R: Pool Data from Several Ratio Objects

pool.rat {spatstat.core} | R Documentation

## Pool Data from Several Ratio Objects

### Description

Pool the data from several ratio objects (objects of class `"rat"`) and compute a pooled estimate.

### Usage

    ## S3 method for class 'rat'
    pool(..., weights=NULL, relabel=TRUE, variance=TRUE)

### Arguments

`...` | Objects of class `"rat"`.
`weights` | Numeric vector of weights.
`relabel` | Logical value indicating whether the result should be relabelled to show that it was obtained by pooling.
`variance` | Logical value indicating whether to compute the sample variance and related terms.

### Details

The function `pool` is generic. This is the method for the class `"rat"` of ratio objects. It is used to combine several estimates of the same quantity when each estimate is a ratio.

Each of the arguments `...` must be an object of class `"rat"` representing a ratio object (basically a numerator and a denominator; see `rat`). We assume that these ratios are all estimates of the same quantity.

If the objects are called R[1], …, R[n] and if R[i] has numerator Y[i] and denominator X[i], so that notionally R[i] = Y[i]/X[i], then the pooled estimate is the ratio-of-sums estimator

R = (Y[1]+…+Y[n])/(X[1]+…+X[n]).

The standard error of R is computed using the delta method as described in Baddeley et al. (1993) or Cochran (1977, pp 154, 161).

If the argument `weights` is given, it should be a numeric vector of length equal to the number of objects to be pooled. The pooled estimator is the ratio-of-sums estimator

R = (w[1] * Y[1]+…+ w[n] * Y[n])/(w[1] * X[1]+…+w[n] * X[n])

where `w_i`w[i] is the `i`th weight.

This calculation is implemented only for certain classes of objects where the arithmetic can be performed.

This calculation is currently implemented only for objects which also belong to the class `"fv"` (function value tables). For example, if `Kest` is called with argument `ratio=TRUE`, the result is a suitable object (belonging to the classes `"rat"` and `"fv"`).

Warnings or errors will be issued if the ratio objects `...` appear to be incompatible. However, the code is not smart enough to decide whether it is sensible to pool the data.

### Value

An object of the same class as the input.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### References

Baddeley, A.J, Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42, 641–668.

Cochran, W.G. (1977) Sampling techniques, 3rd edition. New York: John Wiley and Sons.

### See Also

`rat`, `pool`, `pool.fv`, `Kest`

### Examples

       K1 <- Kest(runifpoint(42), ratio=TRUE, correction="iso")
       K2 <- Kest(runifpoint(42), ratio=TRUE, correction="iso")
       K3 <- Kest(runifpoint(42), ratio=TRUE, correction="iso")
       K <- pool(K1, K2, K3)
       plot(K, pooliso ~ r, shade=c("hiiso", "loiso"))

[Package spatstat.core version 2.3-0 Index]