# rshift.ppp

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##### Randomly Shift a Point Pattern

Randomly shifts the points of a point pattern.

Keywords
spatial, datagen
##### Usage
# S3 method for ppp
rshift(X, …, which=NULL, group)
##### Arguments
X

Point pattern to be subjected to a random shift. An object of class "ppp"

Arguments that determine the random shift. See Details.

group

Optional. Factor specifying a grouping of the points of X, or NULL indicating that all points belong to the same group. Each group will be shifted together, and separately from other groups. By default, points in a marked point pattern are grouped according to their mark values, while points in an unmarked point pattern are treated as a single group.

which

Optional. Identifies which groups of the pattern will be shifted, while other groups are not shifted. A vector of levels of group.

##### Details

This operation randomly shifts the locations of the points in a point pattern.

The function rshift is generic. This function rshift.ppp is the method for point patterns.

The most common use of this function is to shift the points in a multitype point pattern. By default, points of the same type are shifted in parallel (i.e. points of a common type are shifted by a common displacement vector), and independently of other types. This is useful for testing the hypothesis of independence of types (the null hypothesis that the sub-patterns of points of each type are independent point processes).

In general the points of X are divided into groups, then the points within a group are shifted by a common random displacement vector. Different groups of points are shifted independently. The grouping is determined as follows:

• If the argument group is present, then this determines the grouping.

• Otherwise, if X is a multitype point pattern, the marks determine the grouping.

• Otherwise, all points belong to a single group.

The argument group should be a factor, of length equal to the number of points in X. Alternatively group may be NULL, which specifies that all points of X belong to a single group.

By default, every group of points will be shifted. The argument which indicates that only some of the groups should be shifted, while other groups should be left unchanged. which must be a vector of levels of group (for example, a vector of types in a multitype pattern) indicating which groups are to be shifted.

The displacement vector, i.e. the vector by which the data points are shifted, is generated at random. Parameters that control the randomisation and the handling of edge effects are passed through the … argument. They are

Parameters of the random shift vector.

edge

String indicating how to deal with edges of the pattern. Options are "torus", "erode" and "none".

clip

Optional. Window to which the final point pattern should be clipped.

If the window is a rectangle, the default behaviour is to generate a displacement vector at random with equal probability for all possible displacements. This means that the $x$ and $y$ coordinates of the displacement vector are independent random variables, uniformly distributed over the range of possible coordinates.

Alternatively, the displacement vector can be generated by another random mechanism, controlled by the arguments radius, width and height.

rectangular:

if width and height are given, then the displacement vector is uniformly distributed in a rectangle of these dimensions, centred at the origin. The maximum possible displacement in the $x$ direction is width/2. The maximum possible displacement in the $y$ direction is height/2. The $x$ and $y$ displacements are independent. (If width and height are actually equal to the dimensions of the observation window, then this is equivalent to the default.)

if radius is given, then the displacement vector is generated by choosing a random point inside a disc of the given radius, centred at the origin, with uniform probability density over the disc. Thus the argument radius determines the maximum possible displacement distance. The argument radius is incompatible with the arguments width and height.

The argument edge controls what happens when a shifted point lies outside the window of X. Options are:

"none":

Points shifted outside the window of X simply disappear.

"torus":

Toroidal or periodic boundary. Treat opposite edges of the window as identical, so that a point which disappears off the right-hand edge will re-appear at the left-hand edge. This is called a toroidal shift'' because it makes the rectangle topologically equivalent to the surface of a torus (doughnut).

The window must be a rectangle. Toroidal shifts are undefined if the window is non-rectangular.

"erode":

Clip the point pattern to a smaller window.

If the random displacements are generated by a radial mechanism (see above), then the window of X is eroded by a distance equal to the value of the argument radius, using erosion.

If the random displacements are generated by a rectangular mechanism, then the window of X is (if it is not rectangular) eroded by a distance max(height,width) using erosion; or (if it is rectangular) trimmed by a margin of width width at the left and right sides and trimmed by a margin of height height at the top and bottom.

The rationale for this is that the clipping window is the largest window for which edge effects can be ignored.

The optional argument clip specifies a smaller window to which the pattern should be restricted.

##### Value

A point pattern (object of class "ppp").

rshift, rshift.psp

• rshift.ppp
##### Examples
# NOT RUN {
data(amacrine)

# random toroidal shift
# shift "on" and "off" points separately
X <- rshift(amacrine)

# shift "on" points and leave "off" points fixed
X <- rshift(amacrine, which="on")

# shift all points simultaneously
X <- rshift(amacrine, group=NULL)

# maximum displacement distance 0.1 units