Exploratory spatial data analysis
8 important questions on Exploratory spatial data analysis
What is the definition of the spatial system (Dublin 2009) (step 1)?
n x n dimension
W is commonly sparse --> only a small number of elements are neighbors
Statistics are sensitive concering a selected neighborhood definition
What is the definition of a contiguity (step 1)?
Binary weight matrix: 1 if they share a boundry, 0 otherwise
Contiguity most appropriate for areal units
Topologically one can consider nodes and/or edges as boundary (Rooks Case/Queens Case)
What is the definition of k-nearest neighbors (step 1)?
k closest entities are defined as neighbors
Avoids "island effects"
Both require plane and projected coordinates --> Euclidean distance
For latitude longitude --> arc distance/great circle distance
Suitable when units vary in size --> similar number of neighbors
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What is the definition of an interaction (step 1)?
Closer entities have greater influence than more distant ones
Common functions: inverse distance and squared inverse distance
What is the permutation approach (step 3)?
How unusual is our observed pattern?
When we run the Moran's I 999 times --> reference distribution --> if the Moran's I lies in a tail --> statistical evidence against chane --> reject H0
p-value: represents the probability of obtaining a test statistic at least as extreme as the observed one (usually 0,05)
if p < 0,05 --> reject H0 and conclude that similar values are spatially grouped
What are advantages of Local statistics?
Visualization capabilities
Detection of clusters
Explore hetrogeneity
What is the Local Moran's I?
Sum of local coefficients proportional to the global index
Hot or cold spots
Spatial outliers
Explain the moran scatterplot (step 3, local)
- Slope of the regression line corresponds to the global Moran's I
High-high: hot spots --> positive SAC
low-low: cold spot --> positive SAC
High-low: outliers --> negative SAC
low-high: outliers --> negative SAC
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