Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 177

Fig. 7.6 Sample selected with SCPS method
preliminary weights. However, samples will be well-spread over the population,
because the efficiency of the method is independent of the ordering.
Moreover, the maximal weight strategy produces results with many second-
order inclusion probabilities equal to zero. This characteristic makes a design-based
unbiased estimator of the variance impossible. Other weighting strategies can
approximate the second-order inclusion probabilities to obtain an approximately
unbiased estimator (Bondesson and Thorburn 2008 ). However, these weighting
strategies result in less spatially balanced samples and a less efficient HT estimator.
The scps function for selecting SCPS samples was implemented in R in the
BalancedSampling package, and can be used for fairly large populations, with
some limits due to the size of the distance matrix. The author ensures that
“ ... selecting a sample from a population of size 1,000 takes less than 1 second and
selecting a sample from a population of size 10,000 takes about 30 seconds (on a Dell
Latitude E6410). A population size of 100,000 is also feasible and selecting a sample takes
about 1 hour. For really large populations, a rough initial spatial maximal stratification is
recommended to have feasible population sizes. Such a stratification does not significantly
affect the overall spatial balance” (Grafstr¨m 2012 ).
The R code is as follows. The selected sample is mapped in Fig. 7.6 .