R: Indices for assessing class intervals

jenks.tests {classInt} | R Documentation

## 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

### 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

    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)

[Package classInt version 0.1-24 Index]