Pool Data from Several Ratio Objects

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

spatial, nonparametric
## S3 method for class 'rat':
Objects of class "rat".

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.


  • An object of the same class as the input.


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

  • pool.rat
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 1.41-1, License: GPL (>= 2)

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