Discriminant Analysis biplot interpretation

[gianmarco]

Hello All,
it's been a while since I posted something.
I'd like to have some insights on the interpretation of a LDA biplot I am working with.

I have run LDA in R, using MASS::lda(), on a dataset made up by a number of clay samples from 3 geographical areas; the predictors are 9 oxhides coming from a larger body of oxhides whose concentration has been measured and reported in %. The sub-compositional dataset has been log10 transformed before running lda.

I understand that in LDA the Discriminant Functions are linear combinations of the predictors that aim at maximizing the group separation. Now, giving a look at both the LDA biplot (LINK) and to the coefficient of linear discriminant (LINK), I am wondering:

• Am i correct in concluding that LD1 manages to discriminate between the black group to the left-hand side and between the two groups to the right?
• ...and that LD2 discriminates (albeit with some "issues") between the green and the red groups?
• How to interpret the coefficients of linear discriminant? I understand that they "give an idea" of the importance of the predictors in the determination of the LDs; am I right?
• Is there an objective way to single out the "most important" ones?
• How to correctly interpret the direction, length, and position of the predictors' vector both in relation to the LD axis and to the observation data points?

Apologies for such large number of questions. Any pointer to the right interpretation would be appreciated.
Gm

p.s.
I have added LINKs to my dropbox coz I had issues in uploading attachments