multispati {ade4}R Documentation

Multivariate spatial analysis

Description

This function ensures a multivariate extension of the univariate method of spatial autocorrelation analysis. By accounting for the spatial dependence of data observations and their multivariate covariance simultaneously, complex interactions among many variables are analysed. Using a methodological scheme borrowed from duality diagram analysis, a strategy for the exploratory analysis of spatial pattern in the multivariate is developped.

Usage

multispati(dudi, listw, scannf = TRUE, nfposi = 2, nfnega = 0)
plot.multispati(x, xax = 1, yax = 2, ...) 
summary.multispati(object, ...) 
print.multispati(x, ...)

Arguments

dudi an object of class dudi for the duality diagram analysis
listw an object of class listw for the spatial dependence of data observations
scannf a logical value indicating whether the eigenvalues bar plot should be displayed
nfposi an integer indicating the number of kept positive axes
nfnega an integer indicating the number of kept negative axes
x, object an object of class multispati
xax, yax the numbers of the x-axis and the y-axis
... further arguments passed to or from other methods

Details

This analysis generalizes the Wartenberg's multivariate spatial correlation analysis to various duality diagrams created by the functions (dudi.pca, dudi.coa, dudi.acm, dudi.mix...) If dudi is a duality diagram created by the function dudi.pca and listw gives spatial weights created by a row normalized coding scheme, the analysis is equivalent to Wartenberg's analysis.

We note X the data frame with the variables, Q the column weights matrix and D the row weights matrix associated to the duality diagram dudi. We note L the neighbouring weights matrix associated to listw. Then, the 'multispati' analysis gives principal axes v that maximize the spatial autocorrelation :

I(XQv) = t(v)t(Q)t(X)DLXQv / t(v)t(Q)t(X)DXQv

Value

Returns an object of class multispati.

Author(s)

Daniel Chessel chessel@biomserv.univ-lyon1.fr
Sébastien Ollier ollier@biomserv.univ-lyon1.fr

References

Grunsky, E. C. and Agterberg, F. P. (1988) Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario. Mathematical Geology, 20, 825–861.

Switzer, P. and Green, A.A. (1984) Min/max autocorrelation factors for multivariate spatial imagery. Tech. rep. 6, Stanford University.

Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

Wartenberg, D. E. (1985) Multivariate spatial correlation: a method for exploratory geographical analysis. Geographical Analysis, 17, 263–283.

See Also

dudi,listw

Examples

## Not run: 
if (require(maptools, quiet = TRUE) & require(spdep, quiet = TRUE)) {
    data(mafragh)
    maf.xy <- mafragh$xy
    maf.flo <- mafragh$flo
    maf.listw <- nb2listw(neig2nb(mafragh$neig))
    s.label(maf.xy, neig = mafragh$neig, clab = 0.75)
    maf.coa <- dudi.coa(maf.flo,scannf = FALSE)
    maf.coa.ms <- multispati(maf.coa, maf.listw, scannf = FALSE, nfposi = 2, 
        nfnega = 2)
    summary(maf.coa.ms)
    par(mfrow = c(1,3))
    barplot(maf.coa$eig)
    barplot(maf.coa.ms$eig) 
    s.corcircle(maf.coa.ms$as)
 
    par(mfrow = c(2,2))
    s.value(maf.xy, -maf.coa$li[,1])
    s.value(maf.xy, -maf.coa$li[,2])
    s.value(maf.xy, maf.coa.ms$li[,1])
    s.value(maf.xy, maf.coa.ms$li[,2])
    par(mfrow = c(1,1))

    par(mfrow = c(1,2))
    w1 <- -maf.coa$li[,1:2]
    w1m <- apply(w1, 2, lag.listw, x = maf.listw)
    s.match(w1, w1m, clab = 0.75)
    w1.ms <- maf.coa.ms$li[,1:2]
    w1.msm <- apply(w1.ms, 2, lag.listw, x = maf.listw)
    s.match(w1.ms, w1.msm, clab = 0.75)
    par(mfrow = c(1,1))

    maf.pca <- dudi.pca(mafragh$mil, scannf = FALSE)
    multispati.randtest(maf.pca, maf.listw)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf=FALSE)
    plot(maf.pca.ms)
}
## End(Not run)

[Package ade4 version 1.4-0 Index]