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****Date:** Sat, 29 Jul 2006 10:35:59 -0500
**Reply-To:** Anthony Babinec <tbabinec@sbcglobal.net>
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** Anthony Babinec <tbabinec@sbcglobal.net>
**Subject:** Re: Two-step cluster
**In-Reply-To:** <1CAFCFE5F2673F4F881BEEB3A916E7B03C4F34@weyexpress2.corp.cefas.co.uk>
**Content-Type:** text/plain; charset="us-ascii"
In general, when you use a criterion such as AIC or BIC, you select the
model that MINIMIZES the criterion. In your reported data, AIC gets smaller
and smaller as the number of clusters increases, up to the maximum of 15
clusters.

TwoStep Cluster also calculates 2 other column that you report. These are
the "ratio of AIC changes" and the "ratio of distance measures." The ratio
of AIC changes sets the AIC change from K=1 to K=2 as 1, and then scales the
other AIC changes relative to this one. The ratio of distance measures is
the ratio of the distance measure in a given step to the distance measure in
the previous step. TwoStep looks at these measures to choose K. It is argued
that a jump in either measure between two consecutive Ks suggests a
tentative number of clusters. While this is given as a rationale for the
choice of K, some research shows that this model selection approach doesn't
always work - in particular, when there are a mix of continuous and
categorical basis variables, and when there is no underlying cluster
structure.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
Allan Reese (Cefas)
Sent: Thursday, July 27, 2006 10:14 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Two-step cluster

I'm trying twostep cluster in version 13. The documentation states that it
will select "between 1 and the maximum" number of clusters using the
Information Criterion. I assume it is looking for a maximum AIC/BIC so find
this output (apologies that column headings don't line up with values)
inconsistent with it reporting two clusters for this dataset. This seems so
obvious that I'm probably overlooking the obvious.

Auto-Clustering
Number of Clusters Akaike's Information Criterion (AIC) AIC
Change(a) Ratio of AIC Changes(b) Ratio of Distance Measures(c)
1 42679.177
2 29736.437 -12942.740 1.000 3.076
3 25584.939 -4151.498 .321 1.444
4 22736.637 -2848.302 .220 1.751
5 21145.674 -1590.963 .123 1.008
6 19567.475 -1578.199 .122 1.515
7 18554.435 -1013.040 .078 1.257
8 17765.615 -788.819 .061 1.034
9 17005.491 -760.125 .059 1.151
10 16356.395 -649.095 .050 1.150
11 15802.853 -553.542 .043 1.305
12 15398.294 -404.559 .031 1.167
13 15063.487 -334.807 .026 1.095
14 14765.135 -298.352 .023 1.084
15 14496.451 -268.684 .021 1.225
a The changes are from the previous number of clusters in the table.
b The ratios of changes are relative to the change for the two cluster
solution.
c The ratios of distance measures are based on the current number of
clusters against the previous number of clusters.

If there is in fact only one cluster, this may explain why the next output
lists all the variables in their name order, though the command description
states they "will be sorted by the importance rank of each variable."

The documentation for this command is very sparse, so I'd appreciate
feedback from other users. The menu generates syntax for "twostep cluster"
followed by "aim" but I am unable to trace any documentation for AIM.

Allan

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