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defined for equally common classes. A drawback of this approach is that few 3
3 blocks may be
assigned to strata representing rare classes if the rare-class pixels are often found in small patches
of two to four pixels. An alternative is to construct a rule that forces greater numbers of blocks
into rare-class strata. For example, the presence of a single pixel of a rare class may trigger
assignment of that pixel's block to the rare-class stratum. An obvious difficulty of this assignment
protocol is what to do if two or more rare classes are represented within the same cluster. Because
stratification requires that each block be assigned to exactly one stratum, and all blocks in the
region must be assigned to strata, an elaborate set of rules may be needed to encompass all cases.
A two-stage protocol such as implemented in the NLCD would reduce the workload of assigning
blocks to strata because this assignment would be necessary only for the first-stage sample PSUs,
not the entire area mapped. Estimation of accuracy parameters would be straightforward in this
approach because each pixel in the 3
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3 cluster has the same inclusion probability. This is an
advantage of this option compared to the first option in which the pixels within a 3
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3 block may
have different inclusion probabilities. As is true for most complex designs, constructing a variance
estimator and implementing it via existing software may be difficult.
This discussion of how to resolve design conflicts created by the desire to incorporate both
cover type stratification and local spatial control via clustering illustrates that the solutions to
practical problems may not be simple. We know how to implement cluster sampling and stratified
sampling as separate entities, but we do not necessarily have simple, effective ways to construct a
design that simultaneously accommodates both structures. Simple implementation procedures may
lead to complex analysis protocols (e.g., difficulty in specifying the inclusion probabilities), and
procedures permitting simpler analyses may require complex implementation protocols (e.g., defin-
ing strata at the 3
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3 block level). The situation is even more complex than the treatment in this
section indicates. It is likely that these methods focusing on local spatial control will need to be
embedded in a design also incorporating regional spatial control. The 3
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3 pixel clusters would
represent subsamples from a larger primary sampling unit such as a 6-
6-km area. Integrating
regional and local spatial control with stratification raises still additional challenges to the design.
The NLCD case study may also be used as the context for addressing concerns related to pixel-
based assessments. Positional error creates difficulties with any accuracy assessment because of
potential problems in achieving exact spatial correspondence between the reference location and
the map location. Typically, the problem is more strongly associated with pixel-based assessments
relative to polygon-based assessments, but it is not clear that this association is entirely justified.
The effects of positional error are most strongly manifested along the edges of map polygons.
Whether the assessment is based on a pixel, polygon, or other spatial unit does not change the
amount of edge present in the map. What may be changed by choice of assessment unit is how
edges are treated in the collection and use of reference data. For example, suppose a polygon
assessment employs an agreement protocol in which the entire map polygon is judged to be either
in complete agreement or complete disagreement with the reference data. In this approach, the
effect of positional error is greatly diminished because the error associated with a polygon edge
may be obscured when blended with the more homogeneous, polygon interior. The positional error
problem has not disappeared; it has to some extent been swept under the rug. This particular version
of a polygon-based assessment is valid for certain map applications, but not all. For example, if
the assessment objective is site-specific accuracy, the assessment must account for possible classi-
fication error along polygon boundaries. Defining agreement as a binary outcome based on the
entire polygon will not achieve that purpose.
In a pixel-based assessment, provisions should be included to accommodate the reality of
positional error when assessing edge or boundary pixels. No option is perfect, because we are
dealing with a problem that has no practical, ideal solution. However, the option chosen should
address the problem directly. One approach is to construct the reference data protocol so that the
potential influence of positional error can be assessed. The protocol may include a rating of location
confidence (i.e., how confident is the observer that the reference and map locations correspond
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