# pool.rat

##### Pool Data from Several Ratio Objects

Pool the data from several ratio objects
(objects of class `"rat"`

)
and compute a pooled estimate.

- Keywords
- spatial, nonparametric

##### Usage

```
## S3 method for class 'rat':
pool(...)
```

##### Arguments

- ...
- Objects of class
`"rat"`

.

##### 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 $R_1, \ldots, R_n$
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
$$R = \frac{\sum_i Y_i}{\sum_i X_i}.$$
The standard error of $R$ is computed using the delta method
as described in Baddeley *et al.* (1993)
or Cochran (1977, pp 154, 161).

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.

##### 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

##### 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"))
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*