International Journal of Health Geographics 2010, 9:33, 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