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I'm conducting an experiment in R. I am using the rattle library that contains a sample of the wine related data.

Within this data, it sorts the wine into 3 types (1,2,3). That is, K = 3.

So did the following test within R:

test <- lda(Type ~ Malic+Ash , data=wine)

The result was as follows:

Call:
lda(Type ~ Malic + Ash, data = wine)
Prior probabilities of groups:
        1         2         3 
0.3314607 0.3988764 0.2696629 
Group means:
     Malic      Ash
1 2.010678 2.455593
2 1.932676 2.244789
3 3.333750 2.437083
Coefficients of linear discriminants:
             LD1        LD2
Malic -0.9992257  0.3702831
Ash   -1.0283229 -3.7678317
Proportion of trace:
   LD1    LD2 
0.7992 0.2008

My question is, what do LD1 and LD2 mean in practice?

Because by my understanding since K = 3, we should also have an LD3, because we would have three linear discriminant functions, and through these three functions we would classify new data.

Nick Cox
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pedro.parreira
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  • These are the extracted discriminant functions. Their number is always `min(number of variables, number of groups -1)`. – ttnphns Jun 24 '15 at 13:45
  • Yes, let's assume that we have a new data (x *), as I use the LD1 and LD2 to decide which of the three categories it will be classified? – pedro.parreira Jun 24 '15 at 14:29
  • Please see my reply about how [discriminants classify objects](http://stats.stackexchange.com/a/31384/3277) to classes. – ttnphns Jun 24 '15 at 15:27

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