Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

A modified version of Moran's I.

  • Author(s): Jackson, Monica C;
  • Huang, Lan;
  • Xie, Qian;
  • Tiwari, Ram C
  • et al.
Abstract

Background

Investigation of global clustering patterns across regions is very important in spatial data analysis. Moran's I is a widely used spatial statistic for detecting global spatial patterns such as an east-west trend or an unusually large cluster. Here, we intend to improve Moran's I for evaluating global clustering patterns by including the weight function in the variance, introducing a population density (PD) weight function in the statistics, and conducting Monte Carlo simulation for testing. We compare our modified Moran's I with Oden's I*pop for simulated data with homogeneous populations. The proposed method is applied to a census tract data set.

Methods

We present a modified version of Moran's I which includes information about the strength of the neighboring association when estimating the variance for the statistic. We provide a power analysis on Moran's I, a modified version of Moran's I, and I*pop in a simulation study. Data were simulated under two common spatial correlation scenarios of local and global clustering.

Results

For simulated data with a large cluster pattern, the modified Moran's I has the highest power (43.4%) compared to Moran's I (39.9%) and I*pop (12.4%) when the adjacent weight function is used with 5%, 10%, 15%, 20%, or 30% of the total population as the geographic range for the cluster.For two global clustering patterns, the modified Moran's I (power > 25.3%) performed better than both Moran's I (> 24.6%) and I*pop (> 7.9%) with the adjacent weight function. With the population density weight function, all methods performed equally well.In the real data example, all statistics indicate the existence of a global clustering pattern in a leukemia data set. The modified Moran's I has the lowest p-value (.0014) followed by Moran's I (.0156) and I*pop (.011).

Conclusions

Our power analysis and simulation study show that the modified Moran's I achieved higher power than Moran's I and I*pop for evaluating global and local clustering patterns on geographic data with homogeneous populations. The inclusion of the PD weight function which in turn redefines the neighbors seems to have a large impact on the power of detecting global clustering patterns. Our methods to improve the original version of Moran's I for homogeneous populations can also be extended to some alternative versions of Moran's I methods developed for heterogeneous populations.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View