Moran's I Spatial Autocorrelation

Moran's I is a statistic that measures global spatial autocorrelation, indicating whether values of a variable at nearby locations are more similar (clustered) or more dissimilar (dispersed) than expected under spatial randomness.

모란 I는 인접 위치의 변수값이 공간적 무작위 상태에서 기대되는 것보다 더 비슷한지(군집) 또는 더 다른지(분산)를 나타내는 전역 공간자기상관 통계량이다.

How do I test whether values of a variable are spatially clustered on a map?

변수 값이 지도상에서 공간적으로 군집되어 있는지 어떻게 검정하나요?

Moran's I tests whether a variable shows spatial clustering by comparing each location's value with values at neighboring locations defined by a spatial weights matrix. Positive values indicate clustering of similar values, and local Moran's I (LISA) is used to locate specific hot spots.

When to use Moran's I Spatial Autocorrelation

• One variable measured at areal units or points with coordinates
• Checking whether a pattern on a map is spatially clustered
• Testing regression residuals for spatial dependence

When to use something else

• Locating where clusters are; use local Moran's I (LISA) or Getis-Ord Gi*
• Modeling the outcome with spatial dependence; use spatial lag or spatial error regression

Assumptions and requirements

• Appropriate spatial weights matrix
• Stationarity of the mean and variance across the study area
• Inference by normal approximation or permutation

What the analysis reports

• Moran's I statistic
• Expected value under randomness
• z-score and p-value (analytic or permutation)
• Moran scatterplot

How to report it

[Variable] showed significant positive spatial autocorrelation, Moran's I = [value], z = [value], p = [value].

Related methods

• Local Moran's I (LISA)
• Getis-Ord Gi*
• Geary's C

Run Moran's I Spatial Autocorrelation on Quorant