On Tue, 30 May 2000, Karen Scheltema wrote:
> Can someone enlighten me about how partial least squares regression
> works to handle multicollinearity.
Depends partly on whether you're looking at real, or spurious,
multicollinearity; and may depend on where the multicollinearity
actually arises. We may need more description of your particular
problem for a useful conversation.
What I understand by "partial regression" is not really different from
multiple regression: it involves "partialling" out the effects of
various predictors both from other (in general susbequent) predictors
and from the response variable, often either in a sequential manner or
in a way that implies a sequence by assigning an order of hierarchical
importance, if you will, to the several predictors.
If the multicollinearity arises from artificial variables computed as
the product of two or more raw variables, usually in seeking evidence
for or against the presence of interactions between those raw variables,
there is an obvious sort of hierarchy:
raw variables > 2-way interactions > 3-way interactions > ...
If the multicollinearity is "built in", so to speak, because there really
exists a (near-)linear combination among the predictors (or even more
than one such combination), one may need to decide which variable(s) to
EXclude in order to avoid the multicollinearity: this is another way of
saying that one needs to assign a hierarchy of importance to the
predictors.
In any event, the main problem with multicollinearity is
computational: in finite precision, estimation becomes unreliable as the
apparent zero-order correlations become less distinguishable from 1.000...
The most effective approach to the problem that I know of is to (begin
to) orthogonalize at least some of the predictors with respect to some
or all of the others. For an example applying this idea in practice
(where multicollinearity arose from computing raw interaction variables)
see my paper on the Minitab web site (www.minitab.com and look for
Resources, then White Papers).
> Can SPSS do partial least squares regression?
Yes, if we're talking on the same wavelength. Requires computing
residual variables and adjoining them to the variables in the data set,
then using them as predictors in place of the products (or raw variables)
they're residuals from.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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