multispati {adespatial}

Multivariate spatial analysis

Description

This function provides a multivariate extension of the univariate method of spatial autocorrelation analysis. It provides a spatial ordination by maximizing the product of variance by spatial autocorrelation.

Usage

multispati(dudi, listw, scannf = TRUE, nfposi = 2, nfnega = 0)

## S3 method for class 'multispati'
summary(object, ...)

## S3 method for class 'multispati'
print(x, ...)

## S3 method for class 'multispati'
plot(x, xax = 1, yax = 2, pos = -1, storeData = TRUE, plot = TRUE, ...)

Arguments

dudi

an object of class dudi obtained by the simple analysis of a data table

listw

an object of class listw created for example by nb2listw

scannf

a logical value indicating whether the eigenvalues barplot should be displayed

nfposi

an integer indicating the number of axes with positive autocorrelation

nfnega

an integer indicating the number of axes with negative autocorrelation

...

further arguments passed to or from other methods

x, object

an object of class multispati

xax, yax

the numbers of the x-axis and the y-axis

pos

an integer indicating the position of the environment where the data are stored, relative to the environment where the function is called. Useful only if storeData is FALSE

storeData

a logical indicating if the data should be stored in the returned object. If FALSE, only the names of the data arguments are stored

plot

a logical indicating if the graphics is displayed

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 product of spatial autocorrelation and inertia of row scores :

I(XQv)*\|XQv\|^2 = v^{t}Q^{t}X^{t}DLXQv

Value

Returns an object of class multispati, which contains the following elements :

eig

a numeric vector containing the eigenvalues

nfposi

integer, number of kept axes associated to positive eigenvalues

nfnega

integer, number of kept axes associated to negative eigenvalues

c1

principle axes (v), data frame with p rows and (nfposi + nfnega) columns

li

principal components (XQv), data frame with n rows and (nfposi + nfnega) columns

ls

lag vector onto the principal axes (LXQv), data frame with n rows and (nfposi + nfnega) columns

as

principal axes of the dudi analysis (u) onto principal axes of multispati (t(u)Qv), data frame with nf rows and (nfposi + nfnega) columns

Author(s)

Stéphane Dray [e-mail] with contributions by Daniel Chessel, Sebastien Ollier and Thibaut Jombart

References

Dray, S., Said, S. and Debias, F. (2008) Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation. Journal of vegetation science, 19, 45–56.

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,mat2listw

Examples

if (require(spdep, quiet = TRUE) & require(ade4, quiet = TRUE)) {
    data(mafragh)
    maf.xy <- mafragh$xy
    maf.flo <- mafragh$flo
    maf.listw <- nb2listw(mafragh$nb)
    if(adegraphicsLoaded()) {
      g1 <- s.label(maf.xy, nb = mafragh$nb, plab.cex = 0.75)
    } else {
      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)
    maf.coa.ms
    
    ### detail eigenvalues components
    fgraph <- function(obj){
      # use multispati summary
      sum.obj <- summary(obj)
      # compute Imin and Imax
      Ibounds <- moran.bounds(eval(as.list(obj$call)$listw))
      Imin <- Ibounds[1]
      Imax <- Ibounds[2]
      I0 <- -1/(nrow(obj$li)-1)
      # create labels
      labels <- lapply(1:length(obj$eig),function(i) bquote(lambda[.(i)]))
      # draw the plot
      xmax <- eval(as.list(obj$call)$dudi)$eig[1]*1.1
      oldpar <- par(las=1)
      var <- sum.obj[,2]
      moran <- sum.obj[,3]
      plot(x=var,y=moran,type='n',xlab='Inertia',ylab="Spatial autocorrelation (I)",
           xlim=c(0,xmax),ylim=c(Imin*1.1,Imax*1.1),yaxt='n')
      text(x=var,y=moran,do.call(expression,labels))
      ytick <- c(I0,round(seq(Imin,Imax,le=5),1))
      ytlab <- as.character(round(seq(Imin,Imax,le=5),1))
      ytlab <- c(as.character(round(I0,1)),as.character(round(Imin,1)),
           ytlab[2:4],as.character(round(Imax,1)))
      axis(side=2,at=ytick,labels=ytlab)
      rect(0,Imin,xmax,Imax,lty=2)
      segments(0,I0,xmax,I0,lty=2)
      abline(v=0)
      title("Spatial and inertia components of the eigenvalues")
      par(oldpar)
    }
    fgraph(maf.coa.ms)
    ## end eigenvalues details


    if(adegraphicsLoaded()) {
      g2 <- s1d.barchart(maf.coa$eig, p1d.hori = FALSE, plot = FALSE)
      g3 <- s1d.barchart(maf.coa.ms$eig, p1d.hori = FALSE, plot = FALSE) 
      g4 <- s.corcircle(maf.coa.ms$as, plot = FALSE)
      G1 <- ADEgS(list(g2, g3, g4), layout = c(1, 3))
    } else {
      oldpar <- par(mfrow = c(1, 3))
      barplot(maf.coa$eig)
      barplot(maf.coa.ms$eig) 
      s.corcircle(maf.coa.ms$as)
      par(oldpar)
    }
 
 
    if(adegraphicsLoaded()) {
      g5 <- s.value(maf.xy, -maf.coa$li[, 1], plot = FALSE)
      g6 <- s.value(maf.xy, -maf.coa$li[, 2], plot = FALSE)
      g7 <- s.value(maf.xy, maf.coa.ms$li[, 1], plot = FALSE)
      g8 <- s.value(maf.xy, maf.coa.ms$li[, 2], plot = FALSE)
      G2 <- ADEgS(list(g5, g6, g7, g8), layout = c(2, 2))
    } else {
      oldpar <- 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(oldpar)
    }


    w1 <- -maf.coa$li[, 1:2]
    w1m <- apply(w1, 2, lag.listw, x = maf.listw)
    w1.ms <- maf.coa.ms$li[, 1:2]
    w1.msm <- apply(w1.ms, 2, lag.listw, x = maf.listw)
    if(adegraphicsLoaded()) {
      g9 <- s.match(w1, w1m, plab.cex = 0.75, plot = FALSE)
      g10 <- s.match(w1.ms, w1.msm, plab.cex = 0.75, plot = FALSE)
      G3 <- cbindADEg(g9, g10, plot = TRUE)
    } else {
      oldpar <- par(mfrow = c(1,2))
      s.match(w1, w1m, clab = 0.75)
      s.match(w1.ms, w1.msm, clab = 0.75)
      par(oldpar)
    }

    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
    multispati.randtest(maf.pca, maf.listw)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf=FALSE)
    plot(maf.pca.ms)
}