marksum: Mark-sum measure

Description

An exploratory data analysis technique for marked point patterns. The marked point pattern is mapped to a random field for visual inspection.

Usage

marksum(mippp, R = 10, nx = 30, ny = 30)

## S3 method for ploting objects of class 'ecespa.marksum':
## S3 method for class 'ecespa.marksum':
plot(x, what="normalized",  contour=FALSE, grid=FALSE, ribbon=TRUE,col=NULL ,main=NULL,xlab="",ylab="",...)

Arguments

mippp

A marked point pattern. An object with the ppp format of spatstat.

Radius. The distance argument r at which the mark-sum measure should be computed

Grid density (for estimation) in the x-side.

Grid density (for estimation) in the y-side.

An object of class 'ecespa.marksum'. Usually, the result of applying marksum to a point pattern.

what

What to plot. One of "marksum" (raw mark sum measure), "point" (point sum measure) or "normalized" (normalized sum measure).

contour

Logical; if "TRUE" add contour to map.

grid

Logical; if "TRUE" add marked grid to map.

ribbon

Logical; if "TRUE" add legend to map.

col

Color table to use for the map ( see help file on image for details).

main

Text or expression to add as a title to the plot.

xlab

Text or expression to add as a label to axis x.

ylab

Text or expression to add as a label to axis y.

...

Additional parameters to smooth.ppp, density.ppp or as.mask, to control

Value

marksum gives an object of class 'ecespa.marksum'; basically a list with the following elements:
normalizedNormalized mark-sum measure estimated in the grid points.
marksumRaw mark-sum measure estimated in the grid points.
pointsumPoint-sum measure estimated in the grid points.
minusPoint-sum of the grid points. For advanced use only.
gridGrid of points.
nxDensity of the estimating grid in the x-side.
nyDensity of the estimating grid in the x-side.
datanameName of the ppp object analysed.
RRadius. The distance argument r at which the mark-sum measure has been computed.
windowWindow of the point pattern.
plot.ecespa.marksum plots the selected mark-sum measure.

Details

Penttinen (2006) defines the mark-sum measure as a smoothed summary measuring locally the contribution of points and marks. For any fixed location $x$ within the observational window and a distance $R$, the mark-sum measure $S[R](x)$ equals the sum of the marks of the points within the circle of radius $R$ with centre in $x$. The point-sum measure $I[R](x)$ is defined by him as the sum of points within the circle of radius $R$ with centre in $x$, and describes the contribution of points locally near $x$. The normalized mark-sum measure describes the contribution of marks near $x$ and is defined (Penttinen, 2006) as $$S.normalized[R](x) = S[R](x)/I[R](x)$$ This implementation of marksum estimates the mark-sum and the point-sum measures in a grid of points whose density is defined by nx and ny.

References

Penttinen, A. 2006. Statistics for Marked Point Patterns. In The Yearbook of the Finnish Statistical Society, pp. 70-91.

Examples

Run this code

data(seedlings1)
   
 seed.m <- marksum(seedlings1, R=25)

 plot(seed.m, what="marksum", sigma = 5)  # raw mark-sum measure; sigma is bandwith for smoothing

 plot(seed.m, what="pointsum", sigma = 5, col = tim.colors(30),) # point sum measure
   
 plot(seed.m,  what="normalized", dimyx=200, contour=TRUE, sigma = 5) # normalized  mark-sum measure

# the same with added grid
plot(seed.m,  what="normalized", dimyx=200, contour=TRUE, sigma = 5, grid=TRUE) # normalized  mark-sum measure

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