🚀 go-pugleaf

Ken,
    An important problem that I've also been dealing with lately in my work on
 the
classification of forest types in the Sierra (based on species composition, but
 same
idea).  Here is the solution I've come up with--the only one I might add.  If I
understand you right, you can create varying number of classes based on your
 env.
data, but you don't know if one grouping is objectively better than any of the
others.  My first thought was to run a MANOVA on each classification output and
 look
for the most significant result.  But then I found out that two assumptions of
 that
procedure are univariate AND multivariate normality for all variables across all
groups, as well as constancy of the variance/covariance matrix across all
 groups.
The likelihood of that being true is so remote, at least for my data, that I
 didn't
even try it.  Scheiner (Design and Analysis of Ecological Experiments, 1993, pg
 110)
recommends using it, with certain cautions in certain situations and you might
 look
at his chapter in that book.  My decision was to run a chi-square test on each
classification, where each row represents one group of the classification being
tested, and each column is a variable (env variable in your case).  Doing so
 tests
the degree of independence of the row and column variables--"bad"
 classifications
will be less independent than "good" ones. Since all my classifications produced
very highly significant results (the differences between the tests being too
 small
to be reported in the output using SPSS), and were all of the same row by column
dimensions, I simply compared the actual chi-sq value between them.  If table
 sizes
differ, as they would in your case, dividing the total chi-sq by the degrees of
freedom would be required.  I did not run this method by any statisticians, but
 I
see no reason why it wouldn't be valid. My biggest question would be whether or
 not
a maximum chi-sq value would indeed be reached at some certain, optimum # of
groups.  Only doing the tests can show this. The env. variables would have to be
standardized and rescaled to maybe 0 to 100 in your case, to avoid having > 20%
 of
the cells with expected values of less than 5, a requirement for chi-sq tests.
Other approaches that might prove fruitful would be discriminant analyses of
 each
classif., or the use of a randomization test, which, like a chi-sq test, has no
assumptions regarding the distributions of the variables.  I've not tried
 either.

Jim Bouldin
UC Davis
Dept. of Environmental Horticulture

Ken Vance-Borland wrote:

> Dear All:
>
> I have been working in ARCINFO GIS to classify a landscape into ecosystems
 based
>
> on environmental variables, and am now trying to determine the optimal number
 of
>
> classes to use. I have some knowledge of the study region and opinions about
 the
>
> landscape diversity there, but would like to include in my decision an
> interpretation of dendrograms of the classes. The program requires the user to
> specify the number of classes in which to divide the landscape, and I wish to
> use dendrograms from various numbers of classes to help decide the best
> classification. If anyone has experience with objective analysis of
 dendrograms
> to determine suitable number of classes, I would appreciate hearing from you.
>
> Thanks very much,
>
> Ken Vance-Borland
> Department of Forest Science
> Oregon State University