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 \(w_i\) is the ith 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.