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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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Local spatial statistics
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
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 Ripley K

  • Weighted Points

  • Evaluates Pattern of the Weighted Values

  • Must Use Confidence Intervals



High low clustering1
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 clustering2
High/Low Clustering

  • Quantile Map

  • Fraction Hispanic

  • Polygon Contiguity

  • I = 0.83, Z = 19.3


High low clustering3
High/Low Clustering

  • Quantile Map

  • Average Family Size

    • Polygon Contiguity

  • I = 0.6; Z = 14.1


Anselin local moran i i cluster and outlier analysis
Anselin Local Moran Ii Cluster and Outlier Analysis

  • Developed by Anselin (1995)


Anselin local moran i i cluster and outlier analysis1
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 i i cluster and outlier analysis2
Anselin Local Moran Ii Cluster and Outlier Analysis

  • Quantile Map

  • Fraction Hispanic

  • Polygon Contiguity

  • I = 0.83, Z = 19.3


Anselin local moran i i cluster and outlier analysis3
Anselin Local Moran Ii Cluster and Outlier Analysis

  • Quantile Map

  • Med_Age

  • Polygon Contiguity

  • I = 0.48, Z = 11.3


Getis ord g statistic
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.


G i statistic
Gi* Statistic


Getis ord g statistic1
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 statistic2
Getis-Ord G Statistic

  • Quantile Map

  • Fraction Hispanic

  • Polygon Contiguity

  • I = 0.83, Z = 19.3


Getis ord g statistic3
Getis-Ord G Statistic

  • Quantile Map

  • Med_Age

  • Polygon Contiguity

  • I = 0.48, Z = 11.3



Problems
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”.






Bivariate moran hr90 vs gini index of family income inequality
Bivariate MoranHR90 vs. Gini index of family income inequality


Dawn browning
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 browning1
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.


Moran LISA Scatter PlotsNumber of P. velutina plants within 5 X 5-m quadrats



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