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.
homogen.test(distmat, ne = ncol(distmat), testdist = "erdos")
- numeric symmetric distance matrix.
- integer. Number of edges in the data graph, corresponding to smallest distances.
- 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.
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.
A list with components
- p-value for one-sided test.
- p-value for two-sided test, only if
- number of isolated vertices in the data.
- parameter of the Poisson test distribution, only if
- largest distance value for which an edge has been drawn.
- see above.
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.
Documentation reproduced from package prabclus, version 2.2-6. License: GPL