Spatial weights matrix powers traces

The function is used to prepare a vector of traces of powers of a spatial weights matrix

Usage

trW(W=NULL, m = 30, p = 16, type = "mult", listw=NULL, momentsSymmetry=TRUE)
mom_calc(lw, m)
mom_calc_int2(is, m, nb, weights, Card)

Arguments

W: A spatial weights matrix in CsparseMatrix form
m: The number of powers; must be an even number for ‘type’=“moments” (default changed from 100 to 30 (2010-11-17))
p: The number of samples used in Monte Carlo simulation of the traces if type is MC (default changed from 50 to 16 (2010-11-17))
type: Either “mult” (default) for powering a sparse matrix (with moderate or larger N, the matrix becomes dense, and may lead to swapping), or “MC” for Monte Carlo simulation of the traces (the first two simulated traces are replaced by their analytical equivalents), or “moments” to use the looping space saving algorithm proposed by Smirnov and Anselin (2009) - for “moments”, W must be symmetric, for row-standardised weights through a similarity transformation
listw, lw: a listw object, which should either be fully symmetric, or be constructed as similar to symmetric from intrinsically symmetric neighbours using similar.listw, used with ‘type’=“moments”
momentsSymmetry: default TRUE; assert Smirnov/Anselin symmetry assumption
is: (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
nb: (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
weights: (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
Card: (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)

Value

A numeric vector of m traces, with “timings” and “type” attributes; the ‘type’=“MC” also returns the standard deviation of the p-vector V divided by the square root of p as a measure of spread for the trace estimates.

Note

mom_calc and mom_calc_int2 are for internal use only

References

LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 96–105; Smirnov O and L Anselin (2009) An O(N) parallel method of computing the Log-Jacobian of the variable transformation for models with spatial interaction on a lattice. Computational Statistics and Data Analysis 53 (2009) 2983–2984.

Author

Roger Bivand Roger.Bivand@nhh.no

Examples

require("sf", quietly=TRUE) 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
#require(spdep, quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
listw <- spdep::nb2listw(col.gal.nb)
W <- as(listw, "CsparseMatrix")
system.time(trMat <- trW(W, type="mult"))
#>    user  system elapsed 
#>   0.003   0.000   0.004 
str(trMat)
#>  num [1:30] 0 10.91 3.65 5.62 3.66 ...
#>  - attr(*, "timings")= Named num [1:2] 0.003 0.004
#>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
#>  - attr(*, "type")= chr "mult"
#>  - attr(*, "n")= int 49
set.seed(1100)
system.time(trMC <- trW(W, type="MC"))
#>    user  system elapsed 
#>   0.006   0.000   0.006 
str(trMC)
#>  num [1:30] 0 10.91 3.69 5.36 3.64 ...
#>  - attr(*, "sd")= num [1:30] NA NA 0.598 0.495 0.489 ...
#>  - attr(*, "timings")= Named num [1:2] 0.006 0.006
#>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
#>  - attr(*, "type")= chr "MC"
#>  - attr(*, "n")= int 49
plot(trMat, trMC)
abline(a=0, b=1)
for(i in 3:length(trMC)) {
 segments(trMat[i], trMC[i]-2*attr(trMC, "sd")[i], trMat[i],
  trMC[i]+2*attr(trMC, "sd")[i])
}

listwS <- similar.listw(listw)
W <- forceSymmetric(as(listwS, "CsparseMatrix"))
system.time(trmom <- trW(listw=listwS, m=24, type="moments"))
#>    user  system elapsed 
#>   0.002   0.000   0.002 
str(trmom)
#>  num [1:24] 0 10.91 3.65 5.62 3.66 ...
#>  - attr(*, "timings")= Named num [1:2] 0.002 0.002
#>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
#>  - attr(*, "type")= chr "moments"
#>  - attr(*, "n")= int 49
all.equal(trMat[1:24], trmom, check.attributes=FALSE)
#> [1] TRUE
system.time(trMat <- trW(W, m=24, type="mult"))
#>    user  system elapsed 
#>   0.004   0.000   0.003 
str(trMat)
#>  num [1:24] 0 10.91 3.65 5.62 3.66 ...
#>  - attr(*, "timings")= Named num [1:2] 0.003 0.003
#>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
#>  - attr(*, "type")= chr "mult"
#>  - attr(*, "n")= int 49
all.equal(trMat, trmom, check.attributes=FALSE)
#> [1] TRUE
set.seed(1)
system.time(trMC <- trW(W, m=24, type="MC"))
#>    user  system elapsed 
#>   0.007   0.000   0.008 
str(trMC)
#>  num [1:24] 0 10.91 2.44 4.97 2.82 ...
#>  - attr(*, "sd")= num [1:24] NA NA 0.618 0.501 0.451 ...
#>  - attr(*, "timings")= Named num [1:2] 0.007 0.008
#>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
#>  - attr(*, "type")= chr "MC"
#>  - attr(*, "n")= int 49
if (FALSE) { # \dontrun{
data(boston, package="spData")
listw <- spdep::nb2listw(boston.soi)
listwS <- similar.listw(listw)
system.time(trmom <- trW(listw=listwS, m=24, type="moments"))
str(trmom)
library(parallel)
nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L
# set nc to 1L here
if (nc > 1L) nc <- 1L
coresOpt <- get.coresOption()
invisible(set.coresOption(nc))
if(!get.mcOption()) {
  cl <- makeCluster(get.coresOption())
  set.ClusterOption(cl)
}
system.time(trmomp <- trW(listw=listwS, m=24, type="moments"))
if(!get.mcOption()) {
  set.ClusterOption(NULL)
  stopCluster(cl)
}
all.equal(trmom, trmomp, check.attributes=FALSE)
invisible(set.coresOption(coresOpt))
} # }