R help - Aug 2005 - PLSR: model notation and reliabilities

I'm new in both R and statistics. I "did my homework", 
I tried the archives and whatever I managed to get 
from the sources, but still I need assistance with 
the plsr package.


I have a model with 2 core determinants D1 and D2,
made by 3 indicators each (D1a,D1b,D1c and so on).
Also I have 2 moderating variables (m1,m2), where 
m1 moderates D1 and m2 modarates D2. 
The dependent variable (Y) is also constructed by 3 
indicators (Y1,Y2,Y3). Actually my model is far more 
complicated, I just give a simplified example here.

Which is the correct notation for the model 
(I'm skipping the crossvalidation for the moment) : 

  MyModel <- plsr(Y1+Y2+Y3 ~ ((D1a+D1b+D1c)*m1) + ((D2a+D2b+D2c)*m2),ncomp=2)

or :

  Y  <- cbind(Y1,Y2,Y3)
  X1 <- cbind(D1a,D1b,D1c)
  X2 <- cbind(D2a,D2b,D2c)
  MyModel <- plsr( Y ~ (X1*m1) + (X2*m2),ncomp=2) 


How do I calculate the internal composite reliabilty (ICR) ?
Is the Average variable explained (AVE) the mentioned as 
"% variance explained" in summary ?

I tried something like (the model is the first notation 
mentioned above, and the calcualtions below are simplified 
just for clarity) :

ncomp=MyModel$ncomp
P   <- MyModel$loadings[,ncomp]
Q   <- MyModel$Yloadings[,ncomp]
# D1
f1  <- P["D1a"]
f2  <- P["D1b"] 
f3  <- P["D1c"] 
Sp  <- f1 + f2 + f3
Sp2 <- (f1 ^ 2) + (f2^ 2) + (f3^2)
Sth <- (1-(f1 ^ 2)) + (1-(f2 ^ 2)) + (1-(f3^2))
D1_ICR   <- (Sp^2) / ( (Sp^2) + Sth)
D1_AVE <- Sp2 / ( Sp2 + Sth) 

but the results does not seem to give me something meaningfull.  
For example, while  cronbach(cbind(D1a,D1b,D1c)) gives me > 0.90, 
the above computed D1_ICR gives me very low numbers (< .20). 
Also summary says % variance explained for X = 83.1 in 1st component
while my computed D1_AVE is unacceptable (< 10%). 
Where I made it wrong ? Or it is just my data ?

Any help will be much appriciated

TIA

On Sat, Aug 27, 2005 at 04:04:13AM +0300, I.Ioannou
wrote:
> 
> I'm new in both R and statistics. I "did my homework", 
but apparently it was not enough :-( 

I took a look inside the code of the *pls.fit functions
and at least now I know where I got it wrong.

So, I'm rephrasing my question :

I have a model with 2 latent constructs (D1 and D2)
each one made by 3 indicators (D1a, D1b, D1c etc).
Also I have 2 moderating indicators (factors, m1, m2).
The response (Y) is also a latent construct, with 3 
indicators (Y1,Y2,Y3). Actually this is a simplified
description of my model which is far more complicated.

I want to express the regression using the constructs,
both for the response and the predictors, i.e. I need 
to have "inner" and "outer" models. The outer model can be 
expressed as :

Y ~ D1*m1 + D2*m2


How do I create the constructs from the indicators ?
I suspect I have to use somehow mvr or pca, but
I can not figure out how to use mvr for this since it
uses a formula and the response is required, while 
princomp and prcomp gives me either more constructs
than just 1, or ICRs ~ 0.6, while cronbach's alpha >= 0.9
- apparently I'm not using them correctly.

Any help will be much appreciated
 
TIA