# Permutation test for Lee's L statistic

`lee.mc.Rd`

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
#>
```