pairs()

Description:
Create a pairs object from a point object.

Usage:
pairs(point.obj,num.lags=10,type='isotropic', theta=0, dtheta=5, maxdist)

Required arguments:
point.obj: a point object generated by point()

Optional arguments:
num.lags: the number of lags into which to divide the pairs of points in the pairs object. The lags are all of equal size.
type: either 'isotropic' or 'anisotropic'. If 'isotropic' then all nC2 possible pairs of points are represented in the pairs object. If 'anisotropic', then the arguments theta and dtheta are used to determine which pairs of points to include.
theta: an angle, measured in degrees from the horizontal x axis, that determines pairs of points to be included in the pairs object (see Notes below).
dtheta: a tolerance angle, around theta, measured in degrees that determines pairs of points to be included in the pairs object (see Notes below).
maxdist: the distance beyond which not to consider pairs of points. A large number of spatial locations can cause the pairs function to consume a considerable amount of computation time. In most cases, spatial dependence can be adaquately characterized without examining the entire spaital extent of the data set.

Value:
A pairs object.

Notes:
When creating an anisotropic pairs object, the assumption is that the direction, as well as the distance, between pairs of points is important in describing the variation. Using the theta and dtheta arguments, pairs of points that meet direction requirements can be selected. A pair of points will be included when the angle between the positive x axis and the vector formed by the pair of points falls within the tolerance angle given by (theta-dtheta,theta+dtheta).

For example, in the figure below the pair (s1,s2) would be included in the pairs object, but th remaining pairs, (s1,s3), (s2,s1), (s2,s3), (s3,s2) and (s3,s1), would not be.



Examples:
stations.prs <- pairs(stations,15)
stations25.prs <- pairs(stations,type='anisotropic',theta=25)

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