SpatialPoints or SpatialPolygons


numeric upper bound of local distance, not needed if d1 is a neighbours object,


a character string specifying the LISA statistic that should be calculated. This can be one of "I" (or "localmoran" or "moran"), "c" (or "localgeary" or "geary"), "G" (or "localG"), "G*" (or "localG*")


additional arguments including filename (only when x is Raster, specifies the name of the raster file when the output should be written; additional arguments for writeRaster function can also be specified); mi (only when x is Raster and statistic='I', specifies whether raw Local Moran's I statistic (Ii) should be returned, or standardized value (Z.Ii). e.g., mi="I", mi='Z' (default)); zcol (only when x is a Spatial* object specifies the name of the variable column in the data); longlat (logical, only when x is a Spatial* object specifies whether the coordinate system is geographic); drop (logical, only when x is a Spatial* object, if TRUE, the original data structure (Spatial* object) is returned, otherwise a numeric vector is returned)


This function can calculate different LISA statistics at each location in the input dataset. The statistics, implemented in this function, include local Moran's I ("I"), local Geary's c ("c"), local G and G* ("G" and "G*"). This function returns standardized value (Z) for Moran, G and G*.



if x is a RasterLayer


if x is a Spatial* and drop=FALSE

numeric vector

if x is a Spatial* and drop=TRUE


Babak Naimi


Naimi, B., Hamm, N. A., Groen, T. A., Skidmore, A. K., Toxopeus, A. G., & Alibakhshi, S. (2019). ELSA: Entropy-based local indicator of spatial association. Spatial statistics, 29, 66-88. Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, 93–115;

Getis, A. and Ord, J. K. 1996 Local spatial statistics: an overview. In P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment (Cambridge: Geoinformation International), 261–277.


file <- system.file('external/dem_example.grd',package='elsa')
r <- raster(file)

plot(r,main='a continuous raster map')

mo <- lisa(r,d2=2000,statistic='i') # local moran's I (Z.Ii value)

plot(mo, main="local Moran's I (Z.Ii)")

mo <- lisa(r,d2=2000,statistic='i',mi='I') # local moran's I (Ii value  (non-standardized))

plot(mo, main="local Moran's I (Ii))")

gc <- lisa(r,d2=2000,statistic='c') # local Geary's c

plot(gc, main="local Geary's c")

g <- lisa(r,d2=2000,statistic='g') # local G

plot(g, main="local G")

[Package elsa version 1.1-28 Index]