How Cluster and Outlier Analysis (Anselin Local Moran's I) works

Given a set of features (Input Feature Class) and an analysis field (Input Field), the Cluster and Outlier Analysis tool identifies spatial clusters of features with high or low values. The tool also identifies spatial outliers. To do this, the tool calculates a local Moran's I value, a z-score, a p-value, and a code representing the cluster type for each statistically significant feature. The z-scores and p-values represent the statistical significance of the computed index values.

Calculations

Local Moran's I mathematics

View additional mathematics for the local Moran's I statistic.

Interpretation

A positive value for I indicates that a feature has neighboring features with similarly high or low attribute values; this feature is part of a cluster. A negative value for I indicates that a feature has neighboring features with dissimilar values; this feature is an outlier. In either instance, the p-value for the feature must be small enough for the cluster or outlier to be considered statistically significant. For more information on determining statistical significance, see What is a z-score? What is a p-value? Note that the local Moran's I index (I) is a relative measure and can only be interpreted within the context of its computed z-score or p-value. The z-scores and p-values reported in the output feature class are uncorrected for multiple testing or spatial dependency.

The cluster/outlier type (COType) field distinguishes between a statistically significant cluster of high values (HH), cluster of low values (LL), outlier in which a high value is surrounded primarily by low values (HL), and outlier in which a low value is surrounded primarily by high values (LH). Statistical significance is set at the 95 percent confidence level. When no FDR correction is applied, features with p-values smaller than 0.05 are considered statistically significant. The FDR correction reduces this p-value threshold from 0.05 to a value that better reflects the 95 percent confidence level given multiple testing.

Output

This tool creates a new output feature class with the following attributes for each feature in the input feature class: local Moran's I index, z-score, p-value, and COType.

When this tool runs in ArcMap, the output feature class is automatically added to the table of contents (TOC) with default rendering applied to the COType field. The rendering applied is defined by a layer file in <ArcGIS>/ArcToolbox/Templates/Layers. You can reapply the default rendering, if needed, by importing the template layer symbology.

Best practice guidelines

Potential applications

The Cluster and Outlier Analysis (Anselin Local Moran's I) tool identifies concentrations of high values, concentrations of low values, and spatial outliers. It can help you answer questions such as these:

Applications can be found in many fields including economics, resource management, biogeography, political geography, and demographics.

Additional resources

Anselin, Luc. "Local Indicators of Spatial Association—LISA," Geographical Analysis 27(2): 93–115, 1995.

Mitchell, Andy. The ESRI Guide to GIS Analysis, Volume 2. ESRI Press, 2005.

8/26/2014