R: Permutation test for Lee's L statistic

lee.mc {spdep} | R Documentation

## Permutation test for Lee's L statistic

### Description

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=NULL, 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 NULL, 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), 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

### Author(s)

Roger Bivand, Virgilio GÃ³mez-Rubio Virgilio.Gomez@uclm.es

### 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

### See Also

`lee`

### Examples

    data(boston)
    lw<-nb2listw(boston.soi)

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

    lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="less")

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

    lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="less",
       na.action=na.omit)

[Package spdep version 0.6-13 Index]