prabclus (version 2.3-4)

homogen.test: 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")

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.

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.

Author

Christian Hennig https://www.unibo.it/sitoweb/christian.hennig/en

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.

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")