LISA is an
acronym standing for 'Local Indicator of
Spatial Autocorrelation,' a family of statistical methods first introducted by the French
geostatistician Luc Anselin in
1995. The most commonly used variant is the local
Moran coefficient, which is defined as:
Ii=(zi/m2)*sumj(wij*zj)
where zk=xk-avg(x) and m2=sumk(z2k/n), and is computed for each locality i and its neighbouring localities j. The wij parameter allows the researcher to define the spatial extent of the analysis.
This coefficient can be calculated for each locality in a data series, and the significance of each value of the coefficient can be determined by permutation.
What does all of this mean? By way of a LISA analysis, a researcher in possession of a spatial data series can identify hot-spots as those localities where strong spatial processes are underway.