Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 191

It is clear that the spread of units introduced by SCPS, LPM 1, and LPM 2 can
appreciably increase the efficiency of the design. It also proved to be sensitive to the
presence of zones of local behavior, locating the units in such a way to considerably
increase the efficiency with respect to SRS.
It is interesting to note that the gain (compared with SRS and stratified SRS) is
different. The predefined partition helps the distance based methods only for small
sample sizes, but for n ¼ 100 a similar efficiency is achieved without the use of
strata information.
Conclusions
The definition and analysis of appropriate methods for spatial sampling
represent a huge challenge for statisticians and researchers who use geo-
graphical data. In this chapter, we have outlined some statistical background
so that we can effectively deal with spatial sampling issues.
Many populations in environmental, agricultural, and forestry studies are
distributed over space, but it is now clear that spatial units cannot be sampled
as if they were generated within the classical urn model. This is mainly
because of the impacts that the inherent structural characteristics of spatial
data have on sample design. These characteristics include clustering of the
coordinates, homogeneity, spatial trends, and local homogeneity.
The question is how to efficiently incorporate these spatial aspects into the
design, and to what extent these aspects can be exploited to reduce the
variance of the estimators. The common and widely used methods of spatial
systematic sampling and maximal spatial stratified sampling only partially
exploit these features. Therefore, several efficient methods have recently
been developed for sampling from a spatial population.
The main strength of selecting samples according to the distance between
selected units lies in its ability to produce samples that are well-spread over
the population, and that take advantage of any peculiar spatial structures of
geo-coded populations. From the results of our simulations, it is clear that we
can drastically reduce the sampling error when we have reason to assume any
particular characteristic of spatial data.
Above all, a linear or a quadratic relationship between the coordinates
used as covariates and the study variable y proved to be a valuable attribute to
be exploited in a spatial sampling method. This is true even if very high
variance decreases are also found when homogeneity is present in closer units
of data, resulting in a clustering of the coordinates and study variable y.
Although SCPS, LPM 1 and LPM 2 appear to be sensitive to any of these
properties, they are also robust if they are absent because they at least have a
similar variance to SRS.
(continued)