Identifying clusters/ordination based on correlation statistic?

Question

I'm attempting to find a way to judge the similarity of various sample groups, based on the strength of correlation to a set of variables within each group, and I'm trying to figure out if what I'm doing is statistically valid, and if there's a better way.

For example, I have 63 geographic regions. I have a single dependent variable, and a dozen potential explanatory variables that may or may not have a good correlation/explanatory power for the dependent variable within each region. For example, in region 1, rain might be the best variable. In region 2, temperature and 6-month lagged rain might both have strong correlations.

I then want to produce essentially an ordination chart output showing, say, regions where rain was an important explanatory variable grouped together, regions where temperature was an important variable grouped together etc. in ordination space.

The way I've achieved this, so far, is to run GLMs for each variable in each region, and established a table of strength-of-correlation measures, ie.

Region   Rain   Temp   6m_Rain   Evap
1        0.52   0.02   0.34      0.24
2        0.04   0.43   0.49      0.08
.....

(I've tried a number of different measures here; p-value, r² values etc.)

Then I've run this table through an NMDS ordination, with regions as "sites", and variables as "species". The result looks pretty reasonable - regions that I would expect to have similar climatic drivers of my phenomenon of interest are clustered together. But I feel that running an ordination on R² values or p-values is an awkward thing to do, and my background in ecology is probably driving me towards using NMDS/PCA style multivariate techniques when there might be something better out there.

Does anyone have any suggestions as to the best way to do this?

Answer 1

You posted solution may be adequate, I'm not sure. But there is a nice method that has been worked out for exactly your situation, that is, you would like to cluster a set of units (e.g. geographic regions) based on parameter estimates from an initial statistical modeling step (here use the beta weights and associated standard errors from your regression models). It is a generalization of Mahalanobis distance, and it is described in detail in the following paper. They present a hierarchical agglomerative clustering algorithm ("hError," section 4) and a method based on k-means ("kError,", section 5). Section 6 describes using these methods for parameter estimates, and section 7 describes a few example applications of their methods.