# pool.rat

0th

Percentile

##### 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_iw[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.

##### 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.

rat, pool, pool.fv, Kest

• pool.rat
##### 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 1.59-0, License: GPL (>= 2)

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