marksum: Mark-sum measure

In ecespa: Functions for Spatial Point Pattern Analysis

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

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)

ecespa documentation built on Jan. 6, 2023, 1:21 a.m.