# 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 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 \(R_1, \ldots, R_n\)
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).

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
$$
R = \frac{\sum_i w_i Y_i}{\sum_i w_i X_i}
$$
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.

##### 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

```
# NOT RUN {
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 1.55-1, License: GPL (>= 2)*