Spatial Survey Data Modeling - Sampling Spatial Units for Agricultural Surveys - page 309

T , where S and T cover the same geographic domain. The aim of the data conversion
problem is to estimate the values of Y i for the target partition T .
Areal interpolation methods are applied to spatial units sampling in a different
way. In fact, given a fine pre-determined spatial resolution, we have information
about the variable under investigation for the sampled zones, and we want to predict
the values of the target variable for un-sampled zones.
Burrough ( 1986 ) and Lam ( 1983 ) classified areal interpolation methods into
non-volume preserving techniques and volume preserving techniques. In Palma and
Benedetti ( 1998 ) a general framework of spatial data transformation shows that
aggregation and sampling are both a special case of linear transformation of a
stochastic process.
Non-volume preserving methods generally overlay a grid onto the map and
assign a control point to each source zone. Point interpolation schemes are then
applied to interpolate the values at each grid node. Finally, the estimates of the grid
points are averaged within each target zone, yielding the final target-zone estimate.
Thus, this approach is based on point interpolation techniques.
Volume preserving methods preserve volume as an essential requirement for
accurate interpolation (Tobler 1979 ), and use the area values within the interpola-
tion process (Lam 1983 ).
Furthermore, the zone itself is now used as the operational unit. In this case, we
do not need a point interpolation process (see Palma and Benedetti 1998 for an
interesting volume preserving method).
At the end of the estimating process, we know the values of the variable y for
each zone of the target population. If these zones are sufficiently fine, they can be
aggregated in different ways to obtain estimates for different areal systems. It is
worth noting that the results can vary greatly depending on the interpolation and
aggregation methods.
This last application of spatial interpolation to survey sampling represents a very
important tool for policy makers, because it can take advantage of estimates that are
available at different spatial resolutions. Obviously, an appropriate definition of the
target geographical zones becomes crucial. This must be done at the beginning of
each spatial survey.
12.4 Analysis of Spatial Survey Data
The main output of a sample survey is often represented by estimates of totals,
means, and/or proportions of some target variables. We have these objectives in
mind when designing the survey. However, surveys can also be used for a more
complicated analysis of the relationships between variables. In particular, we may
be interested in some study based on linear and/or generalized regression, contin-
gency table analysis, and/or survival analysis.