Local Indicators of Spatial Association (LISA)

Local indicators of spatial association (LISA) are statistics, most commonly local Moran's I, that identify where individual areas form significant clusters of similar values or spatial outliers relative to their neighbors.

국지적 공간연관성 지표(LISA)는 주로 국지적 Moran's I를 이용해 개별 지역이 이웃과 비교하여 유사한 값의 유의한 군집이나 공간 이상치를 이루는 곳을 찾아내는 통계량이다.

How do I find where hot spots, cold spots and spatial outliers are located on a map?

지도에서 핫스팟, 콜드스팟, 공간 이상치가 어디에 있는지 어떻게 찾나요?

LISA decomposes global spatial autocorrelation into a local statistic for each area, classifying locations as high–high or low–low clusters and high–low or low–high outliers. It fits areal data such as districts or grid cells when you need to know where clustering occurs rather than only whether it exists.

When to use Local Indicators of Spatial Association (LISA)

• Areal data such as census tracts, districts or grid cells with a numeric variable
• Mapping high–high and low–low clusters and spatial outliers
• Following up a significant global Moran's I

When to use something else

• You only need an overall measure of clustering: use global Moran's I
• You want to explain the variable with predictors while accounting for spatial dependence: use a spatial lag or spatial error model

Assumptions and requirements

• A defined spatial weights matrix (contiguity or distance based)
• Permutation-based inference for significance
• Adjustment for multiple testing or a stricter significance level
• Results may depend on the zoning and scale of areas (MAUP)

What the analysis reports

• Local Moran's I for each area
• Pseudo p-values from permutations
• LISA cluster map
• Moran scatterplot
• Global Moran's I for reference

How to report it

Global Moran's I was [value] (p = [value]), and the LISA analysis identified [n] high–high clusters and [n] low–low clusters at p < .05.

Related methods

• Moran's I
• Getis-Ord Gi* Hot Spot Analysis
• Geographically Weighted Regression (GWR)

Run Local Indicators of Spatial Association (LISA) on Quorant