[R-sig-Geo] GRTS sampling

Tue Feb 12 10:17:11 CET 2013

Dear Dick,

I have written my own functions for GRTS sampling. The idea is that you create a square matrix with dimensions which are a power of 2. Then it is easy to use a recursive function. The output is a matrix with the order of the cell. Sampling n elements reduces to take the first n elements.

QuadratRanking <- function(Ranking, Level = 0){
  if(ncol(Ranking) > 1){
    Sequence <- sample(0:3)
    Q1 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) <= nrow(Ranking) / 2, seq_len(ncol(Ranking)) <= ncol(Ranking) / 2, drop = FALSE] + Sequence[1] * 4 ^ Level, Level = Level + 1)
    Q2 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) > nrow(Ranking) / 2, seq_len(ncol(Ranking)) <= ncol(Ranking) / 2, drop = FALSE] + Sequence[2] * 4 ^ Level, Level = Level + 1)
    Q3 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) <= nrow(Ranking) / 2, seq_len(ncol(Ranking)) > ncol(Ranking) / 2, drop = FALSE] + Sequence[3] * 4 ^ Level, Level = Level + 1)
    Q4 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) > nrow(Ranking) / 2, seq_len(ncol(Ranking)) > ncol(Ranking) / 2, drop = FALSE] + Sequence[4] * 4 ^ Level, Level = Level + 1)
    cbind(rbind(Q1, Q2), rbind(Q3, Q4))
  } else {
    Ranking
  }
}
DimGrid <- 2 ^2
QuadratRanking(matrix(0L, ncol = DimGrid, nrow = DimGrid), Level = 0)

Here is a solution when you want to sample within a polygon

GRTS <- function(spPolygon, Precision, Subset = TRUE, RandomStart = TRUE){
  library(sp)
  QuadratRanking <- function(Ranking, Level = 0){
    if(ncol(Ranking) > 1){
      Sequence <- sample(0:3)
      Q1 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) <= nrow(Ranking) / 2, seq_len(ncol(Ranking)) <= ncol(Ranking) / 2, drop = FALSE] + Sequence[1] * 4 ^ Level, Level = Level + 1)
      Q2 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) > nrow(Ranking) / 2, seq_len(ncol(Ranking)) <= ncol(Ranking) / 2, drop = FALSE] + Sequence[2] * 4 ^ Level, Level = Level + 1)
      Q3 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) <= nrow(Ranking) / 2, seq_len(ncol(Ranking)) > ncol(Ranking) / 2, drop = FALSE] + Sequence[3] * 4 ^ Level, Level = Level + 1)
      Q4 <- QuadratRanking(Ranking[seq_len(nrow(Ranking)) > nrow(Ranking) / 2, seq_len(ncol(Ranking)) > ncol(Ranking) / 2, drop = FALSE] + Sequence[4] * 4 ^ Level, Level = Level + 1)
      cbind(rbind(Q1, Q2), rbind(Q3, Q4))
    } else {
      Ranking
    }
  }
  Xrange <- bbox(spPolygon)[1, ]
  Yrange <- bbox(spPolygon)[2, ]
  DimGrid <- ceiling(max(diff(Xrange), diff(Yrange)) / Precision)
  DimGrid <- 2 ^ min(seq_len(100)[2 ^ seq_len(100) > DimGrid])

  GRTS <- QuadratRanking(matrix(0L, ncol = DimGrid, nrow = DimGrid), Level = 0)
  GRTS <- GRTS[seq_len(ceiling(diff(Xrange)/Precision)), seq_len(ceiling(diff(Yrange)/Precision))]
  if(RandomStart){
    GRID <- GridTopology(cellcentre.offset = c(x = min(Xrange), y = min(Yrange)) + runif(2, min = 0, max = Precision), cellsize = c(Precision, Precision), cells.dim = dim(GRTS))
  } else {
    GRID <- GridTopology(cellcentre.offset = c(x = min(Xrange), y = min(Yrange)) + 0.5 * Precision, cellsize = c(Precision, Precision), cells.dim = dim(GRTS))
  }
  GRTS <- SpatialGridDataFrame(grid = GRID, data = data.frame(Ranking = as.vector(GRTS)), proj4string = proj4string(spPolygon))
  rm(GRID)
  if(Subset){
    gc()
    gridded(GRTS) <- FALSE
    GRTS <- GRTS[!is.na(over(GRTS, spPolygon)[, 1]), ]
    GRTS <- GRTS[order(GRTS$Ranking), ]
    GRTS$Ranking <- seq_along(GRTS$Ranking)
  }
  GRTS
}

If anyone would like to add it to a package, please feel free to do so. As long as it released under a GPL like license and properly credited.

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

-----Oorspronkelijk bericht-----
Van: r-sig-geo-bounces at r-project.org [mailto:r-sig-geo-bounces at r-project.org] Namens Dick Brus
Verzonden: maandag 11 februari 2013 15:45
Aan: r-sig-geo at r-project.org
Onderwerp: [R-sig-Geo] GRTS sampling

I try to understand the hierarchical randomization as applied in the GRTS design.

I randomized 16 points on a square grid, see R script below. The argument do.sample was set to FALSE, so that the result consists of a dataframe of all 16 points instead of a GRTS sample. When plotting the order of the points it appears that the numbers 1-4 are not always in different subsquares (of which there are four) , for instance points 1 and 3 are both in the lower-right subsquare. What am I doing wrong?

library(spsurvey)

frame<-expand.grid(x=seq(from=1,to=4,by=1),y=seq(from=1,to=4,by=1))

#population size (total number of sampling units in Kandahar)
N<-nrow(frame)

#set number of sampling units (sample size) to be selected
n<-4

design<-list(None=list(panel=c(Panel1=n), seltype="Equal", caty.n=c("Caty 1"=n), over=0)) x<-frame$x y<-frame$y index<-1:N
att<-data.frame(x=x,y=y,ids=index)

#do.sample=FALSE gives all sampling units in hierarchical? randomized order res<-grts(design, DesignID="Site", SiteBegin=1, type.frame="finite",
         src.frame="att.frame", in.shape=NULL, sp.object=NULL, att.frame=att,
         id=NULL, xcoord="x", ycoord="y", stratum=NULL, mdcaty=NULL, startlev=2,
         maxlev=11, maxtry=1000, shift.grid=FALSE, do.sample=rep(FALSE, length(design)),
         shapefile=FALSE, prjfilename=NULL, out.shape="sample")
frame.randomized<-data.frame(res$xcoord,res$ycoord)
names(frame.randomized)<-c("x","y")
frame.randomized$id<-1:N

png(file = "GRTSRandomizedFrameSquare.png", width = 480, height = 480) print(
  ggplot(data = frame.randomized) +
    geom_text(
      data = frame.randomized,
      mapping = aes(
        x = x,
        y = y,
        label = id
      ),
      size = 5
    ) +
    coord_equal()
)
dev.off()

<http://r-sig-geo.2731867.n2.nabble.com/file/n7582569/GRTSRandomizedFrameSquare.png>

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