Reconstruction and normalization of LISA for spatial analysis

Area of Science:

• Geospatial Analysis
• Spatial Statistics
• Regional Science

Background:

• Local Indicators of Spatial Association (LISA) are crucial for spatial autocorrelation analysis.
• Existing LISA calculations, including local Moran and Geary indicators, contain mathematical faults.
• These faults prevent LISA from satisfying the requirement that the sum of local indicators is proportional to a global indicator.

Purpose of the Study:

• To reconstruct the calculation formulae for local Moran indexes and Geary coefficients.
• To address the mathematical inaccuracies in deriving LISA.
• To ensure LISA measures correctly relate to global indicators in spatial autocorrelation analysis.

Main Methods:

• Mathematical derivation was employed to reconstruct LISA formulae.
• Two sets of LISAs were analyzed: non-normalized weights/non-centralized variable (MI1, GC1) and row normalized weights/standardized variable (MI2, GC2).
• A third set of canonical LISAs (MI3, GC3) was proposed and validated using observational data from the Beijing-Tianjin-Hebei region.

Main Results:

• The first set of LISAs (MI1, GC1) satisfies the proportionality requirement.
• The second set of LISAs (MI2, GC2) does not satisfy the requirement.
• The proposed canonical LISAs (MI3, GC3) satisfy the requirement and offer corrected formulae for spatial autocorrelation analysis.

Conclusions:

• The study clarifies mathematical misunderstandings regarding LISA calculations.
• Corrected LISA formulae (MI1, GC1 and MI3, GC3) are provided, enhancing spatial autocorrelation analysis.
• The findings contribute to more accurate geospatial analysis by resolving fundamental issues in LISA computation.