----- Forwarded message from "F. James Rohlf" -----
Date: Tue, 28 Aug 2012 11:31:10 -0400
From: "F. James Rohlf"
Reply-To: [email protected]
Subject: RE: PLS and hierarchical partition
To: [email protected]
The difference between the two analyses is that PLS gives covariances or
correlations between the variables and the extracted linear combinations
whereas the multiple regressions using in the hierarchical partition analyses
gives partial or standardized partial regression coefficients (i.e., a function
of covariances between dependent and independent variables with the other
independent variables held constant). In a PLS the other variables are
explicitly NOT held constant. You will see a nice example of the difference in
the Rohlf and Corti 2000 paper: "The use of two-block partial least-squares to
study covariation in shape" in Systematic Biology. 49:740-753.
Which analysis is "correct" depends on the question you wish to ask. The PLS
results are usually much easier to understand. In multiple regression where,
for example, two variables are highly correlated, one may be shown to be "very
important" and the other not - which does not make much sense for practical
interpretation. It is because holding one of a pair of highly correlated
variables constant leaves very little variation for the other variable to
explain and hence it seems to be unimportant. However, it is only unimportant
given that the other variable is being held constant. If that first variable
where removed from the analysis then the second variable of that pair would
suddenly become very important.
Hope is clarifies the issue.
----------------------
F. James Rohlf, John S. Toll Professor, Stony Brook University
The much revised 4th editions of Biometry and Statistical Tables are now
available:
http://www.whfreeman.com/Catalog/product/biometry-fourthedition-sokal
http://www.whfreeman.com/Catalog/product/statisticaltables-fourthedition-rohlf
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> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]
> Sent: Tuesday, August 28, 2012 9:22 AM
> To: [email protected]
> Subject: PLS and hierarchical partition
>
>
> ----- Forwarded message from [email protected] -
> ----
>
> Date: Wed, 01 Aug 2012 16:57:47 -0700
> From: [email protected]
> Reply-To: [email protected]
> Subject: PLS and hierarchical partition
> To: [email protected]
>
> ----- Forwarded message from Rodrigo Lima -----
>
> Date: Tue, 24 Jul 2012 13:41:22 -0400
> From: Rodrigo Lima
> Reply-To: Rodrigo Lima
> Subject: PLS and hierarchical partition
> To: "[email protected]"
>
> Hello morphometricians,
>
> I'm trying to understand my stats, and any input would be mostly
> appreciated.
>
> The situation: I did a two-block PLS and a hierarchical partition analysis
> using
> my shape variables and 12 environmental variables. The first latent variable
> of PLS explains 96% of the covariation between blocks.
>
> The problem: the most important environmental variables on PLS (loadings
> on LV1) are different from the most important variables on the hierarchical
> partition analysis. Although the calculation is different (hierarchical
> partition
> uses all regressions possible between shape and environmental variables
> while PLS extracts eigenvalues that explain most of the covariation between
> shape and the environmental variables), since LV1 represents 96% of the
> variation the most important variables should be the same, right? Am I
> missing something here?
>
> Thank you very much,
> Rodrigo
>
> ----- End forwarded message -----
>
> ----- End forwarded message -----
----- End forwarded message -----
