GWmodel (version 2.4-1)

gwpca: GWPCA

Description

This function implements basic or robust GWPCA.

Usage

gwpca(data, elocat, vars, k = 2, robust = FALSE, scaling=T, kernel = "bisquare",
                  adaptive = FALSE, bw, p = 2, theta = 0, longlat = F, cv = T, scores=F,
                  dMat)
# S3 method for gwpca
print(x, ...)

Value

A list of class “gwpca”:

GW.arguments

a list class object including the model fitting parameters for generating the report file

pca

an object of class inheriting from “princomp”, see princomp.

loadings

the localised loadings

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package “sp”) or sf object (see package “sf”) integrated with local proportions of variance for each principle components, cumulative proportion and winning variable for the 1st principle component in its "data" slot.

gwpca.scores

the localised scores of the supplied data on the principal components

var

The local amount of variance accounted for by each component

CV

Vector of cross-validation data

timings

starting and ending time.

Arguments

data

a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp, or a sf object defined in package sf

elocat

a two-column numeric array or Spatial*DataFrame object for providing evaluation locations, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

vars

a vector of variable names to be evaluated

k

the number of retained components; k must be less than the number of variables

robust

if TRUE, robust GWPCA will be applied; otherwise basic GWPCA will be applied

scaling

if TRUE, the data is scaled to have zero mean and unit variance (standardized); otherwise the data is centered but not scaled

kernel

function chosen as follows:

gaussian: wgt = exp(-.5*(vdist/bw)^2);

exponential: wgt = exp(-vdist/bw);

bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise;

tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise;

boxcar: wgt=1 if dist < bw, wgt=0 otherwise

adaptive

if TRUE calculate an adaptive kernel where the bandwidth corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance)

bw

bandwidth used in the weighting function, possibly calculated by bw.gwpca;fixed (distance) or adaptive bandwidth(number of nearest neighbours)

p

the power of the Minkowski distance, default is 2, i.e. the Euclidean distance

theta

an angle in radians to rotate the coordinate system, default is 0

longlat

if TRUE, great circle distances will be calculated

cv

If TRUE, cross-validation data will be found that are used to calculate the cross-validation score for the specified bandwidth.

scores

if scores = TRUE, the scores of the supplied data on the principal components will be calculated.

dMat

a pre-specified distance matrix, it can be calculated by the function gw.dist

x

an object of class “gwpca”, returned by the function gwpca

...

arguments passed through (unused)

Author

Binbin Lu

References

Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.

Harris P, Brunsdon C, Charlton M (2011) Geographically weighted principal components analysis. International Journal of Geographical Information Science 25:1717-1736

Harris P, Brunsdon C, Charlton M, Juggins S, Clarke A (2014) Multivariate spatial outlier detection using robust geographically weighted methods. Mathematical Geosciences 46(1) 1-31

Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2014) Geographically weighted methods and their use in network re-designs for environmental monitoring. Stochastic Environmental Research and Risk Assessment 28: 1869-1887

Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2015) Enhancements to a geographically weighted principal components analysis in the context of an application to an environmental data set. Geographical Analysis 47: 146-172

Examples

if (FALSE) {
if(require("mvoutlier") && require("RColorBrewer"))
{
  data(bsstop)
  Data.1 <- bsstop[, 1:14]
  colnames(Data.1)
  Data.1.scaled <- scale(as.matrix(Data.1[5:14]))  # standardised data...
  rownames(Data.1.scaled) <- Data.1[, 1]
  #compute principal components:
  pca <- princomp(Data.1.scaled, cor = FALSE, scores = TRUE)  
  # use covariance matrix to match the following...
  pca$loadings
  data(bss.background)
  backdrop <- function() 
   plot(bss.background, asp = 1, type = "l", xaxt = "n", yaxt = "n", 
   xlab = "", ylab = "", bty = "n", col = "grey")
  pc1 <- pca$scores[, 1]
  backdrop()
  points(Data.1$XCOO[pc1 > 0], Data.1$YCOO[pc1 > 0], pch = 16, col = "blue")
  points(Data.1$XCOO[pc1 < 0], Data.1$YCOO[pc1 < 0], pch = 16, col = "red")
  
  #Geographically Weighted PCA and mapping the local loadings
  # Coordinates of the sites
  Coords1 <- as.matrix(cbind(Data.1$XCOO,Data.1$YCOO)) 
  d1s <- SpatialPointsDataFrame(Coords1,as.data.frame(Data.1.scaled))
  pca.gw <- gwpca(d1s,vars=colnames(d1s@data),bw=1000000,k=10)
  local.loadings <- pca.gw$loadings[, , 1]  
  
  # Mapping the winning variable with the highest absolute loading
  # note first component only - would need to explore all components..
  
  lead.item <- colnames(local.loadings)[max.col(abs(local.loadings))]
  df1p = SpatialPointsDataFrame(Coords1, data.frame(lead = lead.item))
  backdrop()
  colour <- brewer.pal(8, "Dark2")[match(df1p$lead, unique(df1p$lead))]
  plot(df1p, pch = 18, col = colour, add = TRUE)
  legend("topleft", as.character(unique(df1p$lead)), pch = 18, col = 
      brewer.pal(8, "Dark2"))
  backdrop()
  
  #Glyph plots give a view of all the local loadings together
  glyph.plot(local.loadings, Coords1, add = TRUE)
  
  #it is not immediately clear how to interpret the glyphs fully, 
  #so inter-actively identify the full loading information using:
  check.components(local.loadings, Coords1)
  
  # GWPCA with an optimal bandwidth
  bw.choice <- bw.gwpca(d1s,vars=colnames(d1s@data),k=2) 
  pca.gw.auto  <- gwpca(d1s,vars=colnames(d1s@data),bw=bw.choice,k=2)
  # note first component only - would need to explore all components..
  local.loadings <- pca.gw.auto$loadings[, , 1]  
  
  lead.item <- colnames(local.loadings)[max.col(abs(local.loadings))]
  df1p = SpatialPointsDataFrame(Coords1, data.frame(lead = lead.item))
  backdrop()
  colour <- brewer.pal(8, "Dark2")[match(df1p$lead, unique(df1p$lead))]
  plot(df1p, pch = 18, col = colour, add = TRUE)
  legend("topleft", as.character(unique(df1p$lead)), pch = 18, 
  col = brewer.pal(8, "Dark2"))
  
  # GWPCPLOT for investigating the raw multivariate data
  gw.pcplot(d1s, vars=colnames(d1s@data),focus=359, bw = bw.choice) 
}
}