varblock: Estimate Variance of Summary Statistic by Subdivision

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Estimate Variance of Summary Statistic by Subdivision

Description

This command estimates the variance of any summary statistic (such as the K-function) by spatial subdivision of a single point pattern dataset.

Usage

varblock(X, fun = Kest,
         blocks = quadrats(X, nx = nx, ny = ny),
         ...,
         nx = 3, ny = nx,
         confidence=0.95)

Arguments

X	Point pattern dataset (object of class "ppp").
fun	Function that computes the summary statistic.
blocks	Optional. A tessellation that specifies the division of the space into blocks.
...	Arguments passed to fun.
nx, ny	Optional. Number of rectangular blocks in the x and y directions. Incompatible with blocks.
confidence	Confidence level, as a fraction between 0 and 1.

Details

This command computes an estimate of the variance of the summary statistic fun(X) from a single point pattern dataset X using a subdivision method. It can be used to plot confidence intervals for the true value of a summary function such as the K-function.

The window containing X is divided into pieces by an nx * ny array of rectangles (or is divided into pieces of more general shape, according to the argument blocks if it is present). The summary statistic fun is applied to each of the corresponding sub-patterns of X as described below. Then the pointwise sample mean, sample variance and sample standard deviation of these summary statistics are computed. Then pointwise confidence intervals are computed, for the specified level of confidence, defaulting to 95 percent.

The variance is estimated by equation (4.21) of Diggle (2003, page 52). This assumes that the point pattern X is stationary. For further details see Diggle (2003, pp 52–53).

The estimate of the summary statistic from each block is computed as follows. For most functions fun, the estimate from block B is computed by finding the subset of X consisting of points that fall inside B, and applying fun to these points, by calling fun(X[B]).

However if fun is the K-function Kest, or any function which has an argument called domain, the estimate for each block B is computed by calling fun(X, domain=B). In the case of the K-function this means that the estimate from block B is computed by counting pairs of points in which the first point lies in B, while the second point may lie anywhere.

Value

A function value table (object of class "fv") that contains the result of fun(X) as well as the sample mean, sample variance and sample standard deviation of the block estimates, together with the upper and lower two-standard-deviation confidence limits.

Errors

If the blocks are too small, there may be insufficient data in some blocks, and the function fun may report an error. If this happens, you need to take larger blocks.

An error message about incompatibility may occur. The different function estimates may be incompatible in some cases, for example, because they use different default edge corrections (typically because the tiles of the tessellation are not the same kind of geometric object as the window of X, or because the default edge correction depends on the number of points). To prevent this, specify the choice of edge correction, in the correction argument to fun, if it has one.

An alternative to varblock is Loh's mark bootstrap lohboot.

Author(s)

\adrian

and \rolf

References

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

See Also

tess, quadrats for basic manipulation.

lohboot for an alternative bootstrap technique.

Examples

   v <- varblock(amacrine, Kest, nx=4, ny=2)
   v <- varblock(amacrine, Kcross, nx=4, ny=2)
   if(interactive()) plot(v, iso ~ r, shade=c("hiiso", "loiso"))

spatstat.explore documentation built on Oct. 22, 2024, 9:07 a.m.