What is the "listw" argument in the multispati (multivariate Spatial analysis) - R software?

Question

It involves spatial dependency, but I’m not sure how.

Answer 1

The argument listw is a class object listw created by, for example, the nb2listw, as quoted in the commentary by Tomás Barcellos.

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Example of use:

nb2listw(neighbours, glist=NULL, style="W", zero.policy=FALSE)

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nb2listw

  Spatial Weights for Neighbours lists
"Space weights for neighbour lists"

The Function Supplements a Neighbours list with Spatial Weights for the Chosen coding Scheme.
"The function complements a list of neighbors with spatial weights for the chosen coding scheme".

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Neighbours is an object of the class nb

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Example of use of nb2listw:

data(columbus)
cards <- card(col.gal.nb)
col.w <- nb2listw(col.gal.nb)
plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10),
ylim=c(0,10), xlab="number of links", ylab="row sums of weights")
col.b <- nb2listw(col.gal.nb, style="B")
points(cards, unlist(lapply(col.b$weights, sum)), col="red")
col.c <- nb2listw(col.gal.nb, style="C")
points(cards, unlist(lapply(col.c$weights, sum)), col="green")
col.s <- nb2listw(col.gal.nb, style="S")
points(cards, unlist(lapply(col.s$weights, sum)), col="blue")
legend(x=c(0, 1), y=c(7, 9), legend=c("W", "B", "C", "S"),
col=c("black", "red", "green", "blue"), pch=rep(1,4))
dlist <- nbdists(col.gal.nb, coords)
dlist <- lapply(dlist, function(x) 1/x)
col.w.d <- nb2listw(col.gal.nb, glist=dlist)
summary(unlist(col.w$weights))
summary(unlist(col.w.d$weights))

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Example of the use of multispati:

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
  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")
}
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$as, plot = FALSE)
  G1 <- ADEgS(list(g2, g3, g4), layout = c(1, 3))
} else {
  par(mfrow = c(1, 3))
  barplot(maf.coa$eig)
  barplot(maf.coa.ms$eig) 
  s.corcircle(maf.coa.ms$as)
  par(mfrow = c(1, 1))
}


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 {
  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))
}


  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 {
  par(mfrow = c(1,2))
  s.match(w1, w1m, clab = 0.75)
  s.match(w1.ms, w1.msm, clab = 0.75)
  par(mfrow = c(1, 1))
}

  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)
}

References:

1 - https://www.rdocumentation.org/packages/adespatial/versions/0.0-7/topics/multispati
2 - https://www.rdocumentation.org/packages/spdep/versions/0.1-10/topics/nb2listw