R: Estimate Variance of Summary Statistic by Subdivision

varblock {spatstat} | R Documentation

## 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 Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### 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"))

[Package spatstat version 1.54-0 Index]