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2.3 Measures based on absolute adjacency 2.3.1 Area features

Lecture 16: Spatial Autocorrelation III. Topics:. 2.3 Measures based on absolute adjacency 2.3.1 Area features 2.3.1.1 Geary Index (ratio/interval) 2.3.1.2 Moran Coefficient (ratio/interval) 2.3.1.3 Joint Count Statistics (categorical) 2.3.2 Other type of features.

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2.3 Measures based on absolute adjacency 2.3.1 Area features

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  1. Lecture 16: Spatial Autocorrelation III Topics: 2.3 Measures based on absolute adjacency 2.3.1 Area features 2.3.1.1 Geary Index (ratio/interval) 2.3.1.2 Moran Coefficient (ratio/interval) 2.3.1.3 Joint Count Statistics (categorical) 2.3.2 Other type of features References: Goodchild, Michael F., 1986. Spatial Autocorrelation, CATMOG 47, Geo Books, Norwich, UK, 56 pp. Griffith, Daniel A., 1987. Spatial Autocorrelation: A Primer, Resource Publications in Geography, AAG, Washington, 82 pp. Odland, John, 1987. Spatial Autocorrelation, SAGE Pulications, Inc., Beverly Hills, CA, 85 pp.

  2. Outlines 2.3.1 Area Features 2.3.1.3 Joint Count Statistics: Two categories (yes or no): black and white (The Buffalo Figure) 1) Calculation: Counting for number of WW, BB, BW joints J = JWW+JBB+JBW J is the total number of connections 2) Interpretation: a) Under the random arrangement assumption: (1) What is random arrangement The population of spatial patterns for a given number of events over a given number of area units is created by rearranging the number of events over the area units

  3. 2) Interpretation: (continued…) a) Under the random arrangement assumption: (continued…) (2) The expected numbers of different joints Expected EWW = J NW(NW-1)/N(N-1) Expected EBB = J NB(NB-1)/N(N-1) Expected EBW = 2 J NB NW/N(N-1) NW, NB are the occurrence of W and B events, respectively (3) Testing: For BW joints:

  4. 2) Interpretation: (continued…) b) Under the random sampling assumption: (1) What is a random sampling: The population of spatial patterns for a given number of events over a given number of area units is created by sampling with replacement. (2) The expected numbers of different joints Expected EWW = J (NW)2/ N2 Expected EBB = J (NB)2/N2 Expected EBW = 2 J NB NW/N2 NW, NB are the occurrence of W and B events, respectively (3) Testing For BW joints:

  5. 3) Example: (1) The Pattern (The Figure) (2) The Observed Joints (BW): JBW = 6 (3) Interpretation: (a) Under Random Arrangement: EBW = (2x19x5x6)/11x10=10.3636 ∑Li(Li-1) = (Table7.7)=114 σBW = 1.7721 ZBW = (6-10.3635)/1.7721= -2.462 at 95% significant level, the critical value of a negative standard normal deivate is -1.645, thus the BW joints is very unlikely to have occurred by chance.

  6. 3) Example: (continued …) (3) Interpretation: (continued…) (b) Under Random sampling: EBW = (2x19x5x6)/11x11=9.42 ∑Li(Li-1) = 114 σBW = 2.2323 ZBW = (6-9.42)/2.2323= -1.532 at 95% significant level, the critical value of a negative standard normal deivate is -1.645, thus the BW joints is likely to have occurred by chance. 2.3.2 Other Features 2.3.2.1 Point features (Points to Areas Conversion Figure) 2.3.2.2 Linear features

  7. Questions 1. How is similarity in attribute defined in computing joint count statistics and how is similarity in location defined? 2. What is the main difference between Joint Counts and Moran Coefficient? When would you apply the Joint Counts statistics? 3. What is the random arrangement assumption and when should you apply it? 4. What is the random sampling assumption and when should you apply it? What is the difference between the two assumptions? 5. How would you measure spatial autocorrelation using the absolute adjacency approach for point or linear features?

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