Lee's L is a bivariate spatial correlation coefficient which measures the association between two sets of observations made at the same spatial sites. Standard measures of association such as the Pearson correlation coefficient do not account for the spatial dimension of data, in particular they are vulnerable to inflation due to spatial autocorrelation. Lee's L is available in numerous spatial analysis software libraries including spdep and PySAL (where it is called Spatial_Pearson) and has been applied in diverse applications such as studying air pollution, viticulture and housing rent.
Formula For spatial data x i {\displaystyle x_{i}} and y i {\displaystyle y_{i}} measured at N {\displaystyle N} locations connected with the spatial weight matrix w i j {\displaystyle w_{ij}} first define the spatially lagged vector
x ~ i = ∑ j w i j x j {\displaystyle {\tilde {x}}_{i}=\sum _{j}w_{ij}x_{j}}
with a similar definition for y ~ i {\displaystyle {\tilde {y}}_{i}} . Then Lee's L is defined as
L x , y = N ∑ i ( ∑ j w i j ) 2 ∑ i j ( x ~ i − x ¯ ) ( y ~ i − y ¯ ) ∑ i ( x ~ i − x ¯ ) 2 ∑ i ( y ~ i − y ¯ ) 2 {\displaystyle L_{x,y}={\frac {N}{\sum _{i}\left(\sum _{j}w_{ij}\right)^{2}}}{\frac {\sum _{ij}({\tilde {x}}_{i}-{\bar {x}})({\tilde {y}}_{i}-{\bar {y}})}{{\sqrt {\sum _{i}({\tilde {x}}_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i}({\tilde {y}}_{i}-{\bar {y}})^{2}}}}}}
… excerpt ends here. Continue reading the full article.
