Geoscience Reference
In-Depth Information
For example, M(
n
) expresses the agreement that a scientist would expect between the reference
map and the other map when the other map is the adjusted comparison map that is scaled to show
the quantity in each category as 1/
J
. M(
p
) expresses the agreement that a scientist would expect
between the reference map and the other map when the other map is the adjusted comparison map
that is scaled to show the quantity in each category as matching perfectly the reference map.
The definitions of M(
n
) and M(
p
) in Table 17.2 are slightly different from the definitions of
M(
n
) and M(
p
) in Pontius (2000, 2002). Table 17.2 gives expressions for M(
n
) and M(
p
) that
depend on the scaling given by Equation 17.12 through Equation 17.15. The method of scaling
simulates the change in quantity spread evenly across the grid cells as one moves from M(
m
) to
M(
p
) or from M(
m
) to M(
n
). In contrast, Pontius (2000, 2002) does not scale the comparison map
and does not represent an even spread of the change in quantity across the cells. The methods of
Pontius (2000, 2002) define M(
n
) and M(
p
) in a manner that makes sense for applications of land-
cover change simulation modeling and slightly confounds information of quantity with information
of location. Table 17.2 defines M(
n
) and M(
p
) in a manner that is appropriate for a wider variety
of applications, since it maintains complete separation of information of quantity from information
of location.
17.4.3
Stratification and Multiple Resolutions
If we think of grid cells as tiny strata, then the maps of Figure 17.2 show a three-tiered, nested
stratification structure. The cells are 100 tiny strata that are nested within the four substrata that
are nested within the two broadest strata. The multiple-resolution procedure grows the cells such
that at the resolution of 6 the four coarse grid cells constitute the four quadrants of the substrata.
Another similarity between strata and cells is that they both can indicate information of location;
hence, they both appear on the vertical axis of Figure 17.3.
However, there are three major conceptual differences between grid cells and strata. First, the
concept of location within a grid cell does not exist because category membership within a grid
cell is completely homogenous. By definition, we cannot say that a particular category is concen-
trated at a particular location within a cell. In contrast, the concept of location within a stratum
does exist because we can say that a particular category is concentrated at a particular location
within a stratum, since strata usually contain numerous cells. Second, the multiple-resolution
procedure increases the lengths of the sides of the grid cells and thus reduces the number of coarse
grid cells within each stratum, but the multiple-resolution analysis does not change the number of
strata. Third, each cell is a square patch, whereas a stratum can be nonsquare and noncontiguous.
As a consequence of these differences, analysis of multiple resolutions of cells shows how the
landscape is organized in geographic space, whereas analysis of multiple strata shows how the
landscape is organized with respect to the strata definitions.
17.5 CONCLUSIONS
The profession of accuracy assessment is advancing past the point where assessment consists
of only a calculation of percentage correct or Kappa index of agreement (Foody, 2002). Now,
measures of agreement are needed that indicate how to create more-accurate maps. Here we
presented novel methods of accuracy assessment to budget the components of agreement and
disagreement between any two maps that show a categorical variable. The techniques incorporate
stratification, examine multiple resolutions, apply to both hard and soft classifications, and compare
maps in terms of quantity and location. Perhaps most importantly, this chapter shows how to present
the results of a complex analysis in a simple graphical form. We hope that this technique of accuracy
assessment will soon become as common as today's use of percentage correct.
