classInt (version 0.1-24)

jenks.tests: Indices for assessing class intervals

Description

The function returns values of two indices for assessing class intervals: the goodness of variance fit measure, and the tabular accuracy index; optionally the overview accuracy index is also returned if the area argument is not missing.

Usage

jenks.tests(clI, area)

Arguments

clI

a "classIntervals" object

area

an optional vector of object areas if the overview accuracy index is also required

Value

a named vector of index values

Details

The goodness of variance fit measure is given by Armstrong et al. (2003, p. 600) as:

$$GVF = 1 - \frac{\sum_{j=1}^{k}\sum_{i=1}^{N_j}{(z_{ij} - \bar{z}_j)}^2}{\sum_{i=1}^{N}{(z_{i} - \bar{z})}^2}$$

where the \(z_{i}, i=1,\ldots,N\) are the observed values, \(k\) is the number of classes, \(\bar{z}_j\) the class mean for class \(j\), and \(N_j\) the number of counties in class \(j\).

The tabular accuracy index is given by Armstrong et al. (2003, p. 600) as:

$$TAI = 1 - \frac{\sum_{j=1}^{k}\sum_{i=1}^{N_j}{|z_{ij} - \bar{z}_j|}}{\sum_{i=1}^{N}{|z_{i} - \bar{z}|}}$$

The overview accuracy index for polygon observations with known areas is given by Armstrong et al. (2003, p. 600) as:

$$OAI = 1 - \frac{\sum_{j=1}^{k}\sum_{i=1}^{N_j}{|z_{ij} - \bar{z}_j| a_{ij}}}{\sum_{i=1}^{N}{|z_{i} - \bar{z}| a_i}}$$

where \(a_i, i=1,\ldots,N\) are the polygon areas, and as above the \(a_{ij}\) term is indexed over \(j=1,\ldots,k\) classes, and \(i=1,\ldots,N_j\) polygons in class \(j\).

References

Armstrong, M. P., Xiao, N., Bennett, D. A., 2003. "Using genetic algorithms to create multicriteria class intervals for choropleth maps". Annals, Association of American Geographers, 93 (3), 595--623; Jenks, G. F., Caspall, F. C., 1971. "Error on choroplethic maps: definition, measurement, reduction". Annals, Association of American Geographers, 61 (2), 217--244

See Also

classIntervals

Examples

# NOT RUN {
data(jenks71)
fix5 <- classIntervals(jenks71$jenks71, n=5, style="fixed",
 fixedBreaks=c(15.57, 25, 50, 75, 100, 155.30))
jenks.tests(fix5, jenks71$area)
q5 <- classIntervals(jenks71$jenks71, n=5, style="quantile")
jenks.tests(q5, jenks71$area)
set.seed(1)
k5 <- classIntervals(jenks71$jenks71, n=5, style="kmeans")
jenks.tests(k5, jenks71$area)
h5 <- classIntervals(jenks71$jenks71, n=5, style="hclust", method="complete")
jenks.tests(h5, jenks71$area)
jenks.tests(getHclustClassIntervals(h5, k=7), jenks71$area)
jenks.tests(getHclustClassIntervals(h5, k=9), jenks71$area)
set.seed(1)
b5 <- classIntervals(jenks71$jenks71, n=5, style="bclust")
jenks.tests(b5, jenks71$area)
jenks.tests(getBclustClassIntervals(b5, k=7), jenks71$area)
jenks.tests(getBclustClassIntervals(b5, k=9), jenks71$area)
# }