R: BB join count statistic for k-coloured factors

joincount.test {spdep} | R Documentation

## BB join count statistic for k-coloured factors

### Description

The BB join count test for spatial autocorrelation using a spatial weights matrix in weights list form for testing whether same-colour joins occur more frequently than would be expected if the zones were labelled in a spatially random way. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of `joincount.mc` permutations.

### Usage

    joincount.test(fx, listw, zero.policy=NULL, alternative="greater",
     sampling="nonfree", spChk=NULL, adjust.n=TRUE)
    ## S3 method for class 'jclist'
    print(x, ...)

### Arguments

`fx` | a factor of the same length as the neighbours and weights objects in listw
`listw` | a `listw` object created for example by `nb2listw`
`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), "less" or "two.sided".
`sampling` | default “nonfree”, may be “free”
`adjust.n` | default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted consistently (up to and including spdep 0.3-28 the adjustment was inconsistent - thanks to Tomoki NAKAYA for a careful bug report)
`spChk` | should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use `get.spChkOption()`
`x` | object to be printed
`...` | arguments to be passed through for printing

### Value

A list with class `jclist` of lists with class `htest` for each of the k colours containing the following components:

`statistic` | the value of the standard deviate of the join count statistic.
`p.value` | the p-value of the test.
`estimate` | the value of the observed statistic, its expectation and variance under non-free sampling.
`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.

### Note

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, `listw2U()` can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative.

### Author(s)

Roger Bivand Roger.Bivand@nhh.no

### References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.

### See Also

`joincount.mc`, `joincount.multi`, `listw2U`

### Examples

    data(oldcol)
    HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
    names(HICRIME) <- rownames(COL.OLD)
    joincount.test(HICRIME, nb2listw(COL.nb, style="B"))
    joincount.test(HICRIME, nb2listw(COL.nb, style="B"), sampling="free")
    joincount.test(HICRIME, nb2listw(COL.nb, style="C"))
    joincount.test(HICRIME, nb2listw(COL.nb, style="S"))
    joincount.test(HICRIME, nb2listw(COL.nb, style="W"))
    by(card(COL.nb), HICRIME, summary)
    print(is.symmetric.nb(COL.nb))
    coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
    COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
    print(is.symmetric.nb(COL.k4.nb))
    joincount.test(HICRIME, nb2listw(COL.k4.nb, style="B"))
    cat("Note non-symmetric weights matrix - use listw2U()\n")
    joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style="B")))

[Package spdep version 1.2-2 Index]