ecespa (version 1.1-17)

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 ecespa.marksum
plot(x, what="normalized",  contour=FALSE, grid=FALSE,
	ribbon=TRUE,col=NULL ,main=NULL,xlab="",ylab="",...)

Value

marksum gives an object of class 'ecespa.marksum'; basically a list with the following elements:

normalized

Normalized mark-sum measure estimated in the grid points.

marksum

Raw mark-sum measure estimated in the grid points.

pointsum

Point-sum measure estimated in the grid points.

minus

Point-sum of the grid points. For advanced use only.

grid

Grid of points.

nx

Density of the estimating grid in the x-side.

ny

Density of the estimating grid in the x-side.

dataname

Name of the ppp object analysed.

R

Radius. The distance argument r at which the mark-sum measure has been computed.

window

Window of the point pattern.

plot.ecespa.marksum plots the selected mark-sum measure.

Arguments

mippp

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

R

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

nx

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

ny

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

x

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 the parameters of the smoothing kernel, pixel resolution, etc.

Author

Marcelino de la Cruz Rot

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.

See Also

getis, related to the point-sum measure, and markstat for designing different implementations.

Examples

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

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

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

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