latticeDensity (version 1.2.7)

varianceMap: Spatial variance for the regression smoother.

Description

Computes the variance at each location for the non-parametric regression estimator.

Usage

varianceMap(formLatticeOutput, Z, PointPattern, M = 0.5, k)

Value

VarianceMapOut object

• EW_locs EW coordinates for use by contour

• NS_locs NS coordinates for use by contour

• boundaryPoly vertices of the boundary

• hole_list list of polygonal hole boundaries, if any.

• SE_map_grid estimated standard error at each location

Arguments

formLatticeOutput

An object from formLattice or editLattice.

Z

Vector of response values.

PointPattern

2-column matrix or data frame of locations.

M

Maximum probability that the random walk moves.

k

Number of steps in random walk.

Author

Ronald P. Barry

Details

varianceMap computes an estimated variance at each node in the lattice, output in a form for mapping with contour. The approach is the Nadaraya-Watson kernel variance estimator: \(s^2\sum K^2(si,s0)/(\sum K(si,s0))^2\). It's important to note that this should not be overused as a prediction error, as kernel estimators are not unbiased.

References

Ronald P. Barry, Julie McIntyre. Estimating animal densities and home range in regions with irregular boundaries and holes: A lattice-based alternative to the kernel density estimator. Ecological Modelling 222 (2011) 1666-1672. <doi:10.1016/j.ecolmodel.2011.02.016>

Julie McIntyre, Ronald P. Barry (2018) A Lattice-Based Smoother for Regions with Irregular Boundaries and Holes. Journal of Computational and Graphical Statistics. In Press.

Examples

data(nparExample)
attach(nparExample)
plot.new()
#  Simulate a response variable
index1 <- (grid2[,2]<0.8)|(grid2[,1]>0.6)
Z <- rep(NA,length(grid2[,1]))
n1 <- sum(index1)
n2 <- sum(!index1)
Z[index1] <- 3*grid2[index1,1] + 4 + rnorm(n1,0,sd=0.4)
Z[!index1] <- -2*grid2[!index1,1] + 4 + rnorm(n2,0,sd=0.4)
#
plot(polygon2,type="n")

polygon(polygon2)
points(grid2,pch=19,cex=0.5,xlim=c(-0.1,1))
text(grid2,labels=round(Z,1),pos=4,cex=0.5)
#
nodeFillingOutput <- nodeFilling(poly=polygon2, node_spacing=0.025)
plot(nodeFillingOutput)
formLatticeOutput <- formLattice(nodeFillingOutput)
plot(formLatticeOutput)
hold <- crossvalNparReg(formLatticeOutput,Z,
                       PointPattern=grid2,M=0.5,max_steps = 20)
var_map <- varianceMap(formLatticeOutput,Z,
             PointPattern=grid2,M=0.5,k=10)
plot(var_map)