latticeDensity (version 1.2.7)

crossvalNparReg: Crossvalidation for non-parametric regression.

Description

Performs least-squares crossvalidation for the lattice-based non-parametric regression estimator.

Usage

crossvalNparReg(formLatticeOutput, Z, PointPattern, M = 0.5, max_steps = 200)

Value

A list consisting of

• SumSq Vector of crossvalidated sums of squares

• Number of steps that minimizes the crossvalidated SS.

Arguments

formLatticeOutput

An object from formLattice or editLattice.

Z

Vector of response values to be smoothed.

PointPattern

A 2-column matrix or data frame of locations.

M

Maximum probability that the random walk moves.

max_steps

Maximum number of steps attempted.

Author

Ronald P. Barry

Details

For a given k, deleted residuals are computed for each of the observations. The crossvalidation is based on minimization of the squares of the deleted residuals.

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.

Julie McIntyre, Ronald P. Barry (2018) A Lattice-Based Smoother for Regions with Irregular Boundaries and Holes. Journal of Computational and Graphical Statistics. <doi:10.1080/10618600.2017.1375935>

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 = 40)
NparRegOut <- createNparReg(formLatticeOutput,Z,PointPattern=grid2,k=hold$k)
plot(NparRegOut)