Indices for assessing class intervals

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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

1
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{∑_{j=1}^{k}∑_{i=1}^{N_j}{(z_{ij} - \bar{z}_j)}^2}{∑_{i=1}^{N}{(z_{i} - \bar{z})}^2}

where the z_{i}, i=1,…,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{∑_{j=1}^{k}∑_{i=1}^{N_j}{|z_{ij} - \bar{z}_j|}}{∑_{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{∑_{j=1}^{k}∑_{i=1}^{N_j}{|z_{ij} - \bar{z}_j| a_{ij}}}{∑_{i=1}^{N}{|z_{i} - \bar{z}| a_i}}

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

Value

a named vector of index values

Author(s)

Roger Bivand <Roger.Bivand@nhh.no>

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

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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)