0th

Percentile

##### Resample a Point Pattern by Resampling Quadrats

Given a point pattern dataset, create a resampled point pattern by dividing the window into rectangular quadrats and randomly resampling the list of quadrats.

Keywords
spatial, datagen
##### Usage
quadratresample(X, nx, ny=nx, ..., replace = FALSE, nsamples = 1)
##### Arguments
X
A point pattern dataset (object of class "ppp").
nx,ny
Numbers of quadrats in the $x$ and $y$ directions.
...
Ignored.
replace
Logical value. Specifies whether quadrats should be sampled with or without replacement.
nsamples
Number of randomised point patterns to be generated.
##### Details

This command implements a very simple bootstrap resampling procedure for spatial point patterns X.

The dataset X must be a point pattern (object of class "ppp") and its observation window must be a rectangle.

The window is first divided into N = nx * ny rectangular tiles (quadrats) of equal size and shape. To generate one resampled point pattern, a random sample of N quadrats is selected from the list of N quadrats, with replacement (if replace=TRUE) or without replacement (if replace=FALSE). The $i$th quadrat in the original dataset is then replaced by the $i$th sampled quadrat, after the latter is shifted so that it occupies the correct spatial position. The quadrats are then reconstituted into a point pattern inside the same window as X.

If replace=FALSE, this procedure effectively involves a random permutation of the quadrats. The resulting resampled point pattern has the same number of points as X. If replace=TRUE, the number of points in the resampled point pattern is random.

##### Value

• A point pattern (if nsamples = 1) or a list of point patterns (if nsamples > 1).

quadrats, quadratcount
data(bei)
quadratresample(bei, 6, 3)