R: BB, BW and Jtot join count statistic for k-coloured factors

joincount.multi {spdep} | R Documentation

## BB, BW and Jtot join count statistic for k-coloured factors

### Description

A function for tallying join counts between same-colour and different colour spatial objects, where neighbour relations are defined by a weights list. Given the global counts in each colour, expected counts and variances are calculated under non-free sampling, and a z-value reported. Since multiple tests are reported, no p-values are given, allowing the user to adjust the significance level applied. Jtot is the count of all different-colour joins.

### Usage

    joincount.multi(fx, listw, zero.policy = FALSE,
     spChk = NULL, adjust.n=TRUE)
    ## S3 method for class 'jcmulti'
    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` | if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
`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 matrix with class `jcmulti` with row and column names for observed and expected counts, variance, and z-value.

### 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, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis by example: point pattern and quatitative data, Wiley, pp. 158–170.

### See Also

`joincount.test`

### Examples

    data(oldcol)
    HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
    names(HICRIME) <- rownames(COL.OLD)
    joincount.multi(HICRIME, nb2listw(COL.nb, style="B"))
    ## Not run:
    data(hopkins)
    image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),
     col=c("white", "black"))
    box()
    hopkins.rook.nb <- cell2nb(32, 32, type="rook")
    unlist(spweights.constants(nb2listw(hopkins.rook.nb, style="B")))
    hopkins.queen.nb <- cell2nb(32, 32, type="queen")
    hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE)
    hopkins4 <- hopkins[5:36,36:5]
    hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4
    hopkins4.f <- factor(hopkins4)
    table(hopkins4.f)
    joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style="B"))
    cat("replicates Upton & Fingleton table 3.4 (p. 166)\n")
    joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style="B"))
    cat("replicates Upton & Fingleton table 3.6 (p. 168)\n")
    joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style="B"))
    cat("replicates Upton & Fingleton table 3.7 (p. 169)\n")

    ## End(Not run)

[Package spdep version 0.6-13 Index]