Projective Convergence
Projective Convergence
Pointing to unseen targets is a common and natural method of measuring
survey knowledge. One of the more sophisticated and useful versions of
this method, called the method of projective convergence was originally
developed by Siegel (1981), adapted from procedures adapted from Hardwick,
Mcintyre and Pick. (1976). The method involves obtaining estimates of the
distance and the direction to a target location from each of three
sighting locations. The three distance/direction pairs specify three
estimated target locations, forming a hypothetical triangle (see figure
*2-2). From this technique, two measures derive from a simple, direct
analysis of errors:
1. Mean miss distance : Siegel termed this quantity "locational
accuracy" and defined it as the sum of the distances between the vertices
of the hypothetical triangle and the target averaged over the number of
observations. It is equivalent to the average error in distance
estimations.
2. Mean angle error: the absolute difference (in degrees) between
the estimated direction and the actual direction averaged over the number
of observations.
Two dependent measures derive from the relationships between the
hypothetical triangle and the target location:
1. Locational accuracy: A very similar measure as miss distance,
locational accuracy, is defined as the distance between the centroid of
the hypothetical triangle and the target. Some researchers have used this
measure in place of Siegel’s measure (see Witmer et al., 1996).
2. Consistency: the perimeter of the hypothetical triangle.
Figure 2-2
If the environment tested contains several targets, an additional set of
measures can be used based on the overall goodness of fit of all target’s
estimated locations.
5., 6., & 7. Overall spatial goodness of fit – measures of
configurational goodness of fit can be made by comparing the centroid of
each hypothetical triangle to the actual target locations. For these
measures, the centroids of the triangles are treated as location estimates
and entered into the map analysis routines described in Waller’s
dissertation (in preparation), resulting in three measures: mean relative
angle error, the correlation of inter-location distances, and absolute
error adjusted for translation, rotation, and scale.
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