gLISA: Pair correlaton LISA functions

In frajaroco/scdcLISA: Spatial cluster detection and classification through LISA functions

Description

Computes an edge-corrected kernel estimator of the pair correlation LISA functions.

Usage

gLISA(xy, ds, ks = "epanechnikov", hs, inhom=FALSE, correction = "isotropic")

Arguments

xy	Spatial coordinates (x,y) as objects of class 'ppp' to represent a two-dimensional point pattern. Includes information about the window in which the pattern was observed.
ds	A vector of distances u at which g^{(i)}(u) is computed.
ks	A kernel function for the spatial distances. The default is "epanechnikov" the Epanechnikov kernel. It can also be "rectangular" or "biweight".
hs	A bandwidth of the kernel function ks. If hs missing, the bandwidth is calculate using the function bw.pcf function in the R package spatstat which uses composite likelihood or generalised least squares cross-validation methods.
lambda	Values of the estimated intensity function. By default the spatial intensity is computed for the homogeneous case.
correction	A character vector specifying the edge-correction(s) to be applied among "isotropic" and "none". The default is "isotropic".

Details

For more details see Stoyan and Stoyan (1994), Cressie and Collins (2001) and Baddeley et al. (2015).

Value

A list containing:

• lisa.g: A matrix containing the values of the estimation of g^{(i)}(u) for each one of n points of the process by columns.

• ds: If ds is missing, a vector of distances u at which g^{(i)}(u) is computed under the restriction 0<ε<r.

• kernel: A vector of names and bandwidth of the spatial kernel.

• lambda: Vector of values for the estimated spatial intensity function at the points (x,y) in W.

• githeo: Theoretical value under a Poisson point processes model.

Author(s)

Francisco J. Rodriguez-Cortes <[e-mail]> https://fjrodriguezcortes.wordpress.com

References

Baddeley, A. and Turner, J. (2005). spatstat: An R Package for Analyzing Spatial Point Pattens. Journal of Statistical Software 12, 1-42.

Baddeley, A., Rubak, E. and Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R. In: Chapman & Hall Interdisciplinary Statistics Series, CRC Press, Boca Raton, Florida.

Cressie, N. and Collins, L. B. (2001). Analysis of spatial point patterns using bundles of product density LISA functions. Journal of Agricultural, Biological, and Environmental Statistics 6, 118-135.

Cressie, N. and Collins, L. B. (2001). Patterns in spatial point locations: Local indicators of spatial association in a minefield with clutter Naval Research Logistics (NRL), John Wiley & Sons, Inc. 48, 333-34.

Fiksel, T. (1988). Edge-corrected density estimators for point processes, Statistics 19, 67-75.

Illian, J B., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley and Sons, London.

Stoyan, D. and Stoyan, H. (1994). Fractals, random shapes, and point fields: methods of geometrical statistics. Chichester: Wiley.

Examples

## Not run:
#################

# Realisations of the homogeneous Poisson processes
pp <- rpoispp(100)
plot.numbers(pp)

# This function provides an edge-corrected kernel estimator of
# the pair correlation LISA functions assuming homogeneity.
out <- gLISA(pp)
out

# R plot
par(mfrow=c(1,1))
plot.LISA(out)

# This function provides an edge-corrected kernel estimator of
# the pair correlation LISA functions assuming inhomogeneity.
den <- density.ppp(pp, at="points")
outi <- gLISA(pp, lambda = den)
outi

# R plot
par(mfrow=c(1,1))
plot.LISA(outi)

## End(Not run)

frajaroco/scdcLISA documentation built on Nov. 28, 2021, 12:19 a.m.