Anselin Local Moran’s I

[<– 1 Standard Distance](http://giscollective.org/tutorials/gis-techniques/spatial-statistics/standard-distance/)

Given a set of weighted features, the Cluster and Outlier Analysis tool identifies spatial clusters of features with attribute values similar in magnitude. 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 feature. The z-scores a p-values represent the statistical significance of the computed index values.

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.

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.Note: results are only reliable if the input feature class contains at least 30 features.

When to use: Identifies concentrations of high values, concentrations of low values, and spatial outliers. It’s useful for identifying hot spots. For example: Where are the sharpest boundaries between affluence and poverty in a study area? – Are there locations in a study area with anomalous spending patterns? – Where are the unexpectedly high rates of diabetes across the study area?

How to do:

Goal: Identify concentrations of countries with high/low average wages and outliers.

Step 1: Add US_Income feature class from the sample data to a new ArcMap document

Step 2: Select Cluster and Outlier Analysis tool (ArcToolbox > Spatial Statistics > Mapping Clusters > Cluster and Outlier Analysis (Anselin Local Morans I))

Step 3: Fill-in the fields as specified below:

  • Input field:B34_2008is the average wage per county
  • Output Feature Class: We’ll output the feature class to SampleData.gdb and call it US_Income_MoransI
  • Conceptualization of Spatial Relationships: see tool help for explanation of each conceptualization. For this exercise, we will use the inverse distance conceptualization (i.e. Tobler’s First Law of Geography) where nearer features have a greater influence on the computation
  • Distance Method: either straight line (Euclidean) or at right angles (Manhattan).We’ll use Euclidean distance
  • Distance Band: specifies a cutoff distance for Inverse Distance and Fixed Distance options. Leave this blank

Step 4: Hit OK and let the tool run. After the tool completes running, a new feature class will be created and added to the Table of Contents similar to that below.

The output field, cluster/outlier type (COType), distinguishes between a statistically significant (0.05 level) cluster of high values (HH), cluster of low values (LL), outlier in which a high value is surrounded by primarily low values (HL), and outlier in which a low value is surrounded primarily by high values (LH).

[3 Hot Spot Analysis (Getis-Ord Gi*) –>](http://giscollective.org/tutorials/gis-techniques/spatial-statistics/hot-spot-analysis/)