marksum {ecespa}R Documentation

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.
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.

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.

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.

Author(s)

Marcelino de la Cruz Rot marcelino.delacruz@upm.es

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 markstats for designing different implementations.

Examples

 ## Not run: 
   
 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

## End(Not run)

[Package ecespa version 1.1-1 Index]