Compute Lee's statistic

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

Usage

lee(x, y, listw, n, S2, zero.policy=attr(listw, "zero.policy"), 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 attr(listw, "zero.policy") as set when listw was created, if attribute not set, 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 Gómez-Rubio Virgilio.Gomez@uclm.es

See also

lee.mc

Examples

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

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

Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE)
Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)