[R] PLSR: model notation and reliabilities

From: I.Ioannou <r_at_roryt.gr>
Date: Sat 27 Aug 2005 - 11:04:13 EST

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



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