A decomposition of Moran's I for clustering detection

• Published in: Computational statistics & data analysis Vol. 51; no. 12; pp. 6123 - 6137
• Main Authors: Zhang, Tonglin, Lin, Ge
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-08-2007; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Clustering and clusters; Exact sciences and technology; General topics; High-value clustering; Linear inference, regression; Low-value clustering; Mathematics; Multivariate analysis; Negative autocorrelations; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Positive autocorrelations; Probability and statistics; Random permutations; Sciences and techniques of general use; Statistics; Clustering and clusters; Low-value clustering; Negative autocorrelations; High-value clustering; Positive autocorrelations; Random permutations; Cluster analysis (statistics); Decomposition method; Decomposition; Variance; Spatial statistics; Random test; Distribution function; Stream; P value; Data analysis; Test statistic; Permutation; Statistical method; Spatial distribution; Statistical computation; Simulation; Permutation test; Correlation analysis; Asymptotic normality; Autocorrelation
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2006.12.032

The test statistics
I
h
,
I
c
, and
I
n
are derived by decomposing the numerator of the Moran's
I test for high-value clustering, low-value clustering, and negative autocorrelation, respectively. Formulae to compute the means and variances of these test statistics are derived under a random permutation test scheme, and the
p-values of the test statistics are computed by asymptotic normality. A set of simulations shows that test statistic
I
h
is likely to be significant only for high-value clustering, test statistic
I
c
is likely to be significant only for low-value clustering, and test statistic
I
n
is likely to be significant only for negatively correlated spatial structures. These test statistics were used to reexamine spatial distributions of sudden infant death syndrome in North Carolina and the pH values of streams in the Great Smoky Mountains. In both analyses, low-value clustering and high-value clustering were shown to exit simultaneously.