R: Classical distance-based test for homogeneity against...

homogen.test {prabclus} | R Documentation

## Classical distance-based test for homogeneity against clustering

### Description

Classical distance-based test for homogeneity against clustering. Test statistics is number of isolated vertices in the graph of smallest distances. The homogeneity model is a random graph model where `ne` edges are drawn from all possible edges.

### Usage

    homogen.test(distmat, ne = ncol(distmat), testdist = "erdos")

### Arguments

`distmat` | numeric symmetric distance matrix.
`ne` | integer. Number of edges in the data graph, corresponding to smallest distances.
`testdist` | string. If `testdist="erdos"`, the test distribution is a Poisson asymptotic distibution as given by Erdos and Renyi (1960). If `testdist="ling"`, the test distribution is exact as given by Ling (1973), which needs much more computing time.

### Details

The "ling"-test is one-sided (rejection if the number of isolated vertices is too large), the "erdos"-test computes a one-sided as well as a two-sided p-value.

### Value

A list with components

`p` | p-value for one-sided test.
`p.twoside` | p-value for two-sided test, only if `testdist="erdos"`.
`iv` | number of isolated vertices in the data.
`lambda` | parameter of the Poisson test distribution, only if `testdist="erdos"`.
`distcut` | largest distance value for which an edge has been drawn.
`ne` | see above.

### Author(s)

Christian Hennig chrish@stats.ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche

### References

Erdos, P. and Renyi, A. (1960) On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5, 17-61.

Godehardt, E. and Horsch, A. (1995) Graph-Theoretic Models for Testing the Homogeneity of Data. In Gaul, W. and Pfeifer, D. (Eds.) From Data to Knowledge, Springer, Berlin, 167-176.

Ling, R. F. (1973) A probability theory of cluster analysis. Journal of the American Statistical Association 68, 159-164.

### See Also

`prabtest`

### Examples

    options(digits=4)
    data(kykladspecreg)
    j <- jaccard(t(kykladspecreg))
    homogen.test(j, testdist="erdos")
    homogen.test(j, testdist="ling")

[Package prabclus version 2.2-6 Index]