Function to compute and manage Moran's Eigenvector Maps (MEM) of a listw object

These functions compute MEM (i.e., eigenvectors of a doubly centered spatial weighting matrix). Corresponding eigenvalues are linearly related to Moran's index of spatial autocorrelation.

scores.listw(
  listw,
  wt = rep(1, length(listw$neighbours)),
  MEM.autocor = c("non-null", "all", "positive", "negative"),
  store.listw = FALSE
)

mem(
  listw,
  wt = rep(1, length(listw$neighbours)),
  MEM.autocor = c("non-null", "all", "positive", "negative"),
  store.listw = FALSE
)

orthobasis.listw(
  listw,
  wt = rep(1, length(listw$neighbours)),
  MEM.autocor = c("non-null", "all", "positive", "negative"),
  store.listw = FALSE
)

# S3 method for class 'orthobasisSp'
x[i, j, drop = TRUE]

Arguments

listw

An object of the class listw created by functions of the spdep package

wt

A vector of weights. It is used to orthogonalize the eigenvectors. It could be useful if MEM are used in weighted regression or canonical correspondence analysis

MEM.autocor

A string indicating if all MEMs must be returned or only those corresponding to non-null, positive or negative autocorrelation. The difference between options all and non-null is the following: when there are several null eigenvalues, option all removes only one of the eigenvectors with null eigenvalues and returns (n-1) eigenvectors, whereas non-null does not return any of the eigenvectors with null eigenvalues.

store.listw

A logical indicating if the spatial weighting matrix should be stored in the attribute listw of the returned object

x

An object of class orthobasisSp.

i, j

Elements to extract (integer or empty): index of rows (i) and columns (j).

drop

A logical. If TRUE, object containing only one colum is converted in vector

Value

An object of class orthobasisSp , subclass orthobasis. The MEMs are stored as a data.frame. It contains several attributes (see ?attributes) including:

• listw: The associated spatial weighting matrix (if store.listw = TRUE).

Details

Testing the nullity of eigenvalues is based on E(i)/E(1) where E(i) is i-th eigenvalue and E(1) is the maximum absolute value of eigenvalues

References

Dray, S., Legendre, P., and Peres-Neto, P. R. (2006). Spatial modeling: a comprehensive framework for principal coordinate analysis of neighbor matrices (PCNM). Ecological Modelling 196, 483–493.

Griffith D. A. (1996) Spatial autocorrelation and eigenfunctions of the geographic weights matrix accompanying geo-referenced data. Canadian Geographer 40, 351–367.

See also

nb2listw orthobasis

Author

Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

if(require("ade4", quietly = TRUE) & require("spdep", quietly = TRUE)){
data(oribatid)
nbtri <- tri2nb(as.matrix(oribatid$xy))
sc.tri <- scores.listw(nb2listw(nbtri, style = "B"))
summary(sc.tri)
}
#> Orthonormal basis: data.frame with 70 rows and 69 columns
#> ----------------------------------------------------------------
#> Columns form a centred orthonormal basis (i.e. 1n-orthogonal)
#> for the inner product defined by the 'weights' attribute
#> ----------------------------------------------------------------
#> 
#> Attributes:
#> - names: MEM1 ... MEM69 
#> - row.names: 1 ... 70 
#> - weights: 0.01428571 ... 0.01428571 
#> - values: 0.07805391 ... -0.04134591 
#> - class: orthobasisSp orthobasis data.frame 
#> - call: scores.listw(listw = nb2listw(nbtri, style = "B")) 
#> 
if(require("adegraphics", quietly = TRUE)){
s.value(oribatid$xy,sc.tri[,1:9])
plot(sc.tri[,1:6], oribatid$xy, pSp.cex = 5, pSp.alpha = 0.5, pbackground.col = 'lightblue')
}
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'obj' in selecting a method for function 'coordinates': object 'sc.tri' not found