Spatial Weights
Spatial Heterogeneity
Connectiveness, Spatial Regimes
Spatial Dependence
Externality, Interaction, Correlation, and Spillover
First-Order Spatial Dependence
Higher-Order Spatial Dependence
Spatial Weights Matrix
Measures of Overall Connectedness or Dependence:
Location-Specific Weights, K-Nearest Neighbors Weights, Socio-Economic Distance Weights
Binary Contiguity Weights Matrix
N by N positive and symmetric matrix W, with elements w
ij
w
ii
=
0 by convention
w
ij
=
1 for i and j contiguous neighbors
0 otherwise
Characteristics of Spatial Weights Matrix
Sparseness
Weights Distribution
Eigenvalues
Row-Standardized Weights Matrix
w
ij
*
= w
ij
/
å
j
w
ij
å
j
w
ij
*
= 1
Higher-Order Spatial Weights Matrix
W
2
, W
3
, ...
Circularity and Redundancy in Higher Order Weights
Example: China Regional Spatial Weights Matrix
Data
,
Program
.