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.

jenks.tests(clI, area)

Arguments

clI

a "classIntervals" object

area

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

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 \(j\).

Value

a named vector of index values

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

Author

Roger Bivand <Roger.Bivand@nhh.no>

See also

Examples

if (!require("spData", quietly=TRUE)) {
  message("spData package needed for examples")
  run <- FALSE
} else {
  run <- TRUE
}
if (run) {
data(jenks71, package="spData")
fix5 <- classIntervals(jenks71$jenks71, n=5, style="fixed",
 fixedBreaks=c(15.57, 25, 50, 75, 100, 155.30))
print(jenks.tests(fix5, jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         5.0000000         0.9107081         0.6879834         0.6617187 
if (run) {
q5 <- classIntervals(jenks71$jenks71, n=5, style="quantile")
print(jenks.tests(q5, jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         5.0000000         0.8329466         0.6654742         0.6280755 
if (run) {
set.seed(1)
k5 <- classIntervals(jenks71$jenks71, n=5, style="kmeans")
print(jenks.tests(k5, jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         5.0000000         0.9253431         0.7067202         0.6974831 
if (run) {
h5 <- classIntervals(jenks71$jenks71, n=5, style="hclust", method="complete")
print(jenks.tests(h5, jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         5.0000000         0.8705880         0.6098086         0.6099738 
if (run) {
print(jenks.tests(getHclustClassIntervals(h5, k=7), jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         7.0000000         0.9298169         0.6951671         0.6851124 
if (run) {
print(jenks.tests(getHclustClassIntervals(h5, k=9), jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         9.0000000         0.9720995         0.8134540         0.8106422 
if (run) {
set.seed(1)
b5 <- classIntervals(jenks71$jenks71, n=5, style="bclust")
print(jenks.tests(b5, jenks71$area))
}
#> Committee Member: 1(1) 2(1) 3(1) 4(1) 5(1) 6(1) 7(1) 8(1) 9(1) 10(1)
#> Computing Hierarchical Clustering
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         5.0000000         0.8926083         0.6481529         0.6451755 
if (run) {
print(jenks.tests(getBclustClassIntervals(b5, k=7), jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         7.0000000         0.9642511         0.7833643         0.7759815 
if (run) {
print(jenks.tests(getBclustClassIntervals(b5, k=9), jenks71$area))
}
#>         # classes   Goodness of fit  Tabular accuracy Overview accuracy 
#>         9.0000000         0.9708970         0.8081457         0.8034682