Re: [R] PLSR: model notation and reliabilities

From: I.Ioannou <r_at_roryt.gr>
Date: Wed 31 Aug 2005 - 19:31:29 EST

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



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