Hi Jean-Martin,
there are 2 possibilities for handling your multicollinearity problem:
1) do nothing 2) use more (or better) information (=data or theory)
ad 1) Multicollinearity (MC) does not affect >overall< "quality" of
regression, that is, the R2 statistic. The problem is only that the
variances of the estimated >parameters< might be high, so that you
can't trust the single parameter estimates. If you can expect that
the MC pattern will be almost the same for all situations which
you want to describe and ultimately you want to predict (overall)
growth, your problem might not be too important. (e.g., if the
relation between competition and stand age is >always< close for
all situations to be described).
ad 2) If you want to say more about the influence of >single< factors,
try to find data for which the relation between the factors
affected by MC is smaller (in the example above, estimate your
regression with data from different thinning regimes, so that hte
correlation between competition and stand age vanishes). Several
other possibilities: More data; >formalize< relationships between
correlated parameters; form a composite index; use ridge or Stein
estimator.
A good hint is to obtain a copy of "A Guide to Econometrics", by Peter
Kennedy, MIT press 1992 (Chapter 11). Really the best book on regression
I know. (>very< informative; well written; humoruous; best remedy against
desparation...) Hope that helps!
Peter Elsasser, Institute for Economics
Federal Research Station for Forestry and Forest Products
D-21027 Hamburg, Germany
elsasser@aixh0001.holz.uni-hamburg.de
>On Tue, 21 Feb 1995 16:55:46 -0500 (EST),
>Jean-Martin Lussier <Jean-Martin_Lussier@UQAC.UQuebec.CA> wrote:
>Subject: Troubles with statistics...
>My goal is to quantify the importance of each factor on tree growth.
>However most of these "independent" variables are in fact correlated to
>each other . For instance, relative density is strongly correlated
>with stand age, since the competition stress increases with tree size.
>This multicorrelation, or colinearity, seems to be a major obstacle to
>the use of multiple regression (cf Neter, Wasserman & Kutner 1990).
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