A simple function to compute Lee's L statistic for bivariate spatial data; $$L(x,y) = \frac{n}{\sum_{i=1}^{n}(\sum_{j=1}^{n}w_{ij})^2} \frac{\sum_{i=1}^{n}(\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})) ((\sum_{j=1}^{n}w_{ij}(y_j-\bar{y}))}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2} \sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}$$

lee(x, y, listw, n, S2, zero.policy=NULL, NAOK=FALSE)

## Arguments

x

a numeric vector the same length as the neighbours list in listw

y

a numeric vector the same length as the neighbours list in listw

listw

a listw object created for example by nb2listw

n

number of zones

S2

Sum of squared sum of weights by rows.

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

NAOK

if 'TRUE' then any 'NA' or 'NaN' or 'Inf' values in x are passed on to the foreign function. If 'FALSE', the presence of 'NA' or 'NaN' or 'Inf' values is regarded as an error.

## Value

a list of

L

Lee's L statistic

local L

Lee's local L statistic

## References

Lee (2001). Developing a bivariate spatial association measure: An integration of Pearson's r and Moran's I. J Geograph Syst 3: 369-385

## Author

Roger Bivand and Virgiio GÃ³mez-Rubio Virgilio.Gomez@uclm.es

lee.mc

## Examples

data(boston, package="spData")
lw<-nb2listw(boston.soi)

x<-boston.c$CMEDV y<-boston.c$CRIM