Karen Scheltema wrote:
>
> Can someone emlighten me about how partial least squares regression works to
> handle multicollinearity. Can SPSS do partial least squares regression?
Partial Least Squares (PLS) handles multicollinearity by finding
subspace in the X-space that are highly predictive of the response(s).
Image your X-variables are scaled to mean zero and unit variance. The
X-data points form a "cloud" of data, but since they are multicollinear,
they are not spherical (as they would be if they were completely
orthogonal to each other). There is a "long" direction and a "short"
direction through this "cloud" of data (imagine an American football if
your X-data were 3-dimensional). PLS tries to find long directions
through the data which are predictive of the response(s). These long
directions are themselves linear combinations of the original variables,
which is okay when things are collinear -- in other words, if you can't
really tell the difference between X1 and X5 because they are highly
collinear, you use a linear combination of these variables to predict,
rather than X1 and/or X5 individually.
This still does not allow you to determine which of the collinear
variables is the true cause of the changes in your responses; you will
never be able to tell from collinear data. Nevertheless, your
predictions and regression coefficients will be less variable (but more
biased) compared to ordinary least squares. Studies show that the root
mean square error of PLS estimates and predictions are lower than OLS
estimates and predictions for some (many? most?) highly collinear
situations.
SAS has PROC PLS. MATLAB code exists to perform PLS. Since I am not an
SPSS user, I cannot say whether or not you can do this in SPSS.
--
Paige Miller
Eastman Kodak Company
[EMAIL PROTECTED]
"It's nothing until I call it!" -- Bill Klem, NL Umpire
"Those black-eyed peas tasted all right to me" -- Dixie Chicks
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