Local Spatial Statistics

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# Local Spatial Statistics - PowerPoint PPT Presentation

Local Spatial Statistics. Local statistics are developed to measure dependence in only a portion of the area. They measure the association between Xi and its neighbors up to a specific distance from site i. These statistics are well suited for: Identify “hot spots’

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## PowerPoint Slideshow about 'Local Spatial Statistics' - ion

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Presentation Transcript
Local Spatial Statistics

Local statistics are developed to measure dependence in only a portion of

the area.

They measure the association between Xi and its neighbors up to a

specific distance from site i.

These statistics are well suited for:

• Identify “hot spots’
• Assess assumptions of stationarity
• Identify distances beyond which no discernible association obtains.

Members of Local Indicator of Spatial Association (LISA)

Spatial Statistics Tools
• High/Low Clustering (Getis-Ord General G)
• Incremental Spatial Autocorrelation
• Weighted Ripley K Function
• Cluster and Outlier Analysis (Anselin Local Morans I)
• Group Analysis
• Hot Spot Analysis (Getis-OrdGi*)
Weighted Ripley K
• Weighted Points
• Evaluates Pattern of the Weighted Values
• Must Use Confidence Intervals
High/Low Clustering
• To determine weights use:
• Select Fixed Distance
• Polygon Contiguity
• K Nearest Neighbors
• Delauny Triangulation
• Select None for the Standardization parameter.
High/Low Clustering
• Quantile Map
• Fraction Hispanic
• Polygon Contiguity
• I = 0.83, Z = 19.3
High/Low Clustering
• Quantile Map
• Average Family Size
• Polygon Contiguity
• I = 0.6; Z = 14.1
Anselin Local Moran Ii Cluster and Outlier Analysis
• Cluster 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 primarily by low values (HL), and outlier in which a low value is surrounded primarily by high values (LH).
• Unique Feature - Local Moran Ii will identify statistically significant spatial outliers (a high value surrounded by low values or a low value surrounded by high values).
Anselin Local Moran Ii Cluster and Outlier Analysis
• Quantile Map
• Fraction Hispanic
• Polygon Contiguity
• I = 0.83, Z = 19.3
Anselin Local Moran Ii Cluster and Outlier Analysis
• Quantile Map
• Med_Age
• Polygon Contiguity
• I = 0.48, Z = 11.3
Getis-Ord G Statistic
• The null hypothesis is that the sum of values at all the j sites within radius d of site i is not more or less then expect by chance given all the values in the entire study area.
• The Gi statistics does not include site i in computing the sum.
• The Gi* statistic does include site i in computing the sum.
Getis-Ord G Statistic
• Interpretation
• The Gi* statistic returned for each feature in the dataset is a z-score.
• For statistically significant positive z-scores, the larger the z-score is, the more intense the clustering of high values (hot spot).
• For statistically significant negative z-scores, the smaller the z-score is, the more intense the clustering of low values (cold spot).
• The Gi* statistic is a Z score.
Getis-Ord G Statistic
• Quantile Map
• Fraction Hispanic
• Polygon Contiguity
• I = 0.83, Z = 19.3
Getis-Ord G Statistic
• Quantile Map
• Med_Age
• Polygon Contiguity
• I = 0.48, Z = 11.3
Problems
• Correlation Problem
• Overlapping samples of j, similar local statistics.
• Problem if statistical significance is sought.
• Small Sample Problem
• Statistics are based on a normal distribution, which is unlikely for a small sample.
• Effects of Global Autocorrelation Problem
• If there is significant overall global autocorrelation the local statistics will be less useful in detecting “hot spots”.
Dawn Browning
• Disturbance, space, and time: Long-term mesquite (Prosopis velutina) dynamics in Sonoran desert grasslands (1932 – 2006)
• Located on Santa Rita Experimental Range
Dawn Browning
• Trends in plant- and landscape-based aboveground P. velutina biomass derived from field measurements of plant canopy area in 1932, 1948, and 2006.
Local indicator of spatial association (LISA) cluster maps and associated Global Moran’s I values for P. velutina plant density within 5-m X 5-m quadrats.