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)
marksum.plot(mimarksum, what="normalized", gris=FALSE,
            contour=FALSE, interpol=TRUE, leip=100, main="", ...)

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.
mimarksum 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).
gris Logical; if "TRUE" display map in grey levels.
contour Logical; if "TRUE" add contour to map.
interpol Logical; if "TRUE" display interpolated results (with function interp of akima).
leip Number of points in the side of the grid of points to interpolate the results.
main Text or expression to be displayed as a title in the map.
... Additional parametrs to contour.

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 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.
R Radius. The distance argument r at which the mark-sum measure has been computed.
window Window of the point pattern.


marksum.plot 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=20)

 marksum.plot(seed.m, what="marksum")  # raw mark-sum measure

 marksum.plot(seed.m, what="pointsum") # point sum measure
   
 marksum.plot(seed.m,  what="normalized") # normalized  mark-sum measure
  
  ## End(Not run)

[Package ecespa version 1.0-3 Index]