Indices for assessing class intervals
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)
clI |
a "classIntervals" object |
area |
an optional vector of object areas if the overview accuracy index is also required |
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.
a named vector of index values
Roger Bivand <Roger.Bivand@nhh.no>
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
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)) } if (run) { q5 <- classIntervals(jenks71$jenks71, n=5, style="quantile") print(jenks.tests(q5, jenks71$area)) } if (run) { set.seed(1) k5 <- classIntervals(jenks71$jenks71, n=5, style="kmeans") print(jenks.tests(k5, jenks71$area)) } if (run) { h5 <- classIntervals(jenks71$jenks71, n=5, style="hclust", method="complete") print(jenks.tests(h5, jenks71$area)) } if (run) { print(jenks.tests(getHclustClassIntervals(h5, k=7), jenks71$area)) } if (run) { print(jenks.tests(getHclustClassIntervals(h5, k=9), jenks71$area)) } if (run) { set.seed(1) b5 <- classIntervals(jenks71$jenks71, n=5, style="bclust") print(jenks.tests(b5, jenks71$area)) } if (run) { print(jenks.tests(getBclustClassIntervals(b5, k=7), jenks71$area)) } if (run) { print(jenks.tests(getBclustClassIntervals(b5, k=9), jenks71$area)) }
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