multispati: Multivariate spatial analysis

In adespatial: Multivariate Multiscale Spatial Analysis

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)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf=FALSE)
    plot(maf.pca.ms)
}

adespatial documentation built on Sept. 11, 2024, 7:04 p.m.