A modified version of Moran's I

Area of Science:

• Spatial data analysis
• Geostatistics
• Spatial statistics

Background:

• Global clustering patterns are crucial in spatial data analysis.
• Moran's I is a standard statistic for detecting global spatial patterns.
• Existing methods may not fully capture complex spatial relationships.

Purpose of the Study:

• To enhance Moran's I for improved evaluation of global clustering.
• To incorporate population density weighting into spatial statistics.
• To assess the performance of a modified Moran's I via Monte Carlo simulations.

Main Methods:

• A modified Moran's I statistic was developed, integrating a weight function into the variance calculation.
• Population density (PD) weighting was introduced to redefine neighboring associations.
• Monte Carlo simulations were conducted to compare the modified Moran's I with Moran's I and Oden's I*pop.

Main Results:

• The modified Moran's I demonstrated higher statistical power in detecting large cluster patterns (43.4%) compared to Moran's I (39.9%) and I*pop (12.4%) under specific geographic ranges.
• For global clustering patterns, the modified Moran's I consistently outperformed Moran's I and I*pop with adjacent weighting.
• In a real-world leukemia data set, the modified Moran's I yielded the lowest p-value, indicating significant global clustering.

Conclusions:

• The modified Moran's I offers superior power for detecting global and local clustering in homogeneous spatial data.
• Population density weighting significantly impacts the power to detect global clustering patterns.
• The proposed methodology can be extended to alternative Moran's I versions for heterogeneous populations.