classInt (version 0.1-7)

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

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)