p-value for PLS regression model & parameter estimates?
Heidi
I have carried out PLS (Partial Least Square) procedures and couldn't
find the p-values for the PLS model and its predictor variables from
the SPSS output. What should I do next to confirm if my results are
significant (i.e. whether the overall model as well as which
predictors are significant contributors).
Many thanks.
Heidi
Frank
The PLS Extension Module is dependent upon Python software -----
Frank
JKPeck
Perhaps I should clarify things a bit.
First, the PLS extension command is implemented in Python, but it was
written by SPSS staff using the Python language and the excellent
scientific libraries, numpy and scipy, which provided the numerical
linear algebra operations. (I wrote the original version, and another
staff member generalized it to handle multiple dependent variables and
do some charts.) So the features of PLS don't have anything
particular to do with Python.
Second, the PLS algorithm doesn't really provide the kind of
significance testing you get with ordinary regression models. One
clue is that you can run PLS with more independent variables than you
have cases. It's akin to principal components except that both the
y's and the X's are projected.
HTH,
Jon Peck
Heidi
Thanks, Jon. I'm honoured to have my question answered by PLS
extention creator. My sample size is 38 and I also included
interaction effects in the model. Reading other scholars' works that
use PLS methodology, I wonder how they derived p-values for both the
latent factors as well as parameter estimates of independent
variables. Pls advise what further analysis to take.
Otherwise I need some benchmark(?) to decide which independent
variables, by looking at their weights, are significant contributor to
particular latent factor. On top of that, I should be able to select
number of latent factors based on cumulative X variance & cum. Y
variance. Is it sensible to make conclusion based on subjective
judgement?
It would be of great help if anyone here could show me how to write
the PLS results, i.e. what statistics to include.
Many thanks,
Heidi
Bruce Weaver
I have no expertise in PLS to share with you, but I see that David
Garson has some notes on it (including some stuff about SPSS output),
and his stuff is usually very good.
http://faculty.chass.ncsu.edu/garson/PA765/pls.htm
--
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."
Heidi
> "When all else fails, RTFM."- Hide quoted text -
>
> - Show quoted text -
Thanks, Bruce. In fact, I depend entirely on his note to perform PLS.
Anyway, thanks again.
Heidi
thebluecliffrecord
> I have carried out PLS (Partial Least Square) procedures and couldn't
> find the p-values for the PLS model and its predictor variables from
> the SPSS output. What should I do next to confirm if my results are
> significant (i.e. whether the overall model as well as which
> predictors are significant contributors).
Dear Heidi,
PLS provides a p-value for the statistical significance of the
"overall" model. However, PLS can not provide p-values for
"individual" predictors because the extracted PCs are linear
"combinations" of all the predictors and the responses, therefore
there can't be p-values for the individual predictors. PLS extracts
the principal components (PCs) from all raw predictors, the PCs from
the multiple responses, and then those two sets of PCs are modified to
predict the responses ( I believe you already know of this).
> Otherwise I need some benchmark(?) to decide which independent
> variables, by looking at their weights, are significant contributor to
> particular latent factor. On top of that, I should be able to select
> number of latent factors based on cumulative X variance & cum. Y
> variance. Is it sensible to make conclusion based on subjective
> judgement?
The loadings of the individual predictors will provide clues for the
contributions of each predictors. Check the cross-validation to
determine whther the selected number of latent factors overfilts or
not. These are mere suggestions because there are many other things
to consider. For example, the signs of the PLS regression
coefficients ("wrong" sings in regression).
I prefer not to use the term "significant" because it usually
indicates "statistical" significance.
Personally, I perform PCA and PCR before I apply the PLS because I
would like to understand the data first (with and without Y in PCA and
PCR) and PCA will give us clues the "true" dimensions of the X
(orthogonal predictors) and thus the set of predictors to be included
in multiple linear regression.
More importantly, subject knowledge should guide what predictors
should be included before applying "ANY" orthogonal transformations
such as PCR, PLS, and ridge regression. They will extract PCs no
matter what kind of data (good or bad)!
Most importantly, as you are already aware of, if predictors are
collinear, the interpretation of individual predictors is often
unwarrented ("multicollinearity"). PCR and PLS are mere mathmatical
transformation (again, no matter what kind of data!) and therefore the
interpretation of each predictors are unwarrented also, but the
extracted components could provide some clues for interpretation
"hopely".
In other words, if you already know which predictors are related, why
not use such knowledge (you come up with your own model structure)
rather than PCR and PLS.
By the way, I don't have access to SPSS but use MINITAB.
Hope this helps.
Sangdon Lee, Ph.D.,
GM Warren Tech. Center.