[R] PLSR: model notation and reliabilities

[I.Ioannou]

On Mon, Aug 29, 2005 at 08:08:53AM +0200, Bj?rn-Helge Mevik wrote:
 
> It seems to me that what you are looking for, is some sort of
> structured equation models (? la Lisrel).  The pls package implements
> partial least squares regression and principal component regression,
> which is something different.  I quess you could still use plsr for the
> "outer model" (path model), but you would have to build the "inner
> model" (the constructs) with other tools, such as prcomp/princomp or
> other factor analyses (see e.g. ?factanal and ?varimax).
> 
> Alternatively, there is an R package "sem" that implements structured
> equation models.  You might want to take a look at that.


Thank you very much for your hints. I actually tried factanal
to construct the latent variables, and both the reliabilties 
and the explained variance seem to be ok, but I'm afraid that 
this is not my case. I thought that plsr should be used to perform 
this task, and that PLS is prefered under "conditions on non-normality 
and small to medium sample sizes" where you do not "assume error 
free measurement" (Chin et all, 1996, p25). Also Wold suggests 
using PLS or PC scores in each level of hierarchical PLS models 
(Wold et al, 2004, p17). 

It is obvious to me how I should use plsr to perform the final
regression  between the constructs, but I'm missing the procedure 
I have to use in order to construct the factors (constructs) from 
the observed indicators.

Any hints will be much appreciatted.

Rgrds

References:

Chin et al, 1996, "A PARTIAL LEAST SQUARES LATENT VARIABLE 
MODELING APPROACH FOR MEASURING INTERACTION EFFECTS: RESULTS FROM A MONTE 
CARLO SIMULATION STUDY AND VOICE MAIL EMOTION/ADOPTION STUDY",
Available: http://disc-nt.cba.uh.edu/chin/plsfaq/http/disc-nt.cba.uh.edu/chin/icis96.pdf

Wold et al, 2004, "The PLS method -- partial least squares projections to 
latent structures -- and its applications in industrial RDP", 
Available: http://www.umetrics.com/pdfs/events/prague%200408%20__%20PLS_text_wold.pdf   

Ioannis Ioannou