R-square and K-Means cluster analysis

[Nic...@gmail.com]

Hello!

Does anyone know how you can get the Overall R-square of a K-means
cluster solution in SPSS?

In the ANOVA table that you get with a K-means cluster analysis in
SPSS, you can find the Cluster Mean square for each variable and the
Error Mean square for each variable but NOT the Overall R-square of the
solution.

Thanks,
Nick

[Art Kendall]

this is the reply I made in sci.stat.consult

If you wish to send teh same request to more than one list, I suggest
you use a single post sent to all of the groups. That way everybody who
sees the post also sees the replies.

The cluster solution is your model. The cluster memberships are
presented as a pseudo-ANOVA. "cluster" is the name of your variable,
the "gender" or "treatment" might be in other situations.

Since DISCRIMINANT is very useful in interpreting any cluster solution,
I suggest you try it. It will produce the Univariate F's and the over
all fit (depending on which measure you choose). Just remember that
significance's (probabilities) are meaningless in this context.
The measures of fit are useful for comparison of different solutions.
You would need to run it for each number of clusters you ask for in k-means.

The classification phase of the DISCRIMINANT will provide a table of
memberships assigned by the cluster procedure by memberships predicted
by the discriminant model. It will also provide for each case a
"probability" of membership in each cluster, and a "probability" that a
member of the assigned cluster is so far from the centroid of that cluster.

Remember, that in using k-means, it is necessary to do several runs,
each with the input data sorted in a different random order.

When you have k-means under your belt, I suggest that you try TWOSTEP.
It does not capitalize on the order of case input and provides measures
of fit, AIC and BIC, for a range of numbers of cluster solutions that
you choose. This is the short way to overall fit for choosing a number
of clusters.

Whether you get a cluster solution from a slice of a hierarchical tree,
from k-means, or from twostep, discriminant is a good tool for
evaluating and interpreting cluster solutions.

Art Kendall
Social Research Consultants