Re: st: cluster analysis: differences between clusters

[Brendan Halpin <brendan.halpin@ul.ie>]

On Fri, Mar 07 2014, Nick Cox wrote:

> Interesting, but unless there is some clever trick in there I doubt
> that the bootstrapping can do justice to the dependence structure of
> sequence data.
>
> Sequences are correlated (usually) and clusters are similar (by intent
> if not design) and they would be much less interesting or useful
> otherwise. Still an inferential quagmire and nightmare all in one...

The sequence nature of the data is not actually relevant at this stage;
it's just a problem of clustering from a distance matrix (the sequences
are not being dealt with as time-series, simply as linear wholes that
can be more or less similar to each other). But you're right: the
inferential problem is real.

The bootstrapping generates a distribution of pseudo-F-stats by randomly
assigning cases to a partitioning of the same size. If the partitioning
is given by a pre-specified empirical variable (ie a known grouping) the
inference is reasonably sound, but where it is a cluster solution there is
enough circularity that the p-value cannot be valid. However, the
discrepancy statistic is still informative about how well a given
cluster solution captures the patterns in the distances, compared with
other solutions. 


Brendan
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