Permutation test for Lee's L statistic

A permutation test for Lee's L statistic calculated by using nsim random permutations of x and y for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

lee.mc(x, y, listw, nsim, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 na.action=na.fail, spChk=NULL, return_boot=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
nsim: number of permutations
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
alternative: a character string specifying the alternative hypothesis, must be one of "greater" (default), "two.sided", or "less".
na.action: a function (default na.fail), can also be na.omit or na.exclude - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted. na.pass is not permitted because it is meaningless in a permutation test.
spChk: should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
return_boot: return an object of class boot from the equivalent permutation bootstrap rather than an object of class htest

Value

A list with class htest and mc.sim containing the following components:

statistic: the value of the observed Lee's L.
parameter: the rank of the observed Lee's L.
p.value: the pseudo p-value of the test.
alternative: a character string describing the alternative hypothesis.
method: a character string giving the method used.
data.name: a character string giving the name(s) of the data, and the number of simulations.
res: nsim simulated values of statistic, final value is observed 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, Virgilio GÃ³mez-Rubio Virgilio.Gomez@uclm.es

Examples

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

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

lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="two.sided")
#> 
#> 	Monte-Carlo simulation of Lee's L
#> 
#> data:  x ,  y 
#> weights: lw  
#> number of simulations + 1: 100 
#> 
#> statistic = -0.3263, observed rank = 1, p-value = 0.02
#> alternative hypothesis: two.sided
#> 

#Test with missing values
x[1:5]<-NA
y[3:7]<-NA

lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="two.sided", 
   na.action=na.omit)
#> 
#> 	Monte-Carlo simulation of Lee's L
#> 
#> data:  x ,  y 
#> weights: lw 
#> omitted: 1, 2, 3, 4, 5, 6, 7 
#> number of simulations + 1: 100 
#> 
#> statistic = -0.32447, observed rank = 1, p-value = 0.02
#> alternative hypothesis: two.sided
#>