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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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Presentation Transcript

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)

• 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 Points

• Evaluates Pattern of the Weighted Values

• Must Use Confidence Intervals

• To determine weights use:

• Select Fixed Distance

• Polygon Contiguity

• K Nearest Neighbors

• Delauny Triangulation

• Select None for the Standardization parameter.

• Quantile Map

• Fraction Hispanic

• Polygon Contiguity

• I = 0.83, Z = 19.3

• Quantile Map

• Average Family Size

• Polygon Contiguity

• I = 0.6; Z = 14.1

Anselin Local Moran Ii Cluster and Outlier Analysis

• Developed by Anselin (1995)

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

• 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.

Gi* 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.

• Quantile Map

• Fraction Hispanic

• Polygon Contiguity

• I = 0.83, Z = 19.3

• Quantile Map

• Med_Age

• Polygon Contiguity

• I = 0.48, Z = 11.3

• 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 MoranHR90 vs. Gini index of family income inequality

• Disturbance, space, and time: Long-term mesquite (Prosopis velutina) dynamics in Sonoran desert grasslands (1932 – 2006)

• Located on Santa Rita Experimental Range

• 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