Geary's C Spatial Autocorrelation

Geary's C is a global index of spatial autocorrelation based on squared differences between neighbouring values, with an expected value of 1 and smaller values indicating positive autocorrelation.

Geary's C 는 이웃한 값들의 제곱차를 바탕으로 한 전역 공간자기상관 지수로, 기댓값이 1이며 1보다 작을수록 양의 공간자기상관을 뜻합니다.

Do neighbouring regions have more similar unemployment rates than we would expect by chance?

이웃한 지역끼리 실업률이 우연으로 기대되는 것보다 더 비슷한지 확인하고 싶어요.

Build a spatial weights matrix, compute Geary's C from the weighted squared differences between neighbours relative to the overall variance, and test it against 1 with a normal approximation or permutations. Values below 1 mean neighbours are alike and values above 1 mean neighbours differ.

When to use Geary's C Spatial Autocorrelation

• You want a single test of spatial autocorrelation for a numeric variable
• Local differences between neighbours matter more than covariance with the mean
• You want to complement Moran's I with a second global index

When to use something else

• You need to know where clusters are; use Getis-Ord Gi* or local Moran's I
• Observations are on a regular time axis rather than in space; use an autocorrelation function

Assumptions and requirements

• The spatial weights definition is appropriate (6 nearest neighbours from the coordinate columns, row-standardized, by default)
• Under the null hypothesis values are exchangeable across locations
• Every location has at least one neighbour

What the analysis reports

• Geary's C and its expected value
• z score and p-value under normality and randomization
• Permutation p-value with a fixed seed

How to report it

Geary's C with [weights definition] was [value] (E[C] = 1), z = [value], permutation p = [value] ([value] permutations), indicating [positive] spatial autocorrelation.

Related methods

• Moran's I Spatial Autocorrelation
• Getis-Ord Gi* Hot Spot Analysis
• Local Indicators of Spatial Association (LISA)

Run Geary's C Spatial Autocorrelation on Quorant