1% Copyright 2014 by Roger S. Bivand, Virgilio Gómez-Rubio
2\encoding{latin1}
3\name{lee.mc}
4\alias{lee.mc}
5\title{Permutation test for Lee's L statistic}
6\description{
7 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.
8}
9\usage{
10lee.mc(x, y, listw, nsim, zero.policy=NULL, alternative="greater",
11 na.action=na.fail, spChk=NULL, return_boot=FALSE)
12}
13\arguments{
14  \item{x}{a numeric vector the same length as the neighbours list in listw}
15  \item{y}{a numeric vector the same length as the neighbours list in listw}
16  \item{listw}{a \code{listw} object created for example by \code{nb2listw}}
17  \item{nsim}{number of permutations}
18  \item{zero.policy}{default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA}
19  \item{alternative}{a character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".}
20  \item{na.action}{a function (default \code{na.fail}), can also be \code{na.omit} or \code{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 \code{nb2listw} may be subsetted. \code{na.pass} is not permitted because it is meaningless in a permutation test.}
21  \item{spChk}{should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use \code{get.spChkOption()}}
22  \item{return_boot}{return an object of class \code{boot} from the equivalent permutation bootstrap rather than an object of class \code{htest}}
23}
24
25\value{
26A list with class \code{htest} and \code{mc.sim} containing the following components:
27  \item{statistic}{the value of the observed Lee's L.}
28  \item{parameter}{the rank of the observed Lee's L.}
29  \item{p.value}{the pseudo p-value of the test.}
30  \item{alternative}{a character string describing the alternative hypothesis.}
31  \item{method}{a character string giving the method used.}
32  \item{data.name}{a character string giving the name(s) of the data, and the number of simulations.}
33  \item{res}{nsim simulated values of statistic, final value is observed statistic}
34}
35\references{Lee (2001). Developing a bivariate spatial association measure:
36An integration of Pearson's r and Moran's I. J Geograph Syst  3: 369-385}
37
38\author{Roger Bivand, Virgilio Gómez-Rubio \email{Virgilio.Gomez@uclm.es} }
39
40\seealso{\code{\link{lee}}}%, \code{\link{moran.test}}}
41
42\examples{
43data(boston, package="spData")
44lw<-nb2listw(boston.soi)
45
46x<-boston.c$CMEDV
47y<-boston.c$CRIM
48
49lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="less")
50
51#Test with missing values
52x[1:5]<-NA
53y[3:7]<-NA
54
55lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="less",
56   na.action=na.omit)
57
58}
59\keyword{spatial}
60